Daily Papers

While Multimodal Large Language Models (MLLMs) have achieved impressive progress in vision-language understanding, they still struggle with complex multi-step reasoning, often producing logically inconsistent or partially correct solutions. A key limitation lies in the lack of fine-grained supervision over intermediate reasoning steps. To address this, we propose MM-PRM, a process reward model trained within a fully automated, scalable framework. We first build MM-Policy, a strong multimodal model trained on diverse mathematical reasoning data. Then, we construct MM-K12, a curated dataset of 10,000 multimodal math problems with verifiable answers, which serves as seed data. Leveraging a Monte Carlo Tree Search (MCTS)-based pipeline, we generate over 700k step-level annotations without human labeling. The resulting PRM is used to score candidate reasoning paths in the Best-of-N inference setup and achieves significant improvements across both in-domain (MM-K12 test set) and out-of-domain (OlympiadBench, MathVista, etc.) benchmarks. Further analysis confirms the effectiveness of soft labels, smaller learning rates, and path diversity in optimizing PRM performance. MM-PRM demonstrates that process supervision is a powerful tool for enhancing the logical robustness of multimodal reasoning systems. We release all our codes and data at https://github.com/ModalMinds/MM-PRM.

Self-training approach for large language models (LLMs) improves reasoning abilities by training the models on their self-generated rationales. Previous approaches have labeled rationales that produce correct answers for a given question as appropriate for training. However, a single measure risks misjudging rationale quality, leading the models to learn flawed reasoning patterns. To address this issue, we propose CREST (Consistency-driven Rationale Evaluation for Self-Training), a self-training framework that further evaluates each rationale through follow-up questions and leverages this evaluation to guide its training. Specifically, we introduce two methods: (1) filtering out rationales that frequently result in incorrect answers on follow-up questions and (2) preference learning based on mixed preferences from rationale evaluation results of both original and follow-up questions. Experiments on three question-answering datasets using open LLMs show that CREST not only improves the logical robustness and correctness of rationales but also improves reasoning abilities compared to previous self-training approaches.

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models indeed perform logical reasoning by understanding the underlying logical semantics in the language. To this end, we propose RobustLR, a suite of evaluation datasets that evaluate the robustness of these models to minimal logical edits in rulebases and some standard logical equivalence conditions. In our experiments with RoBERTa and T5, we find that the models trained in prior works do not perform consistently on the different perturbations in RobustLR, thus showing that the models are not robust to the proposed logical perturbations. Further, we find that the models find it especially hard to learn logical negation and disjunction operators. Overall, using our evaluation sets, we demonstrate some shortcomings of the deductive reasoning-based language models, which can eventually help towards designing better models for logical reasoning over natural language. All the datasets and code base have been made publicly available.

This paper investigates the rational thinking capability of Large Language Models (LLMs) in multi-round argumentative debates by exploring the impact of fallacious arguments on their logical reasoning performance. More specifically, we present Logic Competence Measurement Benchmark (LOGICOM), a diagnostic benchmark to assess the robustness of LLMs against logical fallacies. LOGICOM involves two agents: a persuader and a debater engaging in a multi-round debate on a controversial topic, where the persuader tries to convince the debater of the correctness of its claim. First, LOGICOM assesses the potential of LLMs to change their opinions through reasoning. Then, it evaluates the debater's performance in logical reasoning by contrasting the scenario where the persuader employs logical fallacies against one where logical reasoning is used. We use this benchmark to evaluate the performance of GPT-3.5 and GPT-4 using a dataset containing controversial topics, claims, and reasons supporting them. Our findings indicate that both GPT-3.5 and GPT-4 can adjust their opinion through reasoning. However, when presented with logical fallacies, GPT-3.5 and GPT-4 are erroneously convinced 41% and 69% more often, respectively, compared to when logical reasoning is used. Finally, we introduce a new dataset containing over 5k pairs of logical vs. fallacious arguments. The source code and dataset of this work are made publicly available.

