Daily Papers

It has been well established that increasing scale in deep transformer networks leads to improved quality and performance. However, this increase in scale often comes with prohibitive increases in compute cost and inference latency. We introduce Alternating Updates (AltUp), a simple-to-implement method to increase a model's capacity without the computational burden. AltUp enables the widening of the learned representation, i.e., the token embedding, while only incurring a negligible increase in latency. AltUp achieves this by working on a subblock of the widened representation at each layer and using a predict-and-correct mechanism to update the inactivated blocks. We present extensions of AltUp, such as its applicability to the sequence dimension, and demonstrate how AltUp can be synergistically combined with existing approaches, such as Sparse Mixture-of-Experts models, to obtain efficient models with even higher capacity. Our experiments on benchmark transformer models and language tasks demonstrate the consistent effectiveness of AltUp on a diverse set of scenarios. Notably, on SuperGLUE and SQuAD benchmarks, AltUp enables up to 87% speedup relative to the dense baselines at the same accuracy.

Interpretability research now offers a variety of techniques for identifying abstract internal mechanisms in neural networks. Can such techniques be used to predict how models will behave on out-of-distribution examples? In this work, we provide a positive answer to this question. Through a diverse set of language modeling tasks--including symbol manipulation, knowledge retrieval, and instruction following--we show that the most robust features for correctness prediction are those that play a distinctive causal role in the model's behavior. Specifically, we propose two methods that leverage causal mechanisms to predict the correctness of model outputs: counterfactual simulation (checking whether key causal variables are realized) and value probing (using the values of those variables to make predictions). Both achieve high AUC-ROC in distribution and outperform methods that rely on causal-agnostic features in out-of-distribution settings, where predicting model behaviors is more crucial. Our work thus highlights a novel and significant application for internal causal analysis of language models.

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

In this paper, we propose DuaShepherd, a novel reward modeling framework that integrates two complementary reward signals, correctness and potential, to enhance the mathematical reasoning capabilities of Large Language Models (LLMs). While correctness-based signals emphasize identification of stepwise errors, potential-based signals focus on the likelihood of reaching the correct final answer. We developed an automated pipeline for constructing large-scale reward modeling dataset with both signals. A unified, multi-head architecture was explored to train the two reward models in a multi-task setup, demonstrating benefits from learning both correctness and potential in parallel. By combining these two signals into a compound probability, our model achieves consistent performance improvements across multiple benchmarks. Empirical evaluations on MATH500 and ProcessBench confirm that this combined reward significantly outperforms models trained on either reward type alone, achieving state-of-the-art performance under comparable resource constraints.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model's reflective ability. Though some studies attempt to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes. In this work, we propose to enhance LLMs' reasoning ability by Learning from Errors for Mathematical Advancement (LEMMA). LEMMA constructs data consisting of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an error-type grounded mistake augmentation method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. Through a model-aware smooth reflection connection, the erroneous solution is transferred to the correct one. By fine-tuning on the constructed dataset, the model is able to self-correct errors autonomously within the generation process without relying on external critique models. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong baselines.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

Addressing the discrepancies between predictions and actual outcomes often aids individuals in expanding their thought processes and engaging in reflection, thereby facilitating reasoning in the correct direction. In this paper, we introduce PreAct, an agent framework that integrates prediction with reasoning and action. Leveraging the information provided by predictions, a large language model (LLM) based agent can offer more diversified and strategically oriented reasoning, which in turn leads to more effective actions that help the agent complete complex tasks. Our experiments demonstrate that PreAct outperforms the ReAct approach in accomplishing complex tasks and that PreAct can be co-enhanced when combined with Reflexion methods. We prompt the model with different numbers of historical predictions and find that historical predictions have a sustained positive effect on LLM planning. The differences in single-step reasoning between PreAct and ReAct show that PreAct indeed offers advantages in terms of diversity and strategic directivity over ReAct.

The recent phenomenal success of language models has reinvigorated machine learning research, and large sequence models such as transformers are being applied to a variety of domains. One important problem class that has remained relatively elusive however is purposeful adaptive behavior. Currently there is a common perception that sequence models "lack the understanding of the cause and effect of their actions" leading them to draw incorrect inferences due to auto-suggestive delusions. In this report we explain where this mismatch originates, and show that it can be resolved by treating actions as causal interventions. Finally, we show that in supervised learning, one can teach a system to condition or intervene on data by training with factual and counterfactual error signals respectively.

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

Recent studies have shown LLMs possess some ability to improve their responses when given external feedback. However, it remains unclear how effectively and thoroughly these models can incorporate extrinsic feedback. In an ideal scenario, if LLMs receive near-perfect and complete feedback, we would expect them to fully integrate the feedback and change their incorrect answers to correct ones. In this paper, we systematically investigate LLMs' ability to incorporate feedback by designing a controlled experimental environment. For each problem, a solver model attempts a solution, then a feedback generator with access to near-complete ground-truth answers produces targeted feedback, after which the solver tries again. We evaluate this pipeline across a diverse range of tasks, including math reasoning, knowledge reasoning, scientific reasoning, and general multi-domain evaluations with state-of-the-art language models including Claude 3.7 (with and without extended thinking). Surprisingly, even under these near-ideal conditions, solver models consistently show resistance to feedback, a limitation that we term FEEDBACK FRICTION. To mitigate this limitation, we experiment with sampling-based strategies like progressive temperature increases and explicit rejection of previously attempted incorrect answers, which yield improvements but still fail to help models achieve target performance. We also perform a rigorous exploration of potential causes of FEEDBACK FRICTION, ruling out factors such as model overconfidence and data familiarity. We hope that highlighting this issue in LLMs and ruling out several apparent causes will help future research in self-improvement.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Future- or return-conditioned supervised learning is an emerging paradigm for offline reinforcement learning (RL), where the future outcome (i.e., return) associated with an observed action sequence is used as input to a policy trained to imitate those same actions. While return-conditioning is at the heart of popular algorithms such as decision transformer (DT), these methods tend to perform poorly in highly stochastic environments, where an occasional high return can arise from randomness in the environment rather than the actions themselves. Such situations can lead to a learned policy that is inconsistent with its conditioning inputs; i.e., using the policy to act in the environment, when conditioning on a specific desired return, leads to a distribution of real returns that is wildly different than desired. In this work, we propose the dichotomy of control (DoC), a future-conditioned supervised learning framework that separates mechanisms within a policy's control (actions) from those beyond a policy's control (environment stochasticity). We achieve this separation by conditioning the policy on a latent variable representation of the future, and designing a mutual information constraint that removes any information from the latent variable associated with randomness in the environment. Theoretically, we show that DoC yields policies that are consistent with their conditioning inputs, ensuring that conditioning a learned policy on a desired high-return future outcome will correctly induce high-return behavior. Empirically, we show that DoC is able to achieve significantly better performance than DT on environments that have highly stochastic rewards and transition

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

A language model's ability to reflect on its own reasoning provides a key advantage for solving complex problems. While most recent research has focused on how this ability develops during reinforcement learning, we show that it actually begins to emerge much earlier - during the model's pre-training. To study this, we introduce deliberate errors into chains-of-thought and test whether the model can still arrive at the correct answer by recognizing and correcting these mistakes. By tracking performance across different stages of pre-training, we observe that this self-correcting ability appears early and improves steadily over time. For instance, an OLMo2-7B model pre-trained on 4 trillion tokens displays self-correction on our six self-reflection tasks.

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970, machine learning with rejection recently gained interest. This machine learning subfield enables machine learning models to abstain from making a prediction when likely to make a mistake. This survey aims to provide an overview on machine learning with rejection. We introduce the conditions leading to two types of rejection, ambiguity and novelty rejection, which we carefully formalize. Moreover, we review and categorize strategies to evaluate a model's predictive and rejective quality. Additionally, we define the existing architectures for models with rejection and describe the standard techniques for learning such models. Finally, we provide examples of relevant application domains and show how machine learning with rejection relates to other machine learning research areas.

This paper presents a case study of coding tasks by the latest reasoning models of OpenAI, i.e. o1-preview and o1-mini, in comparison with other frontier models. The o1 models deliver SOTA results for WebApp1K, a single-task benchmark. To this end, we introduce WebApp1K-Duo, a harder benchmark doubling number of tasks and test cases. The new benchmark causes the o1 model performances to decline significantly, falling behind Claude 3.5. Moreover, they consistently fail when confronted with atypical yet correct test cases, a trap non-reasoning models occasionally avoid. We hypothesize that the performance variability is due to instruction comprehension. Specifically, the reasoning mechanism boosts performance when all expectations are captured, meanwhile exacerbates errors when key expectations are missed, potentially impacted by input lengths. As such, we argue that the coding success of reasoning models hinges on the top-notch base model and SFT to ensure meticulous adherence to instructions.

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the long tail of possible events, which are rarely observed in limited datasets. On the other hand, planning for worst-case motions leads to overtly conservative behavior and a "frozen robot". Instead, we aim to learn forecasts that predict counterfactuals that humans guard against. We propose a novel game-theoretic framework for joint planning and forecasting with the payoff being the performance of the planner against the demonstrator, and present practical algorithms to train models in an end-to-end fashion. We demonstrate that our proposed algorithm results in safer plans in a crowd navigation simulator and real-world datasets of pedestrian motion. We release our code at https://github.com/portal-cornell/Game-Theoretic-Forecasting-Planning.

Large Language Models (LLMs) agents are increasingly pivotal for addressing complex tasks in interactive environments. Existing work mainly focuses on enhancing performance through behavior cloning from stronger experts, yet such approaches often falter in real-world applications, mainly due to the inability to recover from errors. However, step-level critique data is difficult and expensive to collect. Automating and dynamically constructing self-critique datasets is thus crucial to empowering models with intelligent agent capabilities. In this work, we propose an iterative self-training framework, Agent-R, that enables language Agent to Reflect on the fly. Unlike traditional methods that reward or penalize actions based on correctness, Agent-R leverages MCTS to construct training data that recover correct trajectories from erroneous ones. A key challenge of agent reflection lies in the necessity for timely revision rather than waiting until the end of a rollout. To address this, we introduce a model-guided critique construction mechanism: the actor model identifies the first error step (within its current capability) in a failed trajectory. Starting from it, we splice it with the adjacent correct path, which shares the same parent node in the tree. This strategy enables the model to learn reflection based on its current policy, therefore yielding better learning efficiency. To further explore the scalability of this self-improvement paradigm, we investigate iterative refinement of both error correction capabilities and dataset construction. Our findings demonstrate that Agent-R continuously improves the model's ability to recover from errors and enables timely error correction. Experiments on three interactive environments show that Agent-R effectively equips agents to correct erroneous actions while avoiding loops, achieving superior performance compared to baseline methods (+5.59%).

Recent works have shown the benefits to LLMs from fine-tuning golden-standard Chain-of-Thought (CoT) rationales or using them as correct examples in few-shot prompting. While humans can indeed imitate correct examples, learning from our mistakes is another vital aspect of human cognition. Hence, a question naturally arises: can LLMs learn and benefit from their mistakes, especially for their reasoning? This study investigates this problem from both the prompting and model-tuning perspectives. We begin by introducing CoTErrorSet, a new benchmark with 609,432 questions, each designed with both correct and error references, and demonstrating the types and reasons for making such mistakes. To explore the effectiveness of those mistakes, we design two methods: (1) Self-rethinking prompting guides LLMs to rethink whether they have made similar previous mistakes; and (2) Mistake tuning involves finetuning models in both correct and incorrect reasoning domains, rather than only tuning models to learn ground truth in traditional methodology. We conduct a series of experiments to prove LLMs can obtain benefits from mistakes in both directions. Our two methods offer potentially cost-effective strategies by leveraging errors to enhance reasoning capabilities, which costs significantly less than creating meticulously hand-crafted golden references. We ultimately make a thorough analysis of the reasons behind LLMs' errors, which provides directions that future research needs to overcome. CoTErrorSet will be published soon on \url{https://github.com/YookiTong/Learn-from-Mistakes-CotErrorSet}.

In recent years, Multimodal Large Language Models (MLLMs) have been extensively utilized for multimodal reasoning tasks, including Graphical User Interface (GUI) automation. Unlike general offline multimodal tasks, GUI automation is executed in online interactive environments, necessitating step-by-step decision-making based on real-time status of the environment. This task has a lower tolerance for decision-making errors at each step, as any mistakes may cumulatively disrupt the process and potentially lead to irreversible outcomes like deletions or payments. To address these issues, we introduce a pre-operative critic mechanism that provides effective feedback prior to the actual execution, by reasoning about the potential outcome and correctness of actions. Specifically, we propose a Suggestion-aware Gradient Relative Policy Optimization (S-GRPO) strategy to construct our pre-operative critic model GUI-Critic-R1, incorporating a novel suggestion reward to enhance the reliability of the model's feedback. Furthermore, we develop a reasoning-bootstrapping based data collection pipeline to create a GUI-Critic-Train and a GUI-Critic-Test, filling existing gaps in GUI critic data. Static experiments on the GUI-Critic-Test across both mobile and web domains reveal that our GUI-Critic-R1 offers significant advantages in critic accuracy compared to current MLLMs. Dynamic evaluation on GUI automation benchmark further highlights the effectiveness and superiority of our model, as evidenced by improved success rates and operational efficiency.

Language models (LMs) are susceptible to in-context reward hacking, where they exploit flaws in tainted or faulty written specifications or rubrics to achieve high scores without fulfilling the user's true intent. We introduce Specification Self-Correction (SSC), a novel, test-time framework that enables an LM to identify and correct flaws within its own guiding specification. SSC employs a multi-step inference process where the model first generates a response based on a potentially tainted specification, critiques its output, and then revises the specification itself to remove the exploitable loophole. A final, more robust response is then generated using this self-corrected specification. Across experiments spanning creative writing and agentic coding tasks with several LMs, we demonstrate that while models initially game tainted specifications in 50-70\% of cases, the SSC process reduces this vulnerability by over 90\%. This dynamic repair occurs at inference time, requires no weight modification, and leads to more robustly aligned model behavior. Code at https://github.com/vicgalle/specification-self-correction .

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

Large language models (LLMs) have demonstrated exceptional reasoning capabilities, enabling them to solve various complex problems. Recently, this ability has been applied to the paradigm of tool learning. Tool learning involves providing examples of tool usage and their corresponding functions, allowing LLMs to formulate plans and demonstrate the process of invoking and executing each tool. LLMs can address tasks that they cannot complete independently, thereby enhancing their potential across different tasks. However, this approach faces two key challenges. First, redundant error correction leads to unstable planning and long execution time. Additionally, designing a correct plan among multiple tools is also a challenge in tool learning. To address these issues, we propose Tool-Planner, a task-processing framework based on toolkits. Tool-Planner groups tools based on the API functions with the same function into a toolkit and allows LLMs to implement planning across the various toolkits. When a tool error occurs, the language model can reselect and adjust tools based on the toolkit. Experiments show that our approach demonstrates a high pass and win rate across different datasets and optimizes the planning scheme for tool learning in models such as GPT-4 and Claude 3, showcasing the potential of our method.

Self-correction has demonstrated potential in code generation by allowing language models to revise and improve their outputs through successive refinement. Recent studies have explored prompting-based strategies that incorporate verification or feedback loops using proprietary models, as well as training-based methods that leverage their strong reasoning capabilities. However, whether smaller models possess the capacity to effectively guide their outputs through self-reflection remains unexplored. Our findings reveal that smaller models struggle to exhibit reflective revision behavior across both self-correction paradigms. In response, we introduce CoCoS, an approach designed to enhance the ability of small language models for multi-turn code correction. Specifically, we propose an online reinforcement learning objective that trains the model to confidently maintain correct outputs while progressively correcting incorrect outputs as turns proceed. Our approach features an accumulated reward function that aggregates rewards across the entire trajectory and a fine-grained reward better suited to multi-turn correction scenarios. This facilitates the model in enhancing initial response quality while achieving substantial improvements through self-correction. With 1B-scale models, CoCoS achieves improvements of 35.8% on the MBPP and 27.7% on HumanEval compared to the baselines.