Robustness of reasoning remains a significant challenge for large language models, and addressing it is essential for the practical applicability of AI-driven reasoning systems. We introduce Semantic Self-Verification (SSV), a novel approach that addresses the key challenge in combining language models with the rigor of logical solvers: to accurately formulate the reasoning problem from natural language to the formal language of the solver. SSV uses a consistency-based approach to produce strong abstract formalizations of problems using concrete instantiations that are generated by the model and verified by the solver. In addition to significantly advancing the overall reasoning accuracy over the state-of-the-art, a key novelty that this approach presents is a feature of verification that has near-perfect precision over a significant coverage of cases, as we demonstrate on open reasoning benchmarks. We propose such *near-certain reasoning* as a new approach to reduce the need for manual verification in many cases, taking us closer to more dependable and autonomous AI reasoning systems.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Harnessing logical reasoning ability is a comprehensive natural language understanding endeavor. With the release of Generative Pretrained Transformer 4 (GPT-4), highlighted as "advanced" at reasoning tasks, we are eager to learn the GPT-4 performance on various logical reasoning tasks. This report analyses multiple logical reasoning datasets, with popular benchmarks like LogiQA and ReClor, and newly-released datasets like AR-LSAT. We test the multi-choice reading comprehension and natural language inference tasks with benchmarks requiring logical reasoning. We further construct a logical reasoning out-of-distribution dataset to investigate the robustness of ChatGPT and GPT-4. We also make a performance comparison between ChatGPT and GPT-4. Experiment results show that ChatGPT performs significantly better than the RoBERTa fine-tuning method on most logical reasoning benchmarks. With early access to the GPT-4 API we are able to conduct intense experiments on the GPT-4 model. The results show GPT-4 yields even higher performance on most logical reasoning datasets. Among benchmarks, ChatGPT and GPT-4 do relatively well on well-known datasets like LogiQA and ReClor. However, the performance drops significantly when handling newly released and out-of-distribution datasets. Logical reasoning remains challenging for ChatGPT and GPT-4, especially on out-of-distribution and natural language inference datasets. We release the prompt-style logical reasoning datasets as a benchmark suite and name it LogiEval.

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods only compare model outputs to ground-truth answers, obscuring insights into reasoning processes. To address these limitations, we introduce GSM-Ranges, a dataset generator derived from GSM8K that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales. Additionally, we propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy. Our experiments with various models reveal a significant increase in logical error rates-up to 14 percentage points-as numerical complexity rises, demonstrating a general weakness in reasoning with out-of-distribution numerical values. Moreover, while models demonstrate high accuracy on standalone arithmetic tasks, their performance deteriorates substantially when computations are embedded within word problems. These findings provide a comprehensive evaluation of LLMs' mathematical reasoning capabilities and inform future research directions for improving numerical generalization in language models.

The emergence of Large Language Models (LLMs) have fundamentally altered the way we interact with digital systems and have led to the pursuit of LLM powered AI agents to assist in daily workflows. LLMs, whilst powerful and capable of demonstrating some emergent properties, are not logical reasoners and often struggle to perform well at all sub-tasks carried out by an AI agent to plan and execute a workflow. While existing studies tackle this lack of proficiency by generalised pretraining at a huge scale or by specialised fine-tuning for tool use, we assess if a system comprising of a coalition of pretrained LLMs, each exhibiting specialised performance at individual sub-tasks, can match the performance of single model agents. The coalition of models approach showcases its potential for building robustness and reducing the operational costs of these AI agents by leveraging traits exhibited by specific models. Our findings demonstrate that fine-tuning can be mitigated by considering a coalition of pretrained models and believe that this approach can be applied to other non-agentic systems which utilise LLMs.

With the increasing use of large language models (LLMs), ensuring reliable performance in diverse, real-world environments is essential. Despite their remarkable achievements, LLMs often struggle with adversarial inputs, significantly impacting their effectiveness in practical applications. To systematically understand the robustness of LLMs, we present RUPBench, a comprehensive benchmark designed to evaluate LLM robustness across diverse reasoning tasks. Our benchmark incorporates 15 reasoning datasets, categorized into commonsense, arithmetic, logical, and knowledge-intensive reasoning, and introduces nine types of textual perturbations at lexical, syntactic, and semantic levels. By examining the performance of state-of-the-art LLMs such as GPT-4o, Llama3, Phi-3, and Gemma on both original and perturbed datasets, we provide a detailed analysis of their robustness and error patterns. Our findings highlight that larger models tend to exhibit greater robustness to perturbations. Additionally, common error types are identified through manual inspection, revealing specific challenges faced by LLMs in different reasoning contexts. This work provides insights into areas where LLMs need further improvement to handle diverse and noisy inputs effectively.

This study investigates the reasoning robustness of large language models (LLMs) on mathematical problem-solving tasks under systematically introduced input perturbations. Using the GSM8K dataset as a controlled testbed, we evaluate how well state-of-the-art models maintain logical consistency and correctness when confronted with four categories of prompt perturbations: irrelevant context, pathological instructions, factually relevant but non-essential context, and a combination of the latter two. Our experiments, conducted on thirteen open-source and closed-source LLMs, reveal that introducing irrelevant context within the model's context window significantly degrades performance, suggesting that distinguishing essential from extraneous details remains a pressing challenge. Surprisingly, performance regressions are relatively insensitive to the complexity of the reasoning task, as measured by the number of steps required, and are not strictly correlated with model size. Moreover, we observe that certain perturbations inadvertently trigger chain-of-thought-like reasoning behaviors, even without explicit prompting. Our findings highlight critical vulnerabilities in current LLMs and underscore the need for improved robustness against noisy, misleading, and contextually dense inputs, paving the way for more resilient and reliable reasoning in real-world applications.

Large Language Models (LLMs) have demonstrated strong reasoning capabilities across various tasks. However, even minor variations in query phrasing, despite preserving the underlying semantic meaning, can significantly affect their performance. To address this, we focus on enhancing LLMs' awareness of symmetry in query variations and propose syMmetry-ENhanceD (MEND) Data Augmentation, a data-centric approach that improves the model's ability to extract useful information from context. Unlike existing methods that emphasize reasoning chain augmentation, our approach improves model robustness at the knowledge extraction stage through query augmentations, enabling more data-efficient training and stronger generalization to Out-of-Distribution (OOD) settings. Extensive experiments on both logical and arithmetic reasoning tasks show that MEND enhances reasoning performance across diverse query variations, providing new insight into improving LLM robustness through structured dataset curation.

Code generation aims to understand the problem description and generate corresponding code snippets, where existing works generally decompose such complex tasks into intermediate steps by prompting strategies, such as Chain-of-Thought and its variants. While these studies have achieved some success, their effectiveness is highly dependent on the capabilities of advanced Large Language Models (LLMs) such as GPT-4, particularly in terms of API calls, which significantly limits their practical applicability. Consequently, how to enhance the code generation capabilities of small and medium-scale code LLMs without significantly increasing training costs is an appealing challenge. In this paper, we suggest that code comments are the natural logic pivot between natural language and code language and propose using comments to boost the code generation ability of code LLMs. Concretely, we propose MANGO (comMents As Natural loGic pivOts), including a comment contrastive training strategy and a corresponding logical comment decoding strategy. Experiments are performed on HumanEval and MBPP, utilizing StarCoder and WizardCoder as backbone models, and encompassing model parameter sizes between 3B and 7B. The results indicate that MANGO significantly improves the code pass rate based on the strong baselines. Meanwhile, the robustness of the logical comment decoding strategy is notably higher than the Chain-of-thoughts prompting. The code is publicly available at https://github.com/pppa2019/Mango.