Large Language Models have demonstrated remarkable abilities in reasoning and planning by breaking down complex problems into sequential steps. Despite their success in various domains like mathematical problem-solving and coding, LLMs face challenges in ensuring reliable and optimal planning due to their inherent myopic nature of autoregressive decoding. This paper revisits LLM reasoning from an optimal-control perspective, proposing a novel method, Predictive-Decoding, that leverages Model Predictive Control to enhance planning accuracy. By re-weighting LLM distributions based on foresight trajectories, Predictive-Decoding aims to mitigate early errors and promote non-myopic planning. Our experiments show significant improvements in a wide range of tasks for math, coding, and agents. Furthermore, Predictive-Decoding demonstrates computational efficiency, outperforming search baselines with reduced computational resources. This study provides insights into optimizing LLM planning capabilities.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated approach allows a single model to independently guide its reasoning process, offering computational advantages for model deployment. We particularly focus on the representative task of self-correction, where models autonomously detect errors in their responses, revise outputs, and decide when to terminate iterative refinement loops. To enable this, we propose a two-staged algorithmic framework for constructing self-rewarding reasoning models using only self-generated data. In the first stage, we employ sequential rejection sampling to synthesize long chain-of-thought trajectories that incorporate both self-rewarding and self-correction mechanisms. Fine-tuning models on these curated data allows them to learn the patterns of self-rewarding and self-correction. In the second stage, we further enhance the models' ability to assess response accuracy and refine outputs through reinforcement learning with rule-based signals. Experiments with Llama-3 and Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction capabilities and achieves performance comparable to systems that rely on external reward models.

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially, even in scenarios where they are explicitly told that they are making a mistake. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a single-turn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation learning and reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on math reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models. Our analysis shows that RISE makes meaningful improvements to responses to arrive at the correct solution for challenging prompts, without disrupting one-turn abilities as a result of expressing more complex distributions.

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains. To do so, we present basic algorithmic templates for building near-optimal predictors and reinforcement learners which behave as if they had a probabilistic model that allowed them to efficiently exploit task structure. Furthermore, we recast memory-based meta-learning within a Bayesian framework, showing that the meta-learned strategies are near-optimal because they amortize Bayes-filtered data, where the adaptation is implemented in the memory dynamics as a state-machine of sufficient statistics. Essentially, memory-based meta-learning translates the hard problem of probabilistic sequential inference into a regression problem.

While self-correction has shown promise in improving LLM outputs in terms of style and quality (e.g. Chen et al., 2023; Madaan et al., 2023), recent attempts to self-correct logical or reasoning errors often cause correct answers to become incorrect, resulting in worse performances overall (Huang et al., 2023). In this paper, we break down the self-correction process into two core components: mistake finding and output correction. For mistake finding, we release BIG-Bench Mistake, a dataset of logical mistakes in Chain-of-Thought reasoning traces. We provide benchmark numbers for several state-of-the-art LLMs, and demonstrate that LLMs generally struggle with finding logical mistakes. For output correction, we propose a backtracking method which provides large improvements when given information on mistake location. We construe backtracking as a lightweight alternative to reinforcement learning methods, and show that it remains effective with a reward model at 60-70% accuracy.

Effective decision-making in Large Language Models (LLMs) is essential for handling intricate tasks. However, existing approaches prioritize performance but often overlook the balance between effectiveness and computational cost. To address this, we first introduce the 3E Criteria to systematically assess the cost-effectiveness of search strategies, revealing that existing methods often trade significant efficiency for marginal performance gains. To improve LLM decision-making while maintaining efficiency, we propose the Speculative Reward Model (SRM), a plug-and-play framework that seamlessly integrates with existing search strategies. Specifically, SRM employs an external reward assigner to predict optimal actions, reducing reliance on LLMs' internal self-evaluation. And a speculative verification mechanism is used to prune suboptimal choices and guide the search toward more promising steps. We evaluate SRM on several complex decision-making tasks including mathematical reasoning, planning and numerical reasoning in specialized domains. Experimental results show that SRM reduces costs to 1/10 of the original search framework on average while maintaining effectiveness.

Language Agent could be endowed with different mechanisms for autonomous task accomplishment. Current agents typically rely on fixed mechanisms or a set of mechanisms activated in a predefined order, limiting their adaptation to varied potential task solution structures. To this end, this paper proposes Adaptive Language Agent Mechanism Activation Learning with Self-Exploration (ALAMA), which focuses on optimizing mechanism activation adaptability without reliance on expert models. Initially, it builds a harmonized agent framework (UniAct) to Unify different mechanisms via Actions. Then it leverages a training-efficient optimization method based on self-exploration to enable the UniAct to adaptively activate the appropriate mechanisms according to the potential characteristics of the task. Experimental results demonstrate significant improvements in downstream agent tasks, affirming the effectiveness of our approach in facilitating more dynamic and context-sensitive mechanism activation.

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm Learning from Correctness (LeCo), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates "self-consuming loops" which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made exponentially more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

This paper addresses the critical disconnect between prediction and decision quality in portfolio optimization by integrating Large Language Models (LLMs) with decision-focused learning. We demonstrate both theoretically and empirically that minimizing the prediction error alone leads to suboptimal portfolio decisions. We aim to exploit the representational power of LLMs for investment decisions. An attention mechanism processes asset relationships, temporal dependencies, and macro variables, which are then directly integrated into a portfolio optimization layer. This enables the model to capture complex market dynamics and align predictions with the decision objectives. Extensive experiments on S\&P100 and DOW30 datasets show that our model consistently outperforms state-of-the-art deep learning models. In addition, gradient-based analyses show that our model prioritizes the assets most crucial to decision making, thus mitigating the effects of prediction errors on portfolio performance. These findings underscore the value of integrating decision objectives into predictions for more robust and context-aware portfolio management.

Large language models (LLMs) demonstrate impressive reasoning abilities, but translating reasoning into actions in the real world remains challenging. In particular, it remains unclear how to complete a given task provably within a minimum number of interactions with the external environment, e.g., through an internal mechanism of reasoning. To this end, we propose a principled framework with provable regret guarantees to orchestrate reasoning and acting, which we call "reason for future, act for now" (RAFA). Specifically, we design a prompt template for reasoning that learns from the memory buffer and plans a future trajectory over a long horizon ("reason for future"). At each step, the LLM agent takes the initial action of the planned trajectory ("act for now"), stores the collected feedback in the memory buffer, and reinvokes the reasoning routine to replan the future trajectory from the new state. The key idea is to cast reasoning in LLMs as learning and planning in Bayesian adaptive Markov decision processes (MDPs). Correspondingly, we prompt LLMs to form an updated posterior of the unknown environment from the memory buffer (learning) and generate an optimal trajectory for multiple future steps that maximizes a value function (planning). The learning and planning subroutines are performed in an "in-context" manner to emulate the actor-critic update for MDPs. Our theoretical analysis proves that the novel combination of long-term reasoning and short-term acting achieves a T regret. In particular, the regret bound highlights an intriguing interplay between the prior knowledge obtained through pretraining and the uncertainty reduction achieved by reasoning and acting. Our empirical validation shows that it outperforms various existing frameworks and achieves nearly perfect scores on a few benchmarks.

Predictable behavior from scaling advanced AI systems is an extremely desirable property. Although a well-established literature exists on how pretraining performance scales, the literature on how particular downstream capabilities scale is significantly muddier. In this work, we take a step back and ask: why has predicting specific downstream capabilities with scale remained elusive? While many factors are certainly responsible, we identify a new factor that makes modeling scaling behavior on widely used multiple-choice question-answering benchmarks challenging. Using five model families and twelve well-established multiple-choice benchmarks, we show that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrade the statistical relationship between performance and scale. We then reveal the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on specific incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for incorrect choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

As language models regularly make mistakes when solving math problems, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight. In this paper, we introduce ProcessBench for measuring the ability to identify erroneous steps in mathematical reasoning. It consists of 3,400 test cases, primarily focused on competition- and Olympiad-level math problems. Each test case contains a step-by-step solution with error location annotated by human experts. Models are required to identify the earliest step that contains an error, or conclude that all steps are correct. We conduct extensive evaluation on ProcessBench, involving two types of models: process reward models (PRMs) and critic models, where for the latter we prompt general language models to critique each solution step by step. We draw two main observations: (1) Existing PRMs typically fail to generalize to more challenging math problems beyond GSM8K and MATH. They underperform both critic models (i.e., prompted general language models) and our own trained PRM that is straightforwardly fine-tuned on the PRM800K dataset. (2) The best open-source model, QwQ-32B-Preview, has demonstrated the critique capability competitive with the proprietary model GPT-4o, despite that it still lags behind the reasoning-specialized o1-mini. We hope ProcessBench can foster future research in reasoning process assessment, paving the way toward scalable oversight of language models.

The principle of independent causal mechanisms (ICM) states that generative processes of real world data consist of independent modules which do not influence or inform each other. While this idea has led to fruitful developments in the field of causal inference, it is not widely-known in the NLP community. In this work, we argue that the causal direction of the data collection process bears nontrivial implications that can explain a number of published NLP findings, such as differences in semi-supervised learning (SSL) and domain adaptation (DA) performance across different settings. We categorize common NLP tasks according to their causal direction and empirically assay the validity of the ICM principle for text data using minimum description length. We conduct an extensive meta-analysis of over 100 published SSL and 30 DA studies, and find that the results are consistent with our expectations based on causal insights. This work presents the first attempt to analyze the ICM principle in NLP, and provides constructive suggestions for future modeling choices. Code available at https://github.com/zhijing-jin/icm4nlp

Generative AI systems like foundation models (FMs) must align well with human values to ensure their behavior is helpful and trustworthy. While Reinforcement Learning from Human Feedback (RLHF) has shown promise for optimizing model performance using human judgments, existing RLHF pipelines predominantly rely on immediate feedback, which can fail to accurately reflect the downstream impact of an interaction on users' utility. We demonstrate that feedback based on evaluators' foresight estimates of downstream consequences systematically induces Goodhart's Law dynamics, incentivizing misaligned behaviors like sycophancy and deception and ultimately degrading user outcomes. To alleviate this, we propose decoupling evaluation from prediction by refocusing RLHF on hindsight feedback. Our theoretical analysis reveals that conditioning evaluator feedback on downstream observations mitigates misalignment and improves expected human utility, even when these observations are simulated by the AI system itself. To leverage this insight in a practical alignment algorithm, we introduce Reinforcement Learning from Hindsight Simulation (RLHS), which first simulates plausible consequences and then elicits feedback to assess what behaviors were genuinely beneficial in hindsight. We apply RLHS to two widely-employed online and offline preference optimization methods -- Proximal Policy Optimization (PPO) and Direct Preference Optimization (DPO) -- and show empirically that misalignment is significantly reduced with both methods. Through an online human user study, we show that RLHS consistently outperforms RLHF in helping users achieve their goals and earns higher satisfaction ratings, despite being trained solely with simulated hindsight feedback. These results underscore the importance of focusing on long-term consequences, even simulated ones, to mitigate misalignment in RLHF.

Can large language models (LLMs) admit their mistakes when they should know better? In this work, we define the behavior of acknowledging errors in previously generated answers as "retraction" and aim to understand when and why LLMs choose to retract. We first construct model-specific datasets to evaluate whether a model will retract an incorrect answer that contradicts its own parametric knowledge. While LLMs are capable of retraction, they do so only infrequently. We demonstrate that retraction is closely tied to previously identified indicators of models' internal belief: models fail to retract wrong answers that they "believe" to be factually correct. Steering experiments further demonstrate that internal belief causally influences model retraction. In particular, when the model does not believe its answer, this not only encourages the model to attempt to verify the answer, but also alters attention behavior during self-verification. Finally, we demonstrate that simple supervised fine-tuning significantly improves retraction performance by helping the model learn more accurate internal beliefs. Code and datasets are available on https://github.com/ayyyq/llm-retraction.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Large language models (LLMs) are trained to imitate humans to explain human decisions. However, do LLMs explain themselves? Can they help humans build mental models of how LLMs process different inputs? To answer these questions, we propose to evaluate counterfactual simulatability of natural language explanations: whether an explanation can enable humans to precisely infer the model's outputs on diverse counterfactuals of the explained input. For example, if a model answers "yes" to the input question "Can eagles fly?" with the explanation "all birds can fly", then humans would infer from the explanation that it would also answer "yes" to the counterfactual input "Can penguins fly?". If the explanation is precise, then the model's answer should match humans' expectations. We implemented two metrics based on counterfactual simulatability: precision and generality. We generated diverse counterfactuals automatically using LLMs. We then used these metrics to evaluate state-of-the-art LLMs (e.g., GPT-4) on two tasks: multi-hop factual reasoning and reward modeling. We found that LLM's explanations have low precision and that precision does not correlate with plausibility. Therefore, naively optimizing human approvals (e.g., RLHF) may not be a sufficient solution.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Most economic theories typically assume that financial market participants are fully rational individuals and use mathematical models to simulate human behavior in financial markets. However, human behavior is often not entirely rational and is challenging to predict accurately with mathematical models. In this paper, we propose Agent-based Simulated Financial Market (ASFM), which first constructs a simulated stock market with a real order matching system. Then, we propose a large language model based agent as the stock trader, which contains the profile, observation, and tool-learning based action module. The trading agent can comprehensively understand current market dynamics and financial policy information, and make decisions that align with their trading strategy. In the experiments, we first verify that the reactions of our ASFM are consistent with the real stock market in two controllable scenarios. In addition, we also conduct experiments in two popular economics research directions, and we find that conclusions drawn in our \model align with the preliminary findings in economics research. Based on these observations, we believe our proposed ASFM provides a new paradigm for economic research.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Large Language Models (LLMs) are prone to hallucination, especially during multi-hop and reasoning-intensive tasks such as mathematical problem solving. While Outcome Reward Models verify only final answers, Process Reward Models (PRMs) score each intermediate step to steer generation toward coherent solutions. We introduce PathFinder-PRM, a novel hierarchical, error-aware discriminative PRM that first classifies math and consistency errors at each step, then combines these fine-grained signals to estimate step correctness. To train PathFinder-PRM, we construct a 400K-sample dataset by enriching the human-annotated PRM800K corpus and RLHFlow Mistral traces with three-dimensional step-level labels. On PRMBench, PathFinder-PRM achieves a new state-of-the-art PRMScore of 67.7, outperforming the prior best (65.5) while using 3 times less data. When applied to reward guided greedy search, our model yields prm@8 48.3, a +1.5 point gain over the strongest baseline. These results demonstrate that decoupled error detection and reward estimation not only boost fine-grained error detection but also substantially improve end-to-end, reward-guided mathematical reasoning with greater data efficiency.

Today's robot policies exhibit subpar performance when faced with the challenge of generalizing to novel environments. Human corrective feedback is a crucial form of guidance to enable such generalization. However, adapting to and learning from online human corrections is a non-trivial endeavor: not only do robots need to remember human feedback over time to retrieve the right information in new settings and reduce the intervention rate, but also they would need to be able to respond to feedback that can be arbitrary corrections about high-level human preferences to low-level adjustments to skill parameters. In this work, we present Distillation and Retrieval of Online Corrections (DROC), a large language model (LLM)-based system that can respond to arbitrary forms of language feedback, distill generalizable knowledge from corrections, and retrieve relevant past experiences based on textual and visual similarity for improving performance in novel settings. DROC is able to respond to a sequence of online language corrections that address failures in both high-level task plans and low-level skill primitives. We demonstrate that DROC effectively distills the relevant information from the sequence of online corrections in a knowledge base and retrieves that knowledge in settings with new task or object instances. DROC outperforms other techniques that directly generate robot code via LLMs by using only half of the total number of corrections needed in the first round and requires little to no corrections after two iterations. We show further results, videos, prompts and code on https://sites.google.com/stanford.edu/droc .