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks, yet exhibit critical limitations in knowledge-intensive tasks, often generating hallucinations when faced with questions requiring specialized expertise. While retrieval-augmented generation (RAG) mitigates this by integrating external knowledge, it struggles with complex reasoning scenarios due to its reliance on direct semantic retrieval and lack of structured logical organization. Inspired by Cartesian principles from Discours de la m\'ethode, this paper introduces Logic-Augmented Generation (LAG), a novel paradigm that reframes knowledge augmentation through systematic question decomposition and dependency-aware reasoning. Specifically, LAG first decomposes complex questions into atomic sub-questions ordered by logical dependencies. It then resolves these sequentially, using prior answers to guide context retrieval for subsequent sub-questions, ensuring stepwise grounding in logical chain. To prevent error propagation, LAG incorporates a logical termination mechanism that halts inference upon encountering unanswerable sub-questions and reduces wasted computation on excessive reasoning. Finally, it synthesizes all sub-resolutions to generate verified responses. Experiments on four benchmark datasets demonstrate that LAG significantly enhances reasoning robustness, reduces hallucination, and aligns LLM problem-solving with human cognition, offering a principled alternative to existing RAG systems.

Large Language Model (LLM) techniques play an increasingly important role in Natural Language to SQL (NL2SQL) translation. LLMs trained by extensive corpora have strong natural language understanding and basic SQL generation abilities without additional tuning specific to NL2SQL tasks. Existing LLMs-based NL2SQL approaches try to improve the translation by enhancing the LLMs with an emphasis on user intention understanding. However, LLMs sometimes fail to generate appropriate SQL due to their lack of knowledge in organizing complex logical operator composition. A promising method is to input the LLMs with demonstrations, which include known NL2SQL translations from various databases. LLMs can learn to organize operator compositions from the input demonstrations for the given task. In this paper, we propose PURPLE (Pre-trained models Utilized to Retrieve Prompts for Logical Enhancement), which improves accuracy by retrieving demonstrations containing the requisite logical operator composition for the NL2SQL task on hand, thereby guiding LLMs to produce better SQL translation. PURPLE achieves a new state-of-the-art performance of 80.5% exact-set match accuracy and 87.8% execution match accuracy on the validation set of the popular NL2SQL benchmark Spider. PURPLE maintains high accuracy across diverse benchmarks, budgetary constraints, and various LLMs, showing robustness and cost-effectiveness.

Despite their impressive capabilities, large pre-trained language models (LMs) struggle with consistent reasoning; recently, prompting LMs to generate explanations that self-guide the inference has emerged as a promising direction to amend this. However, these approaches are fundamentally bounded by the correctness of explanations, which themselves are often noisy and inconsistent. In this work, we develop Maieutic Prompting, which infers a correct answer to a question even from the noisy and inconsistent generations of LM. Maieutic Prompting induces a tree of explanations abductively (e.g. X is true, because ...) and recursively, then frames the inference as a satisfiability problem over these explanations and their logical relations. We test Maieutic Prompting for true/false QA on three challenging benchmarks that require complex commonsense reasoning. Maieutic Prompting achieves up to 20% better accuracy than state-of-the-art prompting methods, and as a fully unsupervised approach, performs competitively with supervised models. We also show that Maieutic Prompting improves robustness in inference while providing interpretable rationales.

Anomaly detection is valuable for real-world applications, such as industrial quality inspection. However, most approaches focus on detecting local structural anomalies while neglecting compositional anomalies incorporating logical constraints. In this paper, we introduce LogSAD, a novel multi-modal framework that requires no training for both Logical and Structural Anomaly Detection. First, we propose a match-of-thought architecture that employs advanced large multi-modal models (i.e. GPT-4V) to generate matching proposals, formulating interests and compositional rules of thought for anomaly detection. Second, we elaborate on multi-granularity anomaly detection, consisting of patch tokens, sets of interests, and composition matching with vision and language foundation models. Subsequently, we present a calibration module to align anomaly scores from different detectors, followed by integration strategies for the final decision. Consequently, our approach addresses both logical and structural anomaly detection within a unified framework and achieves state-of-the-art results without the need for training, even when compared to supervised approaches, highlighting its robustness and effectiveness. Code is available at https://github.com/zhang0jhon/LogSAD.