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Open-weights reasoning language models generate long chains-of-thought (CoTs) before producing a final response, which improves performance but introduces additional alignment risks, with harmful content often appearing in both the CoTs and the final outputs. In this work, we investigate if we can use CoTs to predict final response misalignment. We evaluate a range of monitoring approaches, including humans, highly-capable large language models, and text classifiers, using either CoT text or activations. First, we find that a simple linear probe trained on CoT activations can significantly outperform all text-based methods in predicting whether a final response will be safe or unsafe. CoT texts are often unfaithful and can mislead humans and classifiers, while model latents (i.e., CoT activations) offer a more reliable predictive signal. Second, the probe makes accurate predictions before reasoning completes, achieving strong performance even when applied to early CoT segments. These findings generalize across model sizes, families, and safety benchmarks, suggesting that lightweight probes could enable real-time safety monitoring and early intervention during generation.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

As models increasingly leverage multi-step reasoning strategies to solve complex problems, supervising the logical validity of these intermediate steps has become a critical research challenge. Process reward models address this by providing step-by-step feedback, but current approaches have two major drawbacks: they typically function as classifiers without providing explanations, and their reliance on supervised fine-tuning with static datasets limits generalization. Inspired by recent advances, we reframe stepwise reward modeling from a classification task to a reasoning task itself. We thus propose a generative judge that reasons about the policy model's reasoning steps (i.e., meta-reasons), outputting thinking tokens before delivering a final verdict. Our model, StepWiser, is trained by reinforcement learning using relative outcomes of rollouts. We show it provides (i) better judgment accuracy on intermediate steps than existing methods; (ii) can be used to improve the policy model at training time; and (iii) improves inference-time search.

Large language models (LLMs) have demonstrated strong reasoning abilities in mathematical tasks, often enhanced through reinforcement learning (RL). However, RL-trained models frequently produce unnecessarily long reasoning traces -- even for simple queries -- leading to increased inference costs and latency. While recent approaches attempt to control verbosity by adding length penalties to the reward function, these methods rely on fixed penalty terms that are hard to tune and cannot adapt as the model's reasoning capability evolves, limiting their effectiveness. In this work, we propose an adaptive reward-shaping method that enables LLMs to "think fast and right" -- producing concise outputs without sacrificing correctness. Our method dynamically adjusts the reward trade-off between accuracy and response length based on model performance: when accuracy is high, the length penalty increases to encourage faster length reduction; when accuracy drops, the penalty is relaxed to preserve correctness. This adaptive reward accelerates early-stage length reduction while avoiding over-compression in later stages. Experiments across multiple datasets show that our approach consistently and dramatically reduces reasoning length while largely maintaining accuracy, offering a new direction for cost-efficient adaptive reasoning in large-scale language models.

Machine learning models are routinely used to support decisions that affect individuals -- be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from datasets with noisy labels. In this paper, we study the instance-level impact of learning under label noise. We introduce a notion of regret for this regime, which measures the number of unforeseen mistakes due to noisy labels. We show that standard approaches to learning under label noise can return models that perform well at a population-level while subjecting individuals to a lottery of mistakes. We present a versatile approach to estimate the likelihood of mistakes at the individual-level from a noisy dataset by training models over plausible realizations of datasets without label noise. This is supported by a comprehensive empirical study of label noise in clinical prediction tasks. Our results reveal how failure to anticipate mistakes can compromise model reliability and adoption -- we demonstrate how we can address these challenges by anticipating and avoiding regretful decisions.

Machine learning models are often used to decide who will receive a loan, a job interview, or a public benefit. Standard techniques to build these models use features about people but overlook their actionability. In turn, models can assign predictions that are fixed, meaning that consumers who are denied loans, interviews, or benefits may be permanently locked out from access to credit, employment, or assistance. In this work, we introduce a formal testing procedure to flag models that assign fixed predictions that we call recourse verification. We develop machinery to reliably determine if a given model can provide recourse to its decision subjects from a set of user-specified actionability constraints. We demonstrate how our tools can ensure recourse and adversarial robustness in real-world datasets and use them to study the infeasibility of recourse in real-world lending datasets. Our results highlight how models can inadvertently assign fixed predictions that permanently bar access, and we provide tools to design algorithms that account for actionability when developing models.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

Recent advancements in large language models (LLMs) have significantly advanced complex reasoning capabilities, particularly through extended chain-of-thought (CoT) reasoning that incorporates mechanisms such as backtracking, self-reflection and self-correction. Despite these developments, the self-correction abilities of LLMs during long CoT reasoning remain underexplored. And recent findings on overthinking suggest that such models often engage in unnecessarily redundant reasoning. In this work, we empirically show that the first reasoning step exerts a disproportionately large influence on the final prediction - errors introduced at this stage can substantially degrade subsequent reasoning quality. This phenomenon is consistently observed across two state-of-the-art open-source reasoning model families: DeepSeek-R1 and Qwen3. To address this, we propose an efficient sampling strategy that leverages a reward model to identify and retain high-quality first reasoning steps while discarding suboptimal ones, achieving up to a 70% reduction in inference cost without sacrificing accuracy. Finally, we introduce a new benchmark specifically constructed with deliberately flawed first reasoning steps to systematically evaluate model self-correction capabilities, offering a foundation for future research on robust reasoning in LLMs.

Machine learning models routinely automate decisions in applications like lending and hiring. In such settings, consumer protection rules require companies that deploy models to explain predictions to decision subjects. These rules are motivated, in part, by the belief that explanations can promote recourse by revealing information that individuals can use to contest or improve their outcomes. In practice, many companies comply with these rules by providing individuals with a list of the most important features for their prediction, which they identify based on feature importance scores from feature attribution methods such as SHAP or LIME. In this work, we show how these practices can undermine consumers by highlighting features that would not lead to an improved outcome and by explaining predictions that cannot be changed. We propose to address these issues by highlighting features based on their responsiveness score -- i.e., the probability that an individual can attain a target prediction by changing a specific feature. We develop efficient methods to compute responsiveness scores for any model and any dataset. We conduct an extensive empirical study on the responsiveness of explanations in lending. Our results show that standard practices in consumer finance can backfire by presenting consumers with reasons without recourse, and demonstrate how our approach improves consumer protection by highlighting responsive features and identifying fixed predictions.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

Accurately predicting the future would be an important milestone in the capabilities of artificial intelligence. However, research on the ability of large language models to provide probabilistic predictions about future events remains nascent. To empirically test this ability, we enrolled OpenAI's state-of-the-art large language model, GPT-4, in a three-month forecasting tournament hosted on the Metaculus platform. The tournament, running from July to October 2023, attracted 843 participants and covered diverse topics including Big Tech, U.S. politics, viral outbreaks, and the Ukraine conflict. Focusing on binary forecasts, we show that GPT-4's probabilistic forecasts are significantly less accurate than the median human-crowd forecasts. We find that GPT-4's forecasts did not significantly differ from the no-information forecasting strategy of assigning a 50% probability to every question. We explore a potential explanation, that GPT-4 might be predisposed to predict probabilities close to the midpoint of the scale, but our data do not support this hypothesis. Overall, we find that GPT-4 significantly underperforms in real-world predictive tasks compared to median human-crowd forecasts. A potential explanation for this underperformance is that in real-world forecasting tournaments, the true answers are genuinely unknown at the time of prediction; unlike in other benchmark tasks like professional exams or time series forecasting, where strong performance may at least partly be due to the answers being memorized from the training data. This makes real-world forecasting tournaments an ideal environment for testing the generalized reasoning and prediction capabilities of artificial intelligence going forward.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

Most learning algorithms with formal regret guarantees assume that no mistake is irreparable and essentially rely on trying all possible behaviors. This approach is problematic when some mistakes are catastrophic, i.e., irreparable. We propose an online learning problem where the goal is to minimize the chance of catastrophe. Specifically, we assume that the payoff in each round represents the chance of avoiding catastrophe that round and aim to maximize the product of payoffs (the overall chance of avoiding catastrophe) while allowing a limited number of queries to a mentor. We first show that in general, any algorithm either constantly queries the mentor or is nearly guaranteed to cause catastrophe. However, in settings where the mentor policy class is learnable in the standard online learning model, we provide an algorithm whose regret and rate of querying the mentor both approach 0 as the time horizon grows. Conceptually, if a policy class is learnable in the absence of catastrophic risk, it is learnable in the presence of catastrophic risk if the agent can ask for help.

Agentic workflows -- where multiple large language model (LLM) instances interact to solve tasks -- are increasingly built on feedback mechanisms, where one model evaluates and critiques another. Despite the promise of feedback-driven improvement, the stability of agentic workflows rests on the reliability of the judge. However, judges may hallucinate information, exhibit bias, or act adversarially -- introducing critical vulnerabilities into the workflow. In this work, we present a systematic analysis of agentic workflows under deceptive or misleading feedback. We introduce a two-dimensional framework for analyzing judge behavior, along axes of intent (from constructive to malicious) and knowledge (from parametric-only to retrieval-augmented systems). Using this taxonomy, we construct a suite of judge behaviors and develop WAFER-QA, a new benchmark with critiques grounded in retrieved web evidence to evaluate robustness of agentic workflows against factually supported adversarial feedback. We reveal that even strongest agents are vulnerable to persuasive yet flawed critiques -- often switching correct answers after a single round of misleading feedback. Taking a step further, we study how model predictions evolve over multiple rounds of interaction, revealing distinct behavioral patterns between reasoning and non-reasoning models. Our findings highlight fundamental vulnerabilities in feedback-based workflows and offer guidance for building more robust agentic systems.

Large language models (LLMs) are increasingly used for tasks that require complex reasoning. Most benchmarks focus on final outcomes but overlook the intermediate reasoning steps - such as planning, revision, and decision making under resource constraints. We argue that measuring these internal processes is essential for understanding model behavior and improving reliability. We propose using strategic games as a natural evaluation environment: closed, rule-based systems with clear states, limited resources, and automatic feedback. We introduce a framework that evaluates LLMs along three core dimensions: planning, revision, and resource-constrained decision making. To operationalize this, we define metrics beyond win rate, including overcorrection risk rate, correction success rate, improvement slope, and over-budget ratio. In 4320 adversarial rounds across 12 leading models, ChatGPT-o3-mini achieves the top composite score, with a win rate of 74.7 percent, a correction success rate of 78.6 percent, and an improvement slope of 0.041. By contrast, Qwen-Plus, despite an overcorrection risk rate of 81.6 percent, wins only 25.6 percent of its matches - primarily due to excessive resource use. We also observe a negative correlation between overcorrection risk rate and correction success rate (Pearson r = -0.51, p = 0.093), suggesting that more frequent edits do not always improve outcomes. Our findings highlight the value of assessing not only what LLMs decide but how they arrive at those decisions

Methods for knowledge editing and unlearning in large language models seek to edit or remove undesirable knowledge or capabilities without compromising general language modeling performance. This work investigates how mechanistic interpretability -- which, in part, aims to identify model components (circuits) associated to specific interpretable mechanisms that make up a model capability -- can improve the precision and effectiveness of editing and unlearning. We find a stark difference in unlearning and edit robustness when training components localized by different methods. We highlight an important distinction between methods that localize components based primarily on preserving outputs, and those finding high level mechanisms with predictable intermediate states. In particular, localizing edits/unlearning to components associated with the lookup-table mechanism for factual recall 1) leads to more robust edits/unlearning across different input/output formats, and 2) resists attempts to relearn the unwanted information, while also reducing unintended side effects compared to baselines, on both a sports facts dataset and the CounterFact dataset across multiple models. We also find that certain localized edits disrupt the latent knowledge in the model more than any other baselines, making unlearning more robust to various attacks.

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X,Y) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X,Y). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

Recent advances in large language models (LLMs) have demonstrated that inference-time computation techniques, such as decoding-time scaling and self-refinement, can significantly enhance reasoning capabilities without relying on external knowledge. A key driver of this success is the emergence of self-correction and self-verification behaviors, often elicited through reinforcement learning (RL). In this paper, we investigate whether these inference-time techniques extend effectively to vision-language models (VLMs), particularly those trained with RL. We find that while decoding strategies such as majority voting and best-of-N selection with self-verification all improve VLM reasoning performance, generation-reliant methods such as the former achieve significantly higher gains versus verification-reliant methods such as the latter. Additionally, the self-correction behavior often associated with RL-tuned models, such as aha moment, does not lead to measurable gains. We show via extensive experimentation within the inference-time scaling framework to identify a key root cause: RL-trained VLMs still lack robust self-verification capabilities across both visual and textual modalities.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% to 12.7% final-answer error and 14.0% to 3.4% reasoning error among final-answer-correct solutions.

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning might serve as a general technique for numerically approximating Bayes-optimal agents - that is, even for task distributions for which we currently don't possess tractable models.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Large language models are being widely used across industries to generate content that contributes directly to key performance metrics, such as conversion rates. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering and logistical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. Using simulation experiments, we demonstrate that DeconfoundLM improves the recovery of causal relationships and mitigates failure modes found in fine-tuning methods that ignore or naively incorporate confounding variables. Our findings highlight that while observational data presents risks, with the right causal corrections, it can be a powerful source of signal for LLM alignment. Please refer to the project page for code and related resources.

Designing robust frameworks for precise prediction of future prices of stocks has always been considered a very challenging research problem. The advocates of the classical efficient market hypothesis affirm that it is impossible to accurately predict the future prices in an efficiently operating market due to the stochastic nature of the stock price variables. However, numerous propositions exist in the literature with varying degrees of sophistication and complexity that illustrate how algorithms and models can be designed for making efficient, accurate, and robust predictions of stock prices. We present a gamut of ten deep learning models of regression for precise and robust prediction of the future prices of the stock of a critical company in the auto sector of India. Using a very granular stock price collected at 5 minutes intervals, we train the models based on the records from 31st Dec, 2012 to 27th Dec, 2013. The testing of the models is done using records from 30th Dec, 2013 to 9th Jan 2015. We explain the design principles of the models and analyze the results of their performance based on accuracy in forecasting and speed of execution.

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce pyhgf: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

We propose and theoretically analyze an approach for planning with an approximate model in reinforcement learning that can reduce the adverse impact of model error. If the model is accurate enough, it accelerates the convergence to the true value function too. One of its key components is the MaxEnt Model Correction (MoCo) procedure that corrects the model's next-state distributions based on a Maximum Entropy density estimation formulation. Based on MoCo, we introduce the Model Correcting Value Iteration (MoCoVI) algorithm, and its sampled-based variant MoCoDyna. We show that MoCoVI and MoCoDyna's convergence can be much faster than the conventional model-free algorithms. Unlike traditional model-based algorithms, MoCoVI and MoCoDyna effectively utilize an approximate model and still converge to the correct value function.

The ability of Large Language Models (LLMs) to critique and refine their reasoning is crucial for their application in evaluation, feedback provision, and self-improvement. This paper introduces CriticBench, a comprehensive benchmark designed to assess LLMs' abilities to critique and rectify their reasoning across a variety of tasks. CriticBench encompasses five reasoning domains: mathematical, commonsense, symbolic, coding, and algorithmic. It compiles 15 datasets and incorporates responses from three LLM families. Utilizing CriticBench, we evaluate and dissect the performance of 17 LLMs in generation, critique, and correction reasoning, i.e., GQC reasoning. Our findings reveal: (1) a linear relationship in GQC capabilities, with critique-focused training markedly enhancing performance; (2) a task-dependent variation in correction effectiveness, with logic-oriented tasks being more amenable to correction; (3) GQC knowledge inconsistencies that decrease as model size increases; and (4) an intriguing inter-model critiquing dynamic, where stronger models are better at critiquing weaker ones, while weaker models can surprisingly surpass stronger ones in their self-critique. We hope these insights into the nuanced critique-correct reasoning of LLMs will foster further research in LLM critique and self-improvement.

Recent advances in large language models (LLMs) have demonstrated significant progress in performing complex tasks. While Reinforcement Learning from Human Feedback (RLHF) has been effective in aligning LLMs with human preferences, it is susceptible to spurious correlations in reward modeling. Consequently, it often introduces biases-such as length bias, sycophancy, conceptual bias, and discrimination that hinder the model's ability to capture true causal relationships. To address this, we propose a novel causal reward modeling approach that integrates causal inference to mitigate these spurious correlations. Our method enforces counterfactual invariance, ensuring reward predictions remain consistent when irrelevant variables are altered. Through experiments on both synthetic and real-world datasets, we show that our approach mitigates various types of spurious correlations effectively, resulting in more reliable and fair alignment of LLMs with human preferences. As a drop-in enhancement to the existing RLHF workflow, our causal reward modeling provides a practical way to improve the trustworthiness and fairness of LLM finetuning.

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further misleading refinement and leading to the failure of self-correction, especially in complex reasoning tasks. In this paper, we propose Program-driven Self-Correction (ProgCo). First, program-driven verification (ProgVe) achieves complex verification logic and extensive validation through self-generated, self-executing verification pseudo-programs. Then, program-driven refinement (ProgRe) receives feedback from ProgVe, conducts dual reflection and refinement on both responses and verification programs to mitigate misleading of incorrect feedback in complex reasoning tasks. Experiments on three instruction-following and mathematical benchmarks indicate that ProgCo achieves effective self-correction, and can be further enhance performance when combined with real program tools.

Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal policy. We show that policy brittleness often stems from non-unique optimal actions, a common occurrence when multiple valid traces exist in a reasoning task. This theoretical lens provides a unified explanation for a range of seemingly disparate failures, reframing them as rational outcomes of optimizing rewards that may be incomplete or noisy, especially in the presence of action degeneracy. We extend this analysis from the fundamental single-reward setting to the more realistic multi-reward RL across diverse domains, showing how stability is governed by an "effective reward" aggregation mechanism. We also prove that entropy regularization restores policy stability at the cost of increased stochasticity. Our framework provides a unified explanation for recent empirical findings on deceptive reasoning, instruction-following trade-offs, and RLHF-induced sophistry, and is further validated through perturbation experiments in multi-reward RL. This work advances policy-stability analysis from empirical heuristics towards a principled theory, offering essential insights for designing safer and more trustworthy AI systems.

Recent improvements in text generation have leveraged human feedback to improve the quality of the generated output. However, human feedback is not always available, especially during inference. In this work, we propose an inference time optimization method FITO to use fine-grained actionable feedback in the form of error type, error location and severity level that are predicted by a learned error pinpoint model for iterative refinement. FITO starts with an initial output, then iteratively incorporates the feedback via a refinement model that generates an improved output conditioned on the feedback. Given the uncertainty of consistent refined samples at iterative steps, we formulate iterative refinement into a local search problem and develop a simulated annealing based algorithm that balances exploration of the search space and optimization for output quality. We conduct experiments on three text generation tasks, including machine translation, long-form question answering (QA) and topical summarization. We observe 0.8 and 0.7 MetricX gain on Chinese-English and English-German translation, 4.5 and 1.8 ROUGE-L gain at long form QA and topic summarization respectively, with a single iteration of refinement. With our simulated annealing algorithm, we see further quality improvements, including up to 1.7 MetricX improvements over the baseline approach.

Reward modeling is crucial for aligning large language models (LLMs) with human preferences, especially in reinforcement learning from human feedback (RLHF). However, current reward models mainly produce scalar scores and struggle to incorporate critiques in a natural language format. We hypothesize that predicting both critiques and the scalar reward would improve reward modeling ability. Motivated by this, we propose Critic-RM, a framework that improves reward models using self-generated critiques without extra supervision. Critic-RM employs a two-stage process: generating and filtering high-quality critiques, followed by joint fine-tuning on reward prediction and critique generation. Experiments across benchmarks show that Critic-RM improves reward modeling accuracy by 3.7%-7.3% compared to standard reward models and LLM judges, demonstrating strong performance and data efficiency. Additional studies further validate the effectiveness of generated critiques in rectifying flawed reasoning steps with 2.5%-3.2% gains in improving reasoning accuracy.

Tasks requiring deductive reasoning, especially those involving multiple steps, often demand adaptive strategies such as intermediate generation of rationales or programs, as no single approach is universally optimal. While Language Models (LMs) can enhance their outputs through iterative self-refinement and strategy adjustments, they frequently fail to apply the most effective strategy in their first attempt. This inefficiency raises the question: Can LMs learn to select the optimal strategy in the first attempt, without a need for refinement? To address this challenge, we introduce SMART (Self-learning Meta-strategy Agent for Reasoning Tasks), a novel framework that enables LMs to autonomously learn and select the most effective strategies for various reasoning tasks. We model the strategy selection process as a Markov Decision Process and leverage reinforcement learning-driven continuous self-improvement to allow the model to find the suitable strategy to solve a given task. Unlike traditional self-refinement methods that rely on multiple inference passes or external feedback, SMART allows an LM to internalize the outcomes of its own reasoning processes and adjust its strategy accordingly, aiming for correct solutions on the first attempt. Our experiments across various reasoning datasets and with different model architectures demonstrate that SMART significantly enhances the ability of models to choose optimal strategies without external guidance (+15 points on the GSM8K dataset). By achieving higher accuracy with a single inference pass, SMART not only improves performance but also reduces computational costs for refinement-based strategies, paving the way for more efficient and intelligent reasoning in LMs.

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.

Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality, which ensures that when there are two groups of agents at different locations, both groups incur the same total cost. We show that although Strong Proportionality is a well-motivated and basic axiom, there is no deterministic strategyproof mechanism satisfying the property. We then identify a randomized mechanism called Random Rank (which uniformly selects a number k between 1 to n and locates the facility at the k'th highest agent location) which satisfies Strong Proportionality in expectation. Our main theorem characterizes Random Rank as the unique mechanism that achieves universal truthfulness, universal anonymity, and Strong Proportionality in expectation among all randomized mechanisms. Finally, we show via the AverageOrRandomRank mechanism that even stronger ex-post fairness guarantees can be achieved by weakening universal truthfulness to strategyproofness in expectation.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Model-free reinforcement learning algorithms can compute policy gradients given sampled environment transitions, but require large amounts of data. In contrast, model-based methods can use the learned model to generate new data, but model errors and bias can render learning unstable or suboptimal. In this paper, we present a novel method that combines real-world data and a learned model in order to get the best of both worlds. The core idea is to exploit the real-world data for on-policy predictions and use the learned model only to generalize to different actions. Specifically, we use the data as time-dependent on-policy correction terms on top of a learned model, to retain the ability to generate data without accumulating errors over long prediction horizons. We motivate this method theoretically and show that it counteracts an error term for model-based policy improvement. Experiments on MuJoCo- and PyBullet-benchmarks show that our method can drastically improve existing model-based approaches without introducing additional tuning parameters.

We study the problem of online prediction, in which at each time step t, an individual x_t arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Large pretrained models, coupled with fine-tuning, are slowly becoming established as the dominant architecture in machine learning. Even though these models offer impressive performance, their practical application is often limited by the prohibitive amount of resources required for every inference. Early-exiting dynamic neural networks (EDNN) circumvent this issue by allowing a model to make some of its predictions from intermediate layers (i.e., early-exit). Training an EDNN architecture is challenging as it consists of two intertwined components: the gating mechanism (GM) that controls early-exiting decisions and the intermediate inference modules (IMs) that perform inference from intermediate representations. As a result, most existing approaches rely on thresholding confidence metrics for the gating mechanism and strive to improve the underlying backbone network and the inference modules. Although successful, this approach has two fundamental shortcomings: 1) the GMs and the IMs are decoupled during training, leading to a train-test mismatch; and 2) the thresholding gating mechanism introduces a positive bias into the predictive probabilities, making it difficult to readily extract uncertainty information. We propose a novel architecture that connects these two modules. This leads to significant performance improvements on classification datasets and enables better uncertainty characterization capabilities.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Identifying procedural errors online from egocentric videos is a critical yet challenging task across various domains, including manufacturing, healthcare, and skill-based training. The nature of such mistakes is inherently open-set, as unforeseen or novel errors may occur, necessitating robust detection systems that do not rely on prior examples of failure. Currently, however, no technique effectively detects open-set procedural mistakes online. We propose a dual branch architecture to address this problem in an online fashion: one branch continuously performs step recognition from the input egocentric video, while the other anticipates future steps based on the recognition module's output. Mistakes are detected as mismatches between the currently recognized action and the action predicted by the anticipation module. The recognition branch takes input frames, predicts the current action, and aggregates frame-level results into action tokens. The anticipation branch, specifically, leverages the solid pattern-matching capabilities of Large Language Models (LLMs) to predict action tokens based on previously predicted ones. Given the online nature of the task, we also thoroughly benchmark the difficulties associated with per-frame evaluations, particularly the need for accurate and timely predictions in dynamic online scenarios. Extensive experiments on two procedural datasets demonstrate the challenges and opportunities of leveraging a dual-branch architecture for mistake detection, showcasing the effectiveness of our proposed approach. In a thorough evaluation including recognition and anticipation variants and state-of-the-art models, our method reveals its robustness and effectiveness in online applications.

Test-time inference has emerged as a powerful paradigm for enabling language models to ``think'' longer and more carefully about complex challenges, much like skilled human experts. While reinforcement learning (RL) can drive self-improvement in language models on verifiable tasks, some models exhibit substantial gains while others quickly plateau. For instance, we find that Qwen-2.5-3B far exceeds Llama-3.2-3B under identical RL training for the game of Countdown. This discrepancy raises a critical question: what intrinsic properties enable effective self-improvement? We introduce a framework to investigate this question by analyzing four key cognitive behaviors -- verification, backtracking, subgoal setting, and backward chaining -- that both expert human problem solvers and successful language models employ. Our study reveals that Qwen naturally exhibits these reasoning behaviors, whereas Llama initially lacks them. In systematic experimentation with controlled behavioral datasets, we find that priming Llama with examples containing these reasoning behaviors enables substantial improvements during RL, matching or exceeding Qwen's performance. Importantly, the presence of reasoning behaviors, rather than correctness of answers, proves to be the critical factor -- models primed with incorrect solutions containing proper reasoning patterns achieve comparable performance to those trained on correct solutions. Finally, leveraging continued pretraining with OpenWebMath data, filtered to amplify reasoning behaviors, enables the Llama model to match Qwen's self-improvement trajectory. Our findings establish a fundamental relationship between initial reasoning behaviors and the capacity for improvement, explaining why some language models effectively utilize additional computation while others plateau.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types-such as neurons that activate when an operand falls within a certain range-and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a "bag of heuristics".

Meta-learning usually refers to a learning algorithm that learns from other learning algorithms. The problem of uncertainty in the predictions of neural networks shows that the world is only partially predictable and a learned neural network cannot generalize to its ever-changing surrounding environments. Therefore, the question is how a predictive model can represent multiple predictions simultaneously. We aim to provide a fundamental understanding of learning to learn in the contents of Decentralized Neural Networks (Decentralized NNs) and we believe this is one of the most important questions and prerequisites to building an autonomous intelligence machine. To this end, we shall demonstrate several pieces of evidence for tackling the problems above with Meta Learning in Decentralized NNs. In particular, we will present three different approaches to building such a decentralized learning system: (1) learning from many replica neural networks, (2) building the hierarchy of neural networks for different functions, and (3) leveraging different modality experts to learn cross-modal representations.

Large Reasoning Models (LRMs) have the ability to self-correct even when they make mistakes in their reasoning paths. However, our study reveals that when the reasoning process starts with a short but poor beginning, it becomes difficult for the model to recover. We refer to this phenomenon as the "Prefix Dominance Trap". Inspired by psychological findings that peer interaction can promote self-correction without negatively impacting already accurate individuals, we propose **Learning from Peers** (LeaP) to address this phenomenon. Specifically, every tokens, each reasoning path summarizes its intermediate reasoning and shares it with others through a routing mechanism, enabling paths to incorporate peer insights during inference. However, we observe that smaller models sometimes fail to follow summarization and reflection instructions effectively. To address this, we fine-tune them into our **LeaP-T** model series. Experiments on AIME 2024, AIME 2025, AIMO 2025, and GPQA Diamond show that LeaP provides substantial improvements. For instance, QwQ-32B with LeaP achieves nearly 5 absolute points higher than the baseline on average, and surpasses DeepSeek-R1-671B on three math benchmarks with an average gain of 3.3 points. Notably, our fine-tuned LeaP-T-7B matches the performance of DeepSeek-R1-Distill-Qwen-14B on AIME 2024. In-depth analysis reveals LeaP's robust error correction by timely peer insights, showing strong error tolerance and handling varied task difficulty. LeaP marks a milestone by enabling LRMs to collaborate during reasoning. Our code, datasets, and models are available at https://learning-from-peers.github.io/ .

In the context of multi-step reasoning, language models (LMs) probabilities are often miscalibrated -- solutions with high probabilities are not always correct. Therefore, greedy decoding, which is the standard decoding method for reasoning tasks, often yields incorrect solutions. In addition, methods such as self-consistency and verifiers rely on sampling from the LM distribution and do not tackle the underlying issue. To address this, we introduce Guiding Multi-step ReAsoning with a CorrectnEss Discriminator (GRACE), a stepwise decoding approach that nudges the model towards producing correct reasoning steps. GRACE employs a discriminator model, which is trained to differentiate correct steps from invalid ones, to adjust decoding preferences based on the correctness of each reasoning step. Importantly, GRACE does not require fine-tuning or re-training the LMs. When compared with conventional decoding strategies over four popular math reasoning benchmarks, GRACE exhibits significant improvements in both final answer accuracy and step correctness, outperforming both greedy decoding and self-consistency.Our code can be found at \url{https://github.com/mukhal/grace.}

Scaling inference compute enhances reasoning in large language models (LLMs), with long chains-of-thought (CoTs) enabling strategies like backtracking and error correction. Reinforcement learning (RL) has emerged as a crucial method for developing these capabilities, yet the conditions under which long CoTs emerge remain unclear, and RL training requires careful design choices. In this study, we systematically investigate the mechanics of long CoT reasoning, identifying the key factors that enable models to generate long CoT trajectories. Through extensive supervised fine-tuning (SFT) and RL experiments, we present four main findings: (1) While SFT is not strictly necessary, it simplifies training and improves efficiency; (2) Reasoning capabilities tend to emerge with increased training compute, but their development is not guaranteed, making reward shaping crucial for stabilizing CoT length growth; (3) Scaling verifiable reward signals is critical for RL. We find that leveraging noisy, web-extracted solutions with filtering mechanisms shows strong potential, particularly for out-of-distribution (OOD) tasks such as STEM reasoning; and (4) Core abilities like error correction are inherently present in base models, but incentivizing these skills effectively for complex tasks via RL demands significant compute, and measuring their emergence requires a nuanced approach. These insights provide practical guidance for optimizing training strategies to enhance long CoT reasoning in LLMs. Our code is available at: https://github.com/eddycmu/demystify-long-cot.

Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the development of effective PRMs faces significant challenges, particularly in data annotation and evaluation methodologies. In this paper, through extensive experiments, we demonstrate that commonly used Monte Carlo (MC) estimation-based data synthesis for PRMs typically yields inferior performance and generalization compared to LLM-as-a-judge and human annotation methods. MC estimation relies on completion models to evaluate current-step correctness, leading to inaccurate step verification. Furthermore, we identify potential biases in conventional Best-of-N (BoN) evaluation strategies for PRMs: (1) The unreliable policy models generate responses with correct answers but flawed processes, leading to a misalignment between the evaluation criteria of BoN and the PRM objectives of process verification. (2) The tolerance of PRMs of such responses leads to inflated BoN scores. (3) Existing PRMs have a significant proportion of minimum scores concentrated on the final answer steps, revealing the shift from process to outcome-based assessment in BoN Optimized PRMs. To address these challenges, we develop a consensus filtering mechanism that effectively integrates MC estimation with LLM-as-a-judge and advocates a more comprehensive evaluation framework that combines response-level and step-level metrics. Based on the mechanisms, we significantly improve both model performance and data efficiency in the BoN evaluation and the step-wise error identification task. Finally, we release a new state-of-the-art PRM that outperforms existing open-source alternatives and provides practical guidelines for future research in building process supervision models.