We evaluate the robustness of several large language models on multiple datasets. Robustness here refers to the relative insensitivity of the model's answers to meaning-preserving variants of their input. Benchmark datasets are constructed by introducing naturally-occurring, non-malicious perturbations, or by generating semantically equivalent paraphrases of input questions or statements. We further propose a novel metric for assessing a model robustness, and demonstrate its benefits in the non-adversarial scenario by empirical evaluation of several models on the created datasets.

The recent success of natural language understanding (NLU) systems has been troubled by results highlighting the failure of these models to generalize in a systematic and robust way. In this work, we introduce a diagnostic benchmark suite, named CLUTRR, to clarify some key issues related to the robustness and systematicity of NLU systems. Motivated by classic work on inductive logic programming, CLUTRR requires that an NLU system infer kinship relations between characters in short stories. Successful performance on this task requires both extracting relationships between entities, as well as inferring the logical rules governing these relationships. CLUTRR allows us to precisely measure a model's ability for systematic generalization by evaluating on held-out combinations of logical rules, and it allows us to evaluate a model's robustness by adding curated noise facts. Our empirical results highlight a substantial performance gap between state-of-the-art NLU models (e.g., BERT and MAC) and a graph neural network model that works directly with symbolic inputs---with the graph-based model exhibiting both stronger generalization and greater robustness.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Recent reasoning large language models (LLMs) have demonstrated remarkable improvements in mathematical reasoning capabilities through long Chain-of-Thought. The reasoning tokens of these models enable self-correction within reasoning chains, enhancing robustness. This motivates our exploration: how vulnerable are reasoning LLMs to subtle errors in their input reasoning chains? We introduce "Compromising Thought" (CPT), a vulnerability where models presented with reasoning tokens containing manipulated calculation results tend to ignore correct reasoning steps and adopt incorrect results instead. Through systematic evaluation across multiple reasoning LLMs, we design three increasingly explicit prompting methods to measure CPT resistance, revealing that models struggle significantly to identify and correct these manipulations. Notably, contrary to existing research suggesting structural alterations affect model performance more than content modifications, we find that local ending token manipulations have greater impact on reasoning outcomes than structural changes. Moreover, we discover a security vulnerability in DeepSeek-R1 where tampered reasoning tokens can trigger complete reasoning cessation. Our work enhances understanding of reasoning robustness and highlights security considerations for reasoning-intensive applications.

Recently, we have witnessed the bloom of neural ranking models in the information retrieval (IR) field. So far, much effort has been devoted to developing effective neural ranking models that can generalize well on new data. There has been less attention paid to the robustness perspective. Unlike the effectiveness which is about the average performance of a system under normal purpose, robustness cares more about the system performance in the worst case or under malicious operations instead. When a new technique enters into the real-world application, it is critical to know not only how it works in average, but also how would it behave in abnormal situations. So we raise the question in this work: Are neural ranking models robust? To answer this question, firstly, we need to clarify what we refer to when we talk about the robustness of ranking models in IR. We show that robustness is actually a multi-dimensional concept and there are three ways to define it in IR: 1) The performance variance under the independent and identically distributed (I.I.D.) setting; 2) The out-of-distribution (OOD) generalizability; and 3) The defensive ability against adversarial operations. The latter two definitions can be further specified into two different perspectives respectively, leading to 5 robustness tasks in total. Based on this taxonomy, we build corresponding benchmark datasets, design empirical experiments, and systematically analyze the robustness of several representative neural ranking models against traditional probabilistic ranking models and learning-to-rank (LTR) models. The empirical results show that there is no simple answer to our question. While neural ranking models are less robust against other IR models in most cases, some of them can still win 1 out of 5 tasks. This is the first comprehensive study on the robustness of neural ranking models.