Building predictive models for robust and accurate prediction of stock prices and stock price movement is a challenging research problem to solve. The well-known efficient market hypothesis believes in the impossibility of accurate prediction of future stock prices in an efficient stock market as the stock prices are assumed to be purely stochastic. However, numerous works proposed by researchers have demonstrated that it is possible to predict future stock prices with a high level of precision using sophisticated algorithms, model architectures, and the selection of appropriate variables in the models. This chapter proposes a collection of predictive regression models built on deep learning architecture for robust and precise prediction of the future prices of a stock listed in the diversified sectors in the National Stock Exchange (NSE) of India. The Metastock tool is used to download the historical stock prices over a period of two years (2013- 2014) at 5 minutes intervals. While the records for the first year are used to train the models, the testing is carried out using the remaining records. The design approaches of all the models and their performance results are presented in detail. The models are also compared based on their execution time and accuracy of prediction.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

Current large-language models (LLMs) typically adopt a fixed reasoning strategy, either simple or complex, for all questions, regardless of their difficulty. This neglect of variation in task and reasoning process complexity leads to an imbalance between performance and efficiency. Existing methods attempt to implement training-free fast-slow thinking system switching to handle problems of varying difficulty, but are limited by coarse-grained solution-level strategy adjustments. To address this issue, we propose a novel reasoning paradigm: Process-Level Adaptive Thinking Mode Switching (PATS), which enables LLMs to dynamically adjust their reasoning strategy based on the difficulty of each step, optimizing the balance between accuracy and computational efficiency. Our approach integrates Process Reward Models (PRMs) with Beam Search, incorporating progressive mode switching and bad-step penalty mechanisms. Experiments on diverse mathematical benchmarks demonstrate that our methodology achieves high accuracy while maintaining moderate token usage. This study emphasizes the significance of process-level, difficulty-aware reasoning strategy adaptation, offering valuable insights into efficient inference for LLMs.

Self-correction has emerged as a promising solution to boost the reasoning performance of large language models (LLMs), where LLMs refine their solutions using self-generated critiques that pinpoint the errors. This work explores whether smaller-size (<= 13B) language models (LMs) have the ability of self-correction on reasoning tasks with minimal inputs from stronger LMs. We propose a novel pipeline that prompts smaller LMs to collect self-correction data that supports the training of self-refinement abilities. First, we leverage correct solutions to guide the model in critiquing their incorrect responses. Second, the generated critiques, after filtering, are used for supervised fine-tuning of the self-correcting reasoner through solution refinement. Our experimental results show improved self-correction abilities of two models on five datasets spanning math and commonsense reasoning, with notable performance gains when paired with a strong GPT-4-based verifier, though limitations are identified when using a weak self-verifier for determining when to correct.

Accuracy and timeliness are indeed often conflicting goals in prediction tasks. Premature predictions may yield a higher rate of false alarms, whereas delaying predictions to gather more information can render them too late to be useful. In applications such as wildfires, crimes, and traffic jams, timely forecasting are vital for safeguarding human life and property. Consequently, finding a balance between accuracy and timeliness is crucial. In this paper, we propose an early spatio-temporal forecasting model based on Multi-Objective reinforcement learning that can either implement an optimal policy given a preference or infer the preference based on a small number of samples. The model addresses two primary challenges: 1) enhancing the accuracy of early forecasting and 2) providing the optimal policy for determining the most suitable prediction time for each area. Our method demonstrates superior performance on three large-scale real-world datasets, surpassing existing methods in early spatio-temporal forecasting tasks.

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Sequence generation applications require satisfying semantic constraints, such as ensuring that programs are correct, using certain keywords, or avoiding undesirable content. Language models, whether fine-tuned or prompted with few-shot demonstrations, frequently violate these constraints, and lack a mechanism to iteratively revise their outputs. Moreover, some powerful language models are of extreme scale or inaccessible, making it inefficient, if not infeasible, to update their parameters for task-specific adaptation. We present Self-Correction, an approach that decouples an imperfect base generator (an off-the-shelf language model or supervised sequence-to-sequence model) from a separate corrector that learns to iteratively correct imperfect generations. To train the corrector, we propose an online training procedure that can use either scalar or natural language feedback on intermediate imperfect generations. We show that Self-Correction improves upon the base generator in three diverse generation tasks - mathematical program synthesis, lexically-constrained generation, and toxicity control - even when the corrector is much smaller than the base generator.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capabilities. In this study, we examine the matching mechanism employed by Transformer for multi-step reasoning on a constructed dataset. We investigate factors that influence the model's matching mechanism and discover that small initialization and post-LayerNorm can facilitate the formation of the matching mechanism, thereby enhancing the model's reasoning ability. Moreover, we propose a method to improve the model's reasoning capability by adding orthogonal noise. Finally, we investigate the parallel reasoning mechanism of Transformers and propose a conjecture on the upper bound of the model's reasoning ability based on this phenomenon. These insights contribute to a deeper understanding of the reasoning processes in large language models and guide designing more effective reasoning architectures and training strategies.

Large language models (LLMs) perform better when they produce step-by-step, "Chain-of-Thought" (CoT) reasoning before answering a question, but it is unclear if the stated reasoning is a faithful explanation of the model's actual reasoning (i.e., its process for answering the question). We investigate hypotheses for how CoT reasoning may be unfaithful, by examining how the model predictions change when we intervene on the CoT (e.g., by adding mistakes or paraphrasing it). Models show large variation across tasks in how strongly they condition on the CoT when predicting their answer, sometimes relying heavily on the CoT and other times primarily ignoring it. CoT's performance boost does not seem to come from CoT's added test-time compute alone or from information encoded via the particular phrasing of the CoT. As models become larger and more capable, they produce less faithful reasoning on most tasks we study. Overall, our results suggest that CoT can be faithful if the circumstances such as the model size and task are carefully chosen.

With the rapid advancement of Large Language Models (LLMs), developing effective critic modules for precise guidance has become crucial yet challenging. In this paper, we initially demonstrate that supervised fine-tuning for building critic modules (which is widely adopted in current solutions) fails to genuinely enhance models' critique abilities, producing superficial critiques with insufficient reflections and verifications. To unlock the unprecedented critique capabilities, we propose RefCritic, a long-chain-of-thought critic module based on reinforcement learning with dual rule-based rewards: (1) instance-level correctness of solution judgments and (2) refinement accuracies of the policy model based on critiques, aiming to generate high-quality evaluations with actionable feedback that effectively guides model refinement. We evaluate RefCritic on Qwen2.5-14B-Instruct and DeepSeek-R1-Distill-Qwen-14B across five benchmarks. On critique and refinement settings, RefCritic demonstrates consistent advantages across all benchmarks, e.g., 6.8\% and 7.2\% gains on AIME25 for the respective base models. Notably, under majority voting, policy models filtered by RefCritic show superior scaling with increased voting numbers. Moreover, despite training on solution-level supervision, RefCritic outperforms step-level supervised approaches on ProcessBench, a benchmark to identify erroneous steps in mathematical reasoning.

Can we better anticipate an actor's future actions (e.g. mix eggs) by knowing what commonly happens after his/her current action (e.g. crack eggs)? What if we also know the longer-term goal of the actor (e.g. making egg fried rice)? The long-term action anticipation (LTA) task aims to predict an actor's future behavior from video observations in the form of verb and noun sequences, and it is crucial for human-machine interaction. We propose to formulate the LTA task from two perspectives: a bottom-up approach that predicts the next actions autoregressively by modeling temporal dynamics; and a top-down approach that infers the goal of the actor and plans the needed procedure to accomplish the goal. We hypothesize that large language models (LLMs), which have been pretrained on procedure text data (e.g. recipes, how-tos), have the potential to help LTA from both perspectives. It can help provide the prior knowledge on the possible next actions, and infer the goal given the observed part of a procedure, respectively. To leverage the LLMs, we propose a two-stage framework, AntGPT. It first recognizes the actions already performed in the observed videos and then asks an LLM to predict the future actions via conditioned generation, or to infer the goal and plan the whole procedure by chain-of-thought prompting. Empirical results on the Ego4D LTA v1 and v2 benchmarks, EPIC-Kitchens-55, as well as EGTEA GAZE+ demonstrate the effectiveness of our proposed approach. AntGPT achieves state-of-the-art performance on all above benchmarks, and can successfully infer the goal and thus perform goal-conditioned "counterfactual" prediction via qualitative analysis. Code and model will be released at https://brown-palm.github.io/AntGPT

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

The pre-train and fine-tune paradigm in machine learning has had dramatic success in a wide range of domains because the use of existing data or pre-trained models on the internet enables quick and easy learning of new tasks. We aim to enable this paradigm in robotic reinforcement learning, allowing a robot to learn a new task with little human effort by leveraging data and models from the Internet. However, reinforcement learning often requires significant human effort in the form of manual reward specification or environment resets, even if the policy is pre-trained. We introduce RoboFuME, a reset-free fine-tuning system that pre-trains a multi-task manipulation policy from diverse datasets of prior experiences and self-improves online to learn a target task with minimal human intervention. Our insights are to utilize calibrated offline reinforcement learning techniques to ensure efficient online fine-tuning of a pre-trained policy in the presence of distribution shifts and leverage pre-trained vision language models (VLMs) to build a robust reward classifier for autonomously providing reward signals during the online fine-tuning process. In a diverse set of five real robot manipulation tasks, we show that our method can incorporate data from an existing robot dataset collected at a different institution and improve on a target task within as little as 3 hours of autonomous real-world experience. We also demonstrate in simulation experiments that our method outperforms prior works that use different RL algorithms or different approaches for predicting rewards. Project website: https://robofume.github.io

In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can turn either to outcome supervision, which provides feedback for a final result, or process supervision, which provides feedback for each intermediate reasoning step. Given the importance of training reliable models, and given the high cost of human feedback, it is important to carefully compare the both methods. Recent work has already begun this comparison, but many questions still remain. We conduct our own investigation, finding that process supervision significantly outperforms outcome supervision for training models to solve problems from the challenging MATH dataset. Our process-supervised model solves 78% of problems from a representative subset of the MATH test set. Additionally, we show that active learning significantly improves the efficacy of process supervision. To support related research, we also release PRM800K, the complete dataset of 800,000 step-level human feedback labels used to train our best reward model.

Reasoning is an essential capacity for large language models (LLMs) to address complex tasks, where the identification of process errors is vital for improving this ability. Recently, process-level reward models (PRMs) were proposed to provide step-wise rewards that facilitate reinforcement learning and data production during training and guide LLMs toward correct steps during inference, thereby improving reasoning accuracy. However, existing benchmarks of PRMs are text-based and focus on error detection, neglecting other scenarios like reasoning search. To address this gap, we introduce MPBench, a comprehensive, multi-task, multimodal benchmark designed to systematically assess the effectiveness of PRMs in diverse scenarios. MPBench employs three evaluation paradigms, each targeting a specific role of PRMs in the reasoning process: (1) Step Correctness, which assesses the correctness of each intermediate reasoning step; (2) Answer Aggregation, which aggregates multiple solutions and selects the best one; and (3) Reasoning Process Search, which guides the search for optimal reasoning steps during inference. Through these paradigms, MPBench makes comprehensive evaluations and provides insights into the development of multimodal PRMs.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

Currently, pre-trained models can be considered the default choice for a wide range of NLP tasks. Despite their SoTA results, there is practical evidence that these models may require a different number of computing layers for different input sequences, since evaluating all layers leads to overconfidence in wrong predictions (namely overthinking). This problem can potentially be solved by implementing adaptive computation time approaches, which were first designed to improve inference speed. Recently proposed PonderNet may be a promising solution for performing an early exit by treating the exit layer's index as a latent variable. However, the originally proposed exit criterion, relying on sampling from trained posterior distribution on the probability of exiting from the i-th layer, introduces major variance in exit layer indices, significantly reducing the resulting model's performance. In this paper, we propose improving PonderNet with a novel deterministic Q-exit criterion and a revisited model architecture. We adapted the proposed mechanism to ALBERT and RoBERTa and compared it with recent methods for performing an early exit. We observed that the proposed changes can be considered significant improvements on the original PonderNet architecture and outperform PABEE on a wide range of GLUE tasks. In addition, we also performed an in-depth ablation study of the proposed architecture to further understand Lambda layers and their performance.

The reasoning capabilities of large language models (LLMs) have been a longstanding focus of research. Recent works have further enhanced these capabilities using reinforcement learning (RL), with many new methods claiming significant improvements with minimal or no external supervision. Surprisingly, some studies even suggest that random or incorrect reward signals can enhance reasoning performance. However, these breakthroughs are mostly reported on the Qwen2.5 model family and evaluated on well-known benchmarks such as MATH-500, AMC, and AIME, while failing to achieve similar gains on other models like Llama, which warrants further investigation. Our analysis shows that although Qwen2.5 achieves strong mathematical reasoning performance, its pretraining on large-scale web corpora makes it vulnerable to data contamination in popular benchmarks. As a result, results derived from these benchmarks may be unreliable. To address this, we introduce a generator that produces fully synthetic arithmetic problems of arbitrary length and difficulty, yielding a clean dataset we call RandomCalculation. Using these leakage-free datasets, we show that only accurate reward signals consistently improve performance, while noisy or incorrect signals do not. We advocate for evaluating RL methods on uncontaminated benchmarks and across diverse model families to ensure trustworthy conclusions.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

The success of Large Language Models (LLMs) has sparked interest in various agentic applications. A key hypothesis is that LLMs, leveraging common sense and Chain-of-Thought (CoT) reasoning, can effectively explore and efficiently solve complex domains. However, LLM agents have been found to suffer from sub-optimal exploration and the knowing-doing gap, the inability to effectively act on knowledge present in the model. In this work, we systematically study why LLMs perform sub-optimally in decision-making scenarios. In particular, we closely examine three prevalent failure modes: greediness, frequency bias, and the knowing-doing gap. We propose mitigation of these shortcomings by fine-tuning via Reinforcement Learning (RL) on self-generated CoT rationales. Our experiments across multi-armed bandits, contextual bandits, and Tic-tac-toe, demonstrate that RL fine-tuning enhances the decision-making abilities of LLMs by increasing exploration and narrowing the knowing-doing gap. Finally, we study both classic exploration mechanisms, such as epsilon-greedy, and LLM-specific approaches, such as self-correction and self-consistency, to enable more effective fine-tuning of LLMs for decision-making.

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

Although large language models (LLMs) have become transformative, they still make mistakes and can explore unproductive reasoning paths. Self-correction is an important capability for a trustworthy LLM, particularly an autoregressive LLM. While LLMs can identify error in user input, they exhibit a systematic 'Self-Correction Blind Spot' - failing to correct identical error in their own outputs. To systematically study this phenomenon, we introduce Self-Correction Bench, a systematic framework to measure this phenomenon through controlled error injection at three complexity levels. Testing 14 models, we find an average 64.5% blind spot rate. We find multiple evidences that this limitation relates to training data composition: human training demonstrations predominantly show error-free responses rather than error-correction sequences, unlike RL-trained models that learn error correction through outcome feedback. Remarkably, simply appending "Wait" reduces blind spots by 89.3%, suggesting that the capability exists but requires activation. Our work highlights a critical limitation in current LLMs and offers potential avenues for improving their reliability and trustworthiness.

Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that the performance is greatly affected by the factuality of the generated explanation. To improve the correctness of the explanations, fine-tuning language models with explanation data is needed. However, there exists only a few datasets that can be used for such approaches, and no data collection tool for building them. Thus, we introduce CoTEVer, a tool-kit for annotating the factual correctness of generated explanations and collecting revision data of wrong explanations. Furthermore, we suggest several use cases where the data collected with CoTEVer can be utilized for enhancing the faithfulness of explanations. Our toolkit is publicly available at https://github.com/SeungoneKim/CoTEVer.

Self-correction is a highly desirable capability of large language models (LLMs), yet it has consistently been found to be largely ineffective in modern LLMs. Existing approaches for training self-correction either require multiple models or rely on a more capable model or other forms of supervision. To this end, we develop a multi-turn online reinforcement learning (RL) approach, SCoRe, that significantly improves an LLM's self-correction ability using entirely self-generated data. To build SCoRe, we first show that variants of supervised fine-tuning (SFT) on offline model-generated correction traces are insufficient for instilling self-correction behavior. In particular, we observe that training via SFT either suffers from a distribution mismatch between the training data and the model's own responses or implicitly prefers only a certain mode of correction behavior that is often not effective at test time. SCoRe addresses these challenges by training under the model's own distribution of self-generated correction traces and using appropriate regularization to steer the learning process into learning a self-correction strategy that is effective at test time as opposed to simply fitting high-reward responses for a given prompt. This regularization prescribes running a first phase of RL on a base model to generate a policy initialization that is less susceptible to collapse and then using a reward bonus to amplify self-correction during training. When applied to Gemini 1.0 Pro and 1.5 Flash models, we find that SCoRe achieves state-of-the-art self-correction performance, improving the base models' self-correction by 15.6% and 9.1% respectively on the MATH and HumanEval benchmarks.

We present an online method for estimating the cost of solving SAT problems. Modern SAT solvers present several challenges to estimate search cost including non-chronological backtracking, learning and restarts. Our method uses a linear model trained on data gathered at the start of search. We show the effectiveness of this method using random and structured problems. We demonstrate that predictions made in early restarts can be used to improve later predictions. We also show that we can use such cost estimations to select a solver from a portfolio.

Large language models (LLMs) recently exhibited remarkable reasoning capabilities on solving math problems. To further improve this capability, this work proposes Learning from Mistakes (LeMa), akin to human learning processes. Consider a human student who failed to solve a math problem, he will learn from what mistake he has made and how to correct it. Mimicking this error-driven learning process, LeMa fine-tunes LLMs on mistake-correction data pairs generated by GPT-4. Specifically, we first collect inaccurate reasoning paths from various LLMs and then employ GPT-4 as a "corrector" to (1) identify the mistake step, (2) explain the reason for the mistake, and (3) correct the mistake and generate the final answer. Experimental results demonstrate the effectiveness of LeMa: across five backbone LLMs and two mathematical reasoning tasks, LeMa consistently improves the performance compared with fine-tuning on CoT data alone. Impressively, LeMa can also benefit specialized LLMs such as WizardMath and MetaMath, achieving 85.4% pass@1 accuracy on GSM8K and 27.1% on MATH. This surpasses the SOTA performance achieved by non-execution open-source models on these challenging tasks. Our code, data and models will be publicly available at https://github.com/microsoft/CodeT.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Large language models (LLMs) have significantly improved their reasoning capabilities; however, they still struggle with complex multi-step mathematical problem-solving due to error propagation, lack of self-correction, and limited adaptability to diverse reasoning styles. Existing methods rely on static fine-tuning or prompt engineering, which fail to generalize across problem complexities, while the scarcity of high-quality preference data further hinders reliable reasoning. We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs) by iteratively generating, correcting, and diversifying reasoning chains. SPHERE operates in three stages: (i) Self-Generation, where the model autonomously constructs problem-solving steps; (ii) Self-Correction, enabling it to identify and rectify errors; and (iii) Diversity Induction, improving robustness through multiple valid reasoning trajectories. This self-evolution mechanism strengthens mathematical reasoning and enhances model reliability. Evaluations on MATH 500, GSM8K, AIME, AMC, and Olympiad show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks. Our findings demonstrate that self-evolving models can close the reasoning gap between SLMs and state-of-the-art LLMs, making mathematical AI more reliable, scalable, and efficient.

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades.

A central goal of cognitive modeling is to develop models that not only predict human behavior but also provide insight into the underlying cognitive mechanisms. While neural network models trained on large-scale behavioral data often achieve strong predictive performance, they typically fall short in offering interpretable explanations of the cognitive processes they capture. In this work, we explore the potential of pretrained large language models (LLMs) to serve as dual-purpose cognitive models--capable of both accurate prediction and interpretable explanation in natural language. Specifically, we employ reinforcement learning with outcome-based rewards to guide LLMs toward generating explicit reasoning traces for explaining human risky choices. Our findings demonstrate that this approach produces high-quality explanations alongside strong quantitative predictions of human decisions.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Image-based reinforcement learning (RL) faces significant challenges in generalization when the visual environment undergoes substantial changes between training and deployment. Under such circumstances, learned policies may not perform well leading to degraded results. Previous approaches to this problem have largely focused on broadening the training observation distribution, employing techniques like data augmentation and domain randomization. However, given the sequential nature of the RL decision-making problem, it is often the case that residual errors are propagated by the learned policy model and accumulate throughout the trajectory, resulting in highly degraded performance. In this paper, we leverage the observation that predicted rewards under domain shift, even though imperfect, can still be a useful signal to guide fine-tuning. We exploit this property to fine-tune a policy using reward prediction in the target domain. We have found that, even under significant domain shift, the predicted reward can still provide meaningful signal and fine-tuning substantially improves the original policy. Our approach, termed Predicted Reward Fine-tuning (PRFT), improves performance across diverse tasks in both simulated benchmarks and real-world experiments. More information is available at project web page: https://sites.google.com/view/prft.

When individuals encounter observations that violate their expectations, when will they adjust their expectations and when will they maintain them despite these observations? For example, when individuals expect objects of type A to be smaller than objects B, but observe the opposite, when will they adjust their expectation about the relationship between the two objects (to A being larger than B)? Naively, one would predict that the larger the violation, the greater the adaptation. However, experiments reveal that when violations are extreme, individuals are more likely to hold on to their prior expectations rather than adjust them. To address this puzzle, we tested the adaptation of artificial neural networks (ANNs) capable of relational learning and found a similar phenomenon: Standard learning dynamics dictates that small violations would lead to adjustments of expected relations while larger ones would be resolved using a different mechanism -- a change in object representation that bypasses the need for adaptation of the relational expectations. These results suggest that the experimentally-observed stability of prior expectations when facing large expectation violations is a natural consequence of learning dynamics and does not require any additional mechanisms. We conclude by discussing the effect of intermediate adaptation steps on this stability.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce Self-Play Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, applying SPC to guide the test-time search of diverse LLMs significantly improves their mathematical reasoning performance on MATH500 and AIME2024, outperforming state-of-the-art process reward models.

The surprisingly likely criterion in the seminal work of Prelec (the Bayesian Truth Serum) guarantees truthfulness in a game-theoretic multi-agent setting, by rewarding rational agents to maximise the expected information gain with their answers w.r.t. their probabilistic beliefs. We investigate the relevance of a similar criterion for responses of LLMs. We hypothesize that if the surprisingly likely criterion works in LLMs, under certain conditions, the responses that maximize the reward under this criterion should be more accurate than the responses that only maximize the posterior probability. Using benchmarks including the TruthfulQA benchmark and using openly available LLMs: GPT-2 and LLaMA-2, we show that the method indeed improves the accuracy significantly (for example, upto 24 percentage points aggregate improvement on TruthfulQA and upto 70 percentage points improvement on individual categories of questions).

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

The recent success of Large Language Models (LLMs) has catalyzed an increasing interest in their self-correction capabilities. This paper presents a comprehensive investigation into the intrinsic self-correction of LLMs, attempting to address the ongoing debate about its feasibility. Our research has identified an important latent factor - the "confidence" of LLMs - during the self-correction process. Overlooking this factor may cause the models to over-criticize themselves, resulting in unreliable conclusions regarding the efficacy of self-correction. We have experimentally observed that LLMs possess the capability to understand the "confidence" in their own responses. It motivates us to develop an "If-or-Else" (IoE) prompting framework, designed to guide LLMs in assessing their own "confidence", facilitating intrinsic self-corrections. We conduct extensive experiments and demonstrate that our IoE-based Prompt can achieve a consistent improvement regarding the accuracy of self-corrected responses over the initial answers. Our study not only sheds light on the underlying factors affecting self-correction in LLMs, but also introduces a practical framework that utilizes the IoE prompting principle to efficiently improve self-correction capabilities with "confidence". The code is available at https://github.com/MBZUAI-CLeaR/IoE-Prompting.git.

We investigate the mechanism design problem faced by a principal who hires multiple agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that optimal mechanisms must correlate agents' efforts, which introduces externalities among the agents, and hence complex incentive compatibility constraints and equilibrium selection problems. First, we design a polynomial-time algorithm to find an optimal incentive compatible mechanism. Then, we study an online problem, where the principal repeatedly interacts with a group of unknown agents. We design a no-regret algorithm that provides mathcal{O}(T^{2/3}) regret with respect to an optimal mechanism, matching the state-of-the-art bound for single-agent settings.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Large-scale high-quality training data is important for improving the performance of models. After trained with data that has rationales (reasoning steps), models gain reasoning capability. However, the dataset with high-quality rationales is relatively scarce due to the high annotation cost. To address this issue, we propose Self-motivated Learning framework. The framework motivates the model itself to automatically generate rationales on existing datasets. Based on the inherent rank from correctness across multiple rationales, the model learns to generate better rationales, leading to higher reasoning capability. Specifically, we train a reward model with the rank to evaluate the quality of rationales, and improve the performance of reasoning through reinforcement learning. Experiment results of Llama2 7B on multiple reasoning datasets show that our method significantly improves the reasoning ability of models, even outperforming text-davinci-002 in some datasets.

Recent research has focused on enhancing the capability of smaller models through imitation learning, drawing on the outputs generated by large foundation models (LFMs). A number of issues impact the quality of these models, ranging from limited imitation signals from shallow LFM outputs; small scale homogeneous training data; and most notably a lack of rigorous evaluation resulting in overestimating the small model's capability as they tend to learn to imitate the style, but not the reasoning process of LFMs. To address these challenges, we develop Orca (We are working with our legal team to publicly release a diff of the model weights in accordance with LLaMA's release policy to be published at https://aka.ms/orca-lm), a 13-billion parameter model that learns to imitate the reasoning process of LFMs. Orca learns from rich signals from GPT-4 including explanation traces; step-by-step thought processes; and other complex instructions, guided by teacher assistance from ChatGPT. To promote this progressive learning, we tap into large-scale and diverse imitation data with judicious sampling and selection. Orca surpasses conventional state-of-the-art instruction-tuned models such as Vicuna-13B by more than 100% in complex zero-shot reasoning benchmarks like Big-Bench Hard (BBH) and 42% on AGIEval. Moreover, Orca reaches parity with ChatGPT on the BBH benchmark and shows competitive performance (4 pts gap with optimized system message) in professional and academic examinations like the SAT, LSAT, GRE, and GMAT, both in zero-shot settings without CoT; while trailing behind GPT-4. Our research indicates that learning from step-by-step explanations, whether these are generated by humans or more advanced AI models, is a promising direction to improve model capabilities and skills.

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase-the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models' ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 285K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation. Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations, and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.

Large reasoning models (LRMs), such as OpenAI o1 and DeepSeek-R1, have significantly enhanced their reasoning capabilities by generating longer chains of thought, demonstrating outstanding performance across a variety of tasks. However, this performance gain comes at the cost of a substantial increase in redundant reasoning during the generation process, leading to high computational overhead and exacerbating the issue of overthinking. Although numerous existing approaches aim to address the problem of overthinking, they often rely on external interventions. In this paper, we propose a novel framework, Self-Braking Tuning (SBT), which tackles overthinking from the perspective of allowing the model to regulate its own reasoning process, thus eliminating the reliance on external control mechanisms. We construct a set of overthinking identification metrics based on standard answers and design a systematic method to detect redundant reasoning. This method accurately identifies unnecessary steps within the reasoning trajectory and generates training signals for learning self-regulation behaviors. Building on this foundation, we develop a complete strategy for constructing data with adaptive reasoning lengths and introduce an innovative braking prompt mechanism that enables the model to naturally learn when to terminate reasoning at an appropriate point. Experiments across mathematical benchmarks (AIME, AMC, MATH500, GSM8K) demonstrate that our method reduces token consumption by up to 60% while maintaining comparable accuracy to unconstrained models.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

We test the hypothesis that language models trained with reinforcement learning from human feedback (RLHF) have the capability to "morally self-correct" -- to avoid producing harmful outputs -- if instructed to do so. We find strong evidence in support of this hypothesis across three different experiments, each of which reveal different facets of moral self-correction. We find that the capability for moral self-correction emerges at 22B model parameters, and typically improves with increasing model size and RLHF training. We believe that at this level of scale, language models obtain two capabilities that they can use for moral self-correction: (1) they can follow instructions and (2) they can learn complex normative concepts of harm like stereotyping, bias, and discrimination. As such, they can follow instructions to avoid certain kinds of morally harmful outputs. We believe our results are cause for cautious optimism regarding the ability to train language models to abide by ethical principles.

Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent developments in steering protein generative models (e.g diffusion models, language models) offer a promising approach. However, by and large, past studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured by low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequence-fitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages compared to alternatives such as reinforcement learning with protein language models.

Existing methods, such as concept bottleneck models (CBMs), have been successful in providing concept-based interpretations for black-box deep learning models. They typically work by predicting concepts given the input and then predicting the final class label given the predicted concepts. However, (1) they often fail to capture the high-order, nonlinear interaction between concepts, e.g., correcting a predicted concept (e.g., "yellow breast") does not help correct highly correlated concepts (e.g., "yellow belly"), leading to suboptimal final accuracy; (2) they cannot naturally quantify the complex conditional dependencies between different concepts and class labels (e.g., for an image with the class label "Kentucky Warbler" and a concept "black bill", what is the probability that the model correctly predicts another concept "black crown"), therefore failing to provide deeper insight into how a black-box model works. In response to these limitations, we propose Energy-based Concept Bottleneck Models (ECBMs). Our ECBMs use a set of neural networks to define the joint energy of candidate (input, concept, class) tuples. With such a unified interface, prediction, concept correction, and conditional dependency quantification are then represented as conditional probabilities, which are generated by composing different energy functions. Our ECBMs address both limitations of existing CBMs, providing higher accuracy and richer concept interpretations. Empirical results show that our approach outperforms the state-of-the-art on real-world datasets.

Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can be ena BHbled in this setting. We propose and theoretically analyze an empirical-risk-based method for incorporating the labeling mechanism. Additionally, we investigate under which assumptions learning is possible when the labeling mechanism is not fully understood and propose a practical method to enable this. Our empirical analysis supports the theoretical results and shows that taking into account the possibility of a selection bias, even when the labeling mechanism is unknown, improves the trained classifiers.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

LLM-based Automatic Prompt Optimization, which typically utilizes LLMs as Prompt Optimizers to self-reflect and refine prompts, has shown promising performance in recent studies. Despite the success, the underlying mechanism of this approach remains unexplored, and the true effectiveness of LLMs as Prompt Optimizers requires further validation. In this work, we conducted a comprehensive study to uncover the actual mechanism of LLM-based Prompt Optimization. Our findings reveal that the LLM optimizers struggle to identify the true causes of errors during reflection, tending to be biased by their own prior knowledge rather than genuinely reflecting on the errors. Furthermore, even when the reflection is semantically valid, the LLM optimizers often fail to generate appropriate prompts for the target models with a single prompt refinement step, partly due to the unpredictable behaviors of the target models. Based on the observations, we introduce a new "Automatic Behavior Optimization" paradigm, which directly optimizes the target model's behavior in a more controllable manner. We hope our study can inspire new directions for automatic prompt optimization development.

Predictive model design for accurately predicting future stock prices has always been considered an interesting and challenging research problem. The task becomes complex due to the volatile and stochastic nature of the stock prices in the real world which is affected by numerous controllable and uncontrollable variables. This paper presents an optimized predictive model built on long-and-short-term memory (LSTM) architecture for automatically extracting past stock prices from the web over a specified time interval and predicting their future prices for a specified forecast horizon, and forecasts the future stock prices. The model is deployed for making buy and sell transactions based on its predicted results for 70 important stocks from seven different sectors listed in the National Stock Exchange (NSE) of India. The profitability of each sector is derived based on the total profit yielded by the stocks in that sector over a period from Jan 1, 2010 to Aug 26, 2021. The sectors are compared based on their profitability values. The prediction accuracy of the model is also evaluated for each sector. The results indicate that the model is highly accurate in predicting future stock prices.

Process-level Reward Models (PRMs) are crucial for complex reasoning and decision-making tasks, where each intermediate step plays an important role in the reasoning process. Since language models are prone to various types of errors during the reasoning process, PRMs are required to possess nuanced capabilities for detecting various implicit error types in real-world scenarios. However, current benchmarks primarily focus on step correctness, failing to evaluate PRMs' performance systematically. To address this gap, we introduce PRMBench, a process-level benchmark specifically designed to assess the fine-grained error detection capabilities of PRMs. PRMBench comprises 6,216 carefully designed problems and 83,456 step-level labels, evaluating models across multiple dimensions, including simplicity, soundness, and sensitivity. In our experiments on 15 models, spanning both open-source PRMs and closed-source large language models prompted as critic models, we uncover significant weaknesses in current PRMs. These findings underscore the challenges inherent in process-level evaluation and highlight key directions for future research. We hope PRMBench can be a robust bench for advancing research on PRM evaluation and development.

Recent advancements in large language models (LLMs) have led to significant successes across various applications, where the most noticeable is to a series of emerging capabilities, particularly in the areas of In-Context Learning (ICL) and Chain-of-Thought (CoT). To better understand and control model performance, many studies have begun investigating the underlying causes of these phenomena and their impact on task outcomes. However, existing explanatory frameworks predominantly focus on isolating and explaining ICL and CoT independently, leading to an incomplete understanding of their combined influence on model performance. To address this gap, we propose the Electronic Circuit Model (ECM), which provides a foundation for developing scalable, learnable policies and improving the management of AI-generated content. Specifically, ECM conceptualizes model behavior as an electronic circuit: ICL is represented as semantic magnetic field to providing an additional voltage following Faraday's Law, while CoT is modeled as series resistors to constrain the model output performance following Ohm's Law. Experimental results demonstrate that the ECM effectively predicts and explains LLM performance across a variety of prompting strategies. Furthermore, we apply ECM to advanced reasoning strategy optimization on a series of tasks, such as the International Olympiad in Informatics (IOI) and the International Mathematical Olympiad (IMO), achieving competitive performance that surpasses nearly 80% of top human competitors.

Concept guidance has emerged as a cheap and simple way to control the behavior of language models by probing their hidden representations for concept vectors and using them to perturb activations at inference time. While the focus of previous work has largely been on truthfulness, in this paper we extend this framework to a richer set of concepts such as appropriateness, humor, creativity and quality, and explore to what degree current detection and guidance strategies work in these challenging settings. To facilitate evaluation, we develop a novel metric for concept guidance that takes into account both the success of concept elicitation as well as the potential degradation in fluency of the guided model. Our extensive experiments reveal that while some concepts such as truthfulness more easily allow for guidance with current techniques, novel concepts such as appropriateness or humor either remain difficult to elicit, need extensive tuning to work, or even experience confusion. Moreover, we find that probes with optimal detection accuracies do not necessarily make for the optimal guides, contradicting previous observations for truthfulness. Our work warrants a deeper investigation into the interplay between detectability, guidability, and the nature of the concept, and we hope that our rich experimental test-bed for guidance research inspires stronger follow-up approaches.

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we demonstrate that this understanding enables performance gains: we can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we provide practical insights, such as that training data format (e.g., free-form vs. multiple-choice) has a far greater impact on reasoning behavior than data domain, underscoring the importance of format-aware model design.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

The trustworthiness of machine learning has emerged as a critical topic in the field, encompassing various applications and research areas such as robustness, security, interpretability, and fairness. The last decade saw the development of numerous methods addressing these challenges. In this survey, we systematically review these advancements from a data-centric perspective, highlighting the shortcomings of traditional empirical risk minimization (ERM) training in handling challenges posed by the data. Interestingly, we observe a convergence of these methods, despite being developed independently across trustworthy machine learning subfields. Pearl's hierarchy of causality offers a unifying framework for these techniques. Accordingly, this survey presents the background of trustworthy machine learning development using a unified set of concepts, connects this language to Pearl's causal hierarchy, and finally discusses methods explicitly inspired by causality literature. We provide a unified language with mathematical vocabulary to link these methods across robustness, adversarial robustness, interpretability, and fairness, fostering a more cohesive understanding of the field. Further, we explore the trustworthiness of large pretrained models. After summarizing dominant techniques like fine-tuning, parameter-efficient fine-tuning, prompting, and reinforcement learning with human feedback, we draw connections between them and the standard ERM. This connection allows us to build upon the principled understanding of trustworthy methods, extending it to these new techniques in large pretrained models, paving the way for future methods. Existing methods under this perspective are also reviewed. Lastly, we offer a brief summary of the applications of these methods and discuss potential future aspects related to our survey. For more information, please visit http://trustai.one.

It has long been hypothesised that causal reasoning plays a fundamental role in robust and general intelligence. However, it is not known if agents must learn causal models in order to generalise to new domains, or if other inductive biases are sufficient. We answer this question, showing that any agent capable of satisfying a regret bound under a large set of distributional shifts must have learned an approximate causal model of the data generating process, which converges to the true causal model for optimal agents. We discuss the implications of this result for several research areas including transfer learning and causal inference.

Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped to correct FOL rules predicted by GPT-3.5, and can achieve similar performance as GPT-4 with a fraction of the cost. This correction ability was achieved by a novel supervised fine-tuning (SFT) + reinforcement learning with human feedback (RLHF) framework, which initially trains on synthetically perturbed NL-FOL pairs to encourage chain-of-thought reasoning and then fine-tunes with RLHF on GPT-3.5 outputs using a FOL verifier as the reward model. To train LogicLLaMA, we present MALLS (large language Model generAted NL-FOL pairS), a dataset of 34K high-quality and diverse sentence-level NL-FOL pairs collected from GPT-4. The dataset was created by implementing a pipeline that prompts GPT-4 for pairs, and dynamically adjusts the prompts to ensure the collection of pairs with rich and diverse contexts at different levels of complexity, and verifies the validity of the generated FOL rules. Codes, weights, and data are available at https://github.com/gblackout/LogicLLaMA{{small https://github.com/gblackout/LogicLLaMA}}.

For a long-time, researchers have been developing a reliable and accurate predictive model for stock price prediction. According to the literature, if predictive models are correctly designed and refined, they can painstakingly and faithfully estimate future stock values. This paper demonstrates a set of time series, econometric, and various learning-based models for stock price prediction. The data of Infosys, ICICI, and SUN PHARMA from the period of January 2004 to December 2019 was used here for training and testing the models to know which model performs best in which sector. One time series model (Holt-Winters Exponential Smoothing), one econometric model (ARIMA), two machine Learning models (Random Forest and MARS), and two deep learning-based models (simple RNN and LSTM) have been included in this paper. MARS has been proved to be the best performing machine learning model, while LSTM has proved to be the best performing deep learning model. But overall, for all three sectors - IT (on Infosys data), Banking (on ICICI data), and Health (on SUN PHARMA data), MARS has proved to be the best performing model in sales forecasting.

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S^2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by both outcome-level and process-level reinforcement learning, with minimized resource requirements, enabling the model to adaptively refine its reasoning process during inference. Our results demonstrate that, with only 3.1k self-verifying and self-correcting behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0\% to 81.6\%, outperforming models trained on an equivalent amount of long-CoT distilled data. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S^2R. Our code and data are available at https://github.com/NineAbyss/S2R.

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly double-check their work after having derived the correct answer. To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved. Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO). LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process. Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression. Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs. Our code is released at https://github.com/zxiangx/LC-R1.

Reasoning before action and imagining potential outcomes (i.e., world models) are essential for embodied agents operating in complex open-world environments. Yet, prior work either incorporates only one of these abilities in an end-to-end agent or integrates multiple specialized models into an agent system, limiting the learning efficiency and generalization of the policy. Thus, this paper makes the first attempt to synergize Reasoning and Imagination in an end-to-end Generalist policy, termed RIG. To train RIG in an end-to-end manner, we construct a data pipeline that progressively integrates and enriches the content of imagination and reasoning in the trajectories collected from existing agents. The joint learning of reasoning and next image generation explicitly models the inherent correlation between reasoning, action, and dynamics of environments, and thus exhibits more than 17times sample efficiency improvements and generalization in comparison with previous works. During inference, RIG first reasons about the next action, produces potential action, and then predicts the action outcomes, which offers the agent a chance to review and self-correct based on the imagination before taking real actions. Experimental results show that the synergy of reasoning and imagination not only improves the robustness, generalization, and interoperability of generalist policy but also enables test-time scaling to enhance overall performance.

Chain-of-Thought (CoT) prompting methods have enabled large language models (LLMs) to generate reasoning paths and solve math word problems (MWPs). However, they are sensitive to mistakes in the paths, as any mistake can result in an incorrect answer. We propose a novel method named Progressive Rectification Prompting (PRP) to improve average accuracy on eight MWP datasets from 77.3 to 90.5. Given an initial answer from CoT, PRP iterates a verify-then-rectify process to progressively identify incorrect answers and rectify the reasoning paths. With the most likely correct answer, the LLM predicts a masked numerical value in the question; if the prediction does not match the masked value, the answer is likely incorrect. Then the LLM is prompted to re-generate the reasoning path hinted with a set of incorrect answers to prevent itself from repeating previous mistakes. PRP achieves the best performance compared against the CoT methods. Our implementation is made publicly available at https://wzy6642.github.io/prp.github.io/.

Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e., the generation of unnecessarily verbose and redundant content), which hinders efficiency and inflates inference cost. In this work, we explore the representational and behavioral origins of this inefficiency, revealing that LRMs inherently possess the capacity for more concise reasoning. Empirical analyses show that correct reasoning paths vary significantly in length, and the shortest correct responses often suffice, indicating untapped efficiency potential. Exploiting these findings, we propose two lightweight methods to enhance LRM efficiency. First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction in the model's representation space. Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity by rewarding concise correct solutions. Extensive experiments on seven LRM backbones across multiple mathematical reasoning benchmarks demonstrate that our methods significantly reduce reasoning length while preserving or improving task performance. Our results highlight that reasoning efficiency can be improved by leveraging and guiding the intrinsic capabilities of existing models in a self-guided manner.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

With the rapid development of large language models (LLMs), natural language explanations (NLEs) have become increasingly important for understanding model predictions. However, these explanations often fail to faithfully represent the model's actual reasoning process. While existing work has demonstrated that LLMs can self-critique and refine their initial outputs for various tasks, this capability remains unexplored for improving explanation faithfulness. To address this gap, we introduce Self-critique and Refinement for Natural Language Explanations (SR-NLE), a framework that enables models to improve the faithfulness of their own explanations -- specifically, post-hoc NLEs -- through an iterative critique and refinement process without external supervision. Our framework leverages different feedback mechanisms to guide the refinement process, including natural language self-feedback and, notably, a novel feedback approach based on feature attribution that highlights important input words. Our experiments across three datasets and four state-of-the-art LLMs demonstrate that SR-NLE significantly reduces unfaithfulness rates, with our best method achieving an average unfaithfulness rate of 36.02%, compared to 54.81% for baseline -- an absolute reduction of 18.79%. These findings reveal that the investigated LLMs can indeed refine their explanations to better reflect their actual reasoning process, requiring only appropriate guidance through feedback without additional training or fine-tuning.

Cascades and speculative decoding are two common approaches to improving language models' inference efficiency. Both approaches involve interleaving models of different sizes, but via fundamentally distinct mechanisms: cascades employ a deferral rule that invokes the larger model only for "hard" inputs, while speculative decoding uses speculative execution to primarily invoke the larger model in parallel verification mode. These mechanisms offer different benefits: empirically, cascades offer better cost-quality trade-offs, often even outperforming the large model, while theoretically, speculative decoding offers a guarantee of quality-neutrality. In this paper, we leverage the best of both these approaches by designing new speculative cascading techniques that implement their deferral rule through speculative execution. We characterize the optimal deferral rule for our speculative cascades, and employ a plug-in approximation to the optimal rule. Experiments with Gemma and T5 models on a range of language benchmarks show that our approach yields better cost quality trade-offs than cascading and speculative decoding baselines.

A Recurrent Neural Network (RNN) was used to perform video frame prediction of microbial growth for a population of two mutants of Pseudomonas aeruginosa. The RNN was trained on videos of 20 frames that were acquired using fluorescence microscopy and microfluidics. The network predicted the last 10 frames of each video, and the accuracy's of the predictions was assessed by comparing raw images, population curves, and the number and size of individual colonies. Overall, we found the predictions to be accurate using this approach. The implications this result has on designing autonomous experiments in microbiology, and the steps that can be taken to make the predictions even more accurate, are discussed.

In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would therefore benefit from control over the finite-sample error rate of interpretations. We reframe black box model interpretability as a multiple hypothesis testing problem. The task is to discover "important" features by testing whether the model prediction is significantly different from what would be expected if the features were replaced with uninformative counterfactuals. We propose two testing methods: one that provably controls the false discovery rate but which is not yet feasible for large-scale applications, and an approximate testing method which can be applied to real-world data sets. In simulation, both tests have high power relative to existing interpretability methods. When applied to state-of-the-art vision and language models, the framework selects features that intuitively explain model predictions. The resulting explanations have the additional advantage that they are themselves easy to interpret.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~80 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

Reinforcement Learning from Human Feedback (RLHF) has been commonly used to align the behaviors of Large Language Models (LLMs) with human preferences. Recently, a popular alternative is Direct Policy Optimization (DPO), which replaces an LLM-based reward model with the policy itself, thus obviating the need for extra memory and training time to learn the reward model. However, DPO does not consider the relative qualities of the positive and negative responses, and can lead to sub-optimal training outcomes. To alleviate this problem, we investigate the use of intrinsic knowledge within the on-the-fly fine-tuning LLM to obtain relative qualities and help to refine the loss function. Specifically, we leverage the knowledge of the LLM to design a refinement function to estimate the quality of both the positive and negative responses. We show that the constructed refinement function can help self-refine the loss function under mild assumptions. The refinement function is integrated into DPO and its variant Identity Policy Optimization (IPO). Experiments across various evaluators indicate that they can improve the performance of the fine-tuned models over DPO and IPO.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving loops to let the model correct its own mistakes. However, existing self-correction approaches treat corrections as standalone post-generation refinements, relying on extra prompt and system designs to elicit self-corrections, instead of performing real-time, spontaneous self-corrections in a single pass. To address this, we propose SPOC, a spontaneous self-correction approach that enables LLMs to generate interleaved solutions and verifications in a single inference pass, with generation dynamically terminated based on verification outcomes, thereby effectively scaling inference time compute. SPOC considers a multi-agent perspective by assigning dual roles -- solution proposer and verifier -- to the same model. We adopt a simple yet effective approach to generate synthetic data for fine-tuning, enabling the model to develop capabilities for self-verification and multi-agent collaboration. We further improve its solution proposal and verification accuracy through online reinforcement learning. Experiments on mathematical reasoning benchmarks show that SPOC significantly improves performance. Notably, SPOC boosts the accuracy of Llama-3.1-8B and 70B Instruct models, achieving gains of 8.8% and 11.6% on MATH500, 10.0% and 20.0% on AMC23, and 3.3% and 6.7% on AIME24, respectively.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Recent advances in applying reinforcement learning (RL) to large language models (LLMs) have led to substantial progress. In particular, a series of remarkable yet often counterintuitive phenomena have been reported in LLMs, exhibiting patterns not typically observed in traditional RL settings. For example, notable claims include that a single training example can match the performance achieved with an entire dataset, that the reward signal does not need to be very accurate, and that training solely with negative samples can match or even surpass sophisticated reward-based methods. However, the precise conditions under which these observations hold - and, critically, when they fail - remain unclear. In this work, we identify a key factor that differentiates RL observations: whether the pretrained model already exhibits strong Model-Task Alignment, as measured by pass@k accuracy on the evaluated task. Through a systematic and comprehensive examination of a series of counterintuitive claims, supported by rigorous experimental validation across different model architectures and task domains, our findings show that while standard RL training remains consistently robust across settings, many of these counterintuitive results arise only when the model and task already exhibit strong model-task alignment. In contrast, these techniques fail to drive substantial learning in more challenging regimes, where standard RL methods remain effective.

Recent advances in multimodal Reward Models (RMs) have shown significant promise in delivering reward signals to align vision models with human preferences. However, current RMs are generally restricted to providing direct responses or engaging in shallow reasoning processes with limited depth, often leading to inaccurate reward signals. We posit that incorporating explicit long chains of thought (CoT) into the reward reasoning process can significantly strengthen their reliability and robustness. Furthermore, we believe that once RMs internalize CoT reasoning, their direct response accuracy can also be improved through implicit reasoning capabilities. To this end, this paper proposes UnifiedReward-Think, the first unified multimodal CoT-based reward model, capable of multi-dimensional, step-by-step long-chain reasoning for both visual understanding and generation reward tasks. Specifically, we adopt an exploration-driven reinforcement fine-tuning approach to elicit and incentivize the model's latent complex reasoning ability: (1) We first use a small amount of image generation preference data to distill the reasoning process of GPT-4o, which is then used for the model's cold start to learn the format and structure of CoT reasoning. (2) Subsequently, by leveraging the model's prior knowledge and generalization capabilities, we prepare large-scale unified multimodal preference data to elicit the model's reasoning process across various vision tasks. During this phase, correct reasoning outputs are retained for rejection sampling to refine the model (3) while incorrect predicted samples are finally used for Group Relative Policy Optimization (GRPO) based reinforcement fine-tuning, enabling the model to explore diverse reasoning paths and optimize for correct and robust solutions. Extensive experiments across various vision reward tasks demonstrate the superiority of our model.

In recent years, large language models (LLMs) have shown remarkable capabilities in various artificial intelligence problems. However, they fail to plan reliably, even when prompted with a detailed definition of the planning task. Attempts to improve their planning capabilities, such as chain-of-thought prompting, fine-tuning, and explicit "reasoning" still yield incorrect plans and usually fail to generalize to larger tasks. In this paper, we show how to use LLMs to generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks within a greedy best-first search, and choose the strongest one. The resulting LLM-generated heuristics solve many more unseen test tasks than state-of-the-art domain-independent heuristics for classical planning. They are even competitive with the strongest learning algorithm for domain-dependent planning. These findings are especially remarkable given that our proof-of-concept implementation is based on an unoptimized Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, revealing that they are not only efficiently computable, but sometimes even more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic function programs can significantly improve the planning capabilities of LLMs.

Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.

As Large Language Models (LLMs) are rapidly evolving, providing accurate feedback and scalable oversight on their outputs becomes an urgent and critical problem. Leveraging LLMs as critique models to achieve automated supervision is a promising solution. In this work, we focus on studying and enhancing the math critique ability of LLMs. Current LLM critics provide critiques that are too shallow and superficial on each step, leading to low judgment accuracy and struggling to offer sufficient feedback for the LLM generator to correct mistakes. To tackle this issue, we propose a novel and effective two-stage framework to develop LLM critics that are capable of deliberately critiquing on each reasoning step of math solutions. In the first stage, we utilize Qwen2.5-72B-Instruct to generate 4.5K long-form critiques as seed data for supervised fine-tuning. Each seed critique consists of deliberate step-wise critiques that includes multi-perspective verifications as well as in-depth critiques of initial critiques for each reasoning step. Then, we perform reinforcement learning on the fine-tuned model with either existing human-labeled data from PRM800K or our automatically annotated data obtained via Monte Carlo sampling-based correctness estimation, to further incentivize its critique ability. Our developed critique model built on Qwen2.5-7B-Instruct not only significantly outperforms existing LLM critics (including the same-sized DeepSeek-R1-distill models and GPT-4o) on various error identification benchmarks, but also more effectively helps the LLM generator refine erroneous steps through more detailed feedback.

Existing approaches to language model alignment often treat safety as a tradeoff against helpfulness, which can lead to unacceptable responses in sensitive domains. To ensure reliable performance in such settings, we propose High-Confidence Safe Reinforcement Learning from Human Feedback (HC-RLHF), a method that provides high-confidence safety guarantees while maximizing helpfulness. Similar to previous methods, HC-RLHF explicitly decouples human preferences into helpfulness and harmlessness (safety), which are learned by training a reward model and a cost model, respectively. It then employs a two-step process to find safe solutions. In the first step, it optimizes the reward function under an intentionally pessimistic version of the cost constraint. In the second step, the trained model undergoes a safety test to verify whether its performance stays within an upper-confidence bound of the actual cost constraint. We provide a theoretical analysis of HC-RLHF, including proof that it will not return an unsafe solution with a probability greater than a user-specified threshold. For our empirical analysis, we apply HC-RLHF to align three different language models (Qwen2-1.5B, Qwen2.5-3B, and LLaMa3.2-3B) with human preferences. Our results demonstrate that HC-RLHF produces safe models with high probability and can improve harmlessness and helpfulness compared to previous methods.

Complex reasoning tasks often rely on the ability to consistently and accurately apply simple rules across incremental steps, a foundational capability which we term "level-0" reasoning. To systematically evaluate this capability, we introduce L0-Bench, a language model benchmark for testing procedural correctness -- the ability to generate correct reasoning processes, complementing existing benchmarks that primarily focus on outcome correctness. Given synthetic Python functions with simple operations, L0-Bench grades models on their ability to generate step-by-step, error-free execution traces. The synthetic nature of L0-Bench enables systematic and scalable generation of test programs along various axes (e.g., number of trace steps). We evaluate a diverse array of recent closed-source and open-weight models on a baseline test set. All models exhibit degradation as the number of target trace steps increases, while larger models and reasoning-enhanced models better maintain correctness over multiple steps. Additionally, we use L0-Bench to explore test-time scaling along three dimensions: input context length, number of solutions for majority voting, and inference steps. Our results suggest substantial room to improve "level-0" reasoning and potential directions to build more reliable reasoning systems.

Self-correction is a novel method that can stimulate the potential reasoning abilities of large language models (LLMs). It involves detecting and correcting errors during the inference process when LLMs solve reasoning problems. However, recent works do not regard self-correction as a spontaneous and intrinsic capability of LLMs. Instead, such correction is achieved through post-hoc generation, external knowledge introduction, multi-model collaboration, and similar techniques. In this paper, we propose a series of mathematical LLMs called S^3c-Math, which are able to perform Spontaneous Step-level Self-correction for Mathematical reasoning. This capability helps LLMs to recognize whether their ongoing inference tends to contain errors and simultaneously correct these errors to produce a more reliable response. We proposed a method, which employs a step-level sampling approach to construct step-wise self-correction data for achieving such ability. Additionally, we implement a training strategy that uses above constructed data to equip LLMs with spontaneous step-level self-correction capacities. Our data and methods have been demonstrated to be effective across various foundation LLMs, consistently showing significant progress in evaluations on GSM8K, MATH, and other mathematical benchmarks. To the best of our knowledge, we are the first to introduce the spontaneous step-level self-correction ability of LLMs in mathematical reasoning.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

The reliability of deep time series models is often compromised by their tendency to rely on confounding factors, which may lead to misleading results. Our newly recorded, naturally confounded dataset named P2S from a real mechanical production line emphasizes this. To tackle the challenging problem of mitigating confounders in time series data, we introduce Right on Time (RioT). Our method enables interactions with model explanations across both the time and frequency domain. Feedback on explanations in both domains is then used to constrain the model, steering it away from the annotated confounding factors. The dual-domain interaction strategy is crucial for effectively addressing confounders in time series datasets. We empirically demonstrate that RioT can effectively guide models away from the wrong reasons in P2S as well as popular time series classification and forecasting datasets.

Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of 76,321 responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at https://mathcritique.github.io/{https://mathcritique.github.io/}.

Recent works have extended notions of feature importance to semantic concepts that are inherently interpretable to the users interacting with a black-box predictive model. Yet, precise statistical guarantees, such as false positive rate control, are needed to communicate findings transparently and to avoid unintended consequences in real-world scenarios. In this paper, we formalize the global (i.e., over a population) and local (i.e., for a sample) statistical importance of semantic concepts for the predictions of opaque models, by means of conditional independence, which allows for rigorous testing. We use recent ideas of sequential kernelized testing (SKIT) to induce a rank of importance across concepts, and showcase the effectiveness and flexibility of our framework on synthetic datasets as well as on image classification tasks using vision-language models such as CLIP.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Reward Models (RMs) are crucial for aligning language models with human preferences. Currently, the evaluation of RMs depends on measuring accuracy against a validation set of manually annotated preference data. Although this method is straightforward and widely adopted, the relationship between RM accuracy and downstream policy performance remains under-explored. In this work, we conduct experiments in a synthetic setting to investigate how differences in RM measured by accuracy translate into gaps in optimized policy performance. Our findings reveal that while there is a weak positive correlation between accuracy and downstream performance, policies optimized towards RMs with similar accuracy can exhibit quite different performance. Moreover, we discover that the way of measuring accuracy significantly impacts its ability to predict the final policy performance. Through the lens of the Regressional Goodhart effect, we recognize that accuracy, when used for measuring RM quality, can fail to fully capture the potential RM overoptimization. This underscores the inadequacy of relying solely on accuracy to reflect their impact on policy optimization.

In light of recent work on scheduling with predicted job sizes, we consider the effect of the cost of predictions in queueing systems, removing the assumption in prior research that predictions are external to the system's resources and/or cost-free. In particular, we introduce a novel approach to utilizing predictions, SkipPredict, designed to address their inherent cost. Rather than uniformly applying predictions to all jobs, we propose a tailored approach that categorizes jobs based on their prediction requirements. To achieve this, we employ one-bit "cheap predictions" to classify jobs as either short or long. SkipPredict prioritizes predicted short jobs over long jobs, and for the latter, SkipPredict applies a second round of more detailed "expensive predictions" to approximate Shortest Remaining Processing Time for these jobs. Our analysis takes into account the cost of prediction. We examine the effect of this cost for two distinct models. In the external cost model, predictions are generated by some external method without impacting job service times but incur a cost. In the server time cost model, predictions themselves require server processing time, and are scheduled on the same server as the jobs.

Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF) are two fundamental processes for enhancing the capabilities of Language Models (LMs) post pre-training, aligning them better with human preferences. Although SFT advances in training efficiency, RLHF delivers better alignment, thus they are often combined. However, common practices simply apply them sequentially without unifying their optimization targets, resulting in a trade-off between fitting different objectives, and ignoring the opportunities to bridge the paradigm gap and take the strength from both. To obtain a unified understanding, we interpret SFT and RLHF using two sub-processes -- Preference Estimation and Transition Optimization -- defined at token level within the Markov Decision Process (MDP) framework. This modeling shows that SFT is only a specialized case of RLHF with inferior estimation and optimization. RLHF evaluates the quality of model's entire generated answer, whereas SFT only scores predicted tokens based on preceding tokens from target answers. Therefore, SFT overestimates the ability of model, leading to inferior optimization. Building on this view, we introduce Intuitive Fine-tuning (IFT) to integrate SFT and RLHF into a single process. IFT captures LMs' intuitive sense of the entire answers through a temporal residual connection, while using a single policy and the same volume of non-preference-labeled data as SFT. Our experiments show that IFT performs comparably or even superiorly to sequential recipes of SFT and some typical alignment methods across several tasks, particularly those requires generation, reasoning, and fact-following abilities. An explainable Frozen Lake game further validates the effectiveness of IFT.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific ``skills,'' but there has been limited study of where these newly-learnt skills reside inside the massive model. This paper introduces the term skill localization for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters (sim0.01% of model parameters) responsible for (>95%) of the model's performance, in the sense that grafting the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further re-training is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution (40-90% error reduction) as well as the quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms of continual learning.

Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the next word. This division method provides more decision-making information at each step, enhancing downstream tasks, such as reward model learning. Moreover, our method does not require manual annotation. We demonstrate its effectiveness through experiments with AdaptiveStep-trained PRMs in mathematical reasoning and code generation tasks. Experimental results indicate that the outcome PRM achieves state-of-the-art Best-of-N performance, surpassing greedy search strategy with token-level value-guided decoding, while also reducing construction costs by over 30% compared to existing open-source PRMs. In addition, we provide a thorough analysis and case study on the PRM's performance, transferability, and generalization capabilities.

Despite the remarkable capabilities of large language models (LLMs) in various reasoning tasks, they still struggle with table reasoning tasks, particularly in maintaining consistency throughout multi-step reasoning processes. While existing approaches have explored various decomposition strategies, they often lack effective mechanisms to identify and correct errors in intermediate reasoning steps, leading to cascading error propagation. To address these issues, we propose Table-Critic, a novel multi-agent framework that facilitates collaborative criticism and iterative refinement of the reasoning process until convergence to correct solutions. Our framework consists of four specialized agents: a Judge for error identification, a Critic for comprehensive critiques, a Refiner for process improvement, and a Curator for pattern distillation. To effectively deal with diverse and unpredictable error types, we introduce a self-evolving template tree that systematically accumulates critique knowledge through experience-driven learning and guides future reflections. Extensive experiments have demonstrated that Table-Critic achieves substantial improvements over existing methods, achieving superior accuracy and error correction rates while maintaining computational efficiency and lower solution degradation rate.

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

We introduce ALaRM, the first framework modeling hierarchical rewards in reinforcement learning from human feedback (RLHF), which is designed to enhance the alignment of large language models (LLMs) with human preferences. The framework addresses the limitations of current alignment approaches, which often struggle with the inconsistency and sparsity of human supervision signals, by integrating holistic rewards with aspect-specific rewards. This integration enables more precise and consistent guidance of language models towards desired outcomes, particularly in complex and open text generation tasks. By employing a methodology that filters and combines multiple rewards based on their consistency, the framework provides a reliable mechanism for improving model alignment. We validate our approach through applications in long-form question answering and machine translation tasks, employing gpt-3.5-turbo for pairwise comparisons, and demonstrate improvements over existing baselines. Our work underscores the effectiveness of hierarchical rewards modeling in refining LLM training processes for better human preference alignment. We release our code at https://ALaRM-fdu.github.io.

While large language models demonstrate impressive performance on static benchmarks, the true potential of large language models as self-learning and reasoning agents in dynamic environments remains unclear. This study systematically evaluates the efficacy of self-reflection, heuristic mutation, and planning as prompting techniques to test the adaptive capabilities of agents. We conduct experiments with various open-source language models in dynamic environments and find that larger models generally outperform smaller ones, but that strategic prompting can close this performance gap. Second, a too-long prompt can negatively impact smaller models on basic reactive tasks, while larger models show more robust behaviour. Third, advanced prompting techniques primarily benefit smaller models on complex games, but offer less improvement for already high-performing large language models. Yet, we find that advanced reasoning methods yield highly variable outcomes: while capable of significantly improving performance when reasoning and decision-making align, they also introduce instability and can lead to big performance drops. Compared to human performance, our findings reveal little evidence of true emergent reasoning. Instead, large language model performance exhibits persistent limitations in crucial areas such as planning, reasoning, and spatial coordination, suggesting that current-generation large language models still suffer fundamental shortcomings that may not be fully overcome through self-reflective prompting alone. Reasoning is a multi-faceted task, and while reasoning methods like Chain of thought improves multi-step reasoning on math word problems, our findings using dynamic benchmarks highlight important shortcomings in general reasoning capabilities, indicating a need to move beyond static benchmarks to capture the complexity of reasoning.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Multi-Agent Debate~(MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components--Majority Voting and inter-agent Debate--and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings. Code is released in https://github.com/deeplearning-wisc/debate-or-vote.

Large language models have demonstrated impressive reasoning capabilities but are inherently limited by their knowledge reservoir. Retrieval-augmented reasoning mitigates this limitation by allowing LLMs to query external resources, but existing methods often retrieve irrelevant or noisy information, hindering accurate reasoning. In this paper, we propose AutoRefine, a reinforcement learning post-training framework that adopts a new ``search-and-refine-during-think'' paradigm. AutoRefine introduces explicit knowledge refinement steps between successive search calls, enabling the model to iteratively filter, distill, and organize evidence before generating an answer. Furthermore, we incorporate tailored retrieval-specific rewards alongside answer correctness rewards using group relative policy optimization. Experiments on single-hop and multi-hop QA benchmarks demonstrate that AutoRefine significantly outperforms existing approaches, particularly in complex, multi-hop reasoning scenarios. Detailed analysis shows that AutoRefine issues frequent, higher-quality searches and synthesizes evidence effectively.