Large language models (LLMs) showcase impressive reasoning capabilities when coupled with Chain-of-Thought (CoT) prompting. However, the robustness of this approach warrants further investigation. In this paper, we introduce a novel scenario termed preemptive answers, where the LLM obtains an answer before engaging in reasoning. This situation can arise inadvertently or induced by malicious users by prompt injection attacks. Experiments reveal that preemptive answers significantly impair the model's reasoning capability across various CoT methods and a broad spectrum of datasets. To bolster the robustness of reasoning, we propose two measures aimed at mitigating this issue to some extent.

A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector representations. While the robustness with respect to changes of continuous inputs is well-understood, the situation is less clear when considering discrete changes, for instance replacing a word by another in an input sentence. Our work formally proves that popular embedding schemes, such as concatenation, TF-IDF, and Paragraph Vector (a.k.a. doc2vec), exhibit robustness in the H\"older or Lipschitz sense with respect to the Hamming distance. We provide quantitative bounds for these schemes and demonstrate how the constants involved are affected by the length of the document. These findings are exemplified through a series of numerical examples.

As NLP models achieved state-of-the-art performances over benchmarks and gained wide applications, it has been increasingly important to ensure the safe deployment of these models in the real world, e.g., making sure the models are robust against unseen or challenging scenarios. Despite robustness being an increasingly studied topic, it has been separately explored in applications like vision and NLP, with various definitions, evaluation and mitigation strategies in multiple lines of research. In this paper, we aim to provide a unifying survey of how to define, measure and improve robustness in NLP. We first connect multiple definitions of robustness, then unify various lines of work on identifying robustness failures and evaluating models' robustness. Correspondingly, we present mitigation strategies that are data-driven, model-driven, and inductive-prior-based, with a more systematic view of how to effectively improve robustness in NLP models. Finally, we conclude by outlining open challenges and future directions to motivate further research in this area.

We conduct experiments on the impact of increasing inference-time compute in reasoning models (specifically OpenAI o1-preview and o1-mini) on their robustness to adversarial attacks. We find that across a variety of attacks, increased inference-time compute leads to improved robustness. In many cases (with important exceptions), the fraction of model samples where the attack succeeds tends to zero as the amount of test-time compute grows. We perform no adversarial training for the tasks we study, and we increase inference-time compute by simply allowing the models to spend more compute on reasoning, independently of the form of attack. Our results suggest that inference-time compute has the potential to improve adversarial robustness for Large Language Models. We also explore new attacks directed at reasoning models, as well as settings where inference-time compute does not improve reliability, and speculate on the reasons for these as well as ways to address them.

Recently, Zaremba et al. demonstrated that increasing inference-time computation improves robustness in large proprietary reasoning LLMs. In this paper, we first show that smaller-scale, open-source models (e.g., DeepSeek R1, Qwen3, Phi-reasoning) can also benefit from inference-time scaling using a simple budget forcing strategy. More importantly, we reveal and critically examine an implicit assumption in prior work: intermediate reasoning steps are hidden from adversaries. By relaxing this assumption, we identify an important security risk, intuitively motivated and empirically verified as an inverse scaling law: if intermediate reasoning steps become explicitly accessible, increased inference-time computation consistently reduces model robustness. Finally, we discuss practical scenarios where models with hidden reasoning chains are still vulnerable to attacks, such as models with tool-integrated reasoning and advanced reasoning extraction attacks. Our findings collectively demonstrate that the robustness benefits of inference-time scaling depend heavily on the adversarial setting and deployment context. We urge practitioners to carefully weigh these subtle trade-offs before applying inference-time scaling in security-sensitive, real-world applications.

Large Language Models (LLMs) can be misused to spread online spam and misinformation. Content watermarking deters misuse by hiding a message in model-generated outputs, enabling their detection using a secret watermarking key. Robustness is a core security property, stating that evading detection requires (significant) degradation of the content's quality. Many LLM watermarking methods have been proposed, but robustness is tested only against non-adaptive attackers who lack knowledge of the watermarking method and can find only suboptimal attacks. We formulate the robustness of LLM watermarking as an objective function and propose preference-based optimization to tune adaptive attacks against the specific watermarking method. Our evaluation shows that (i) adaptive attacks substantially outperform non-adaptive baselines. (ii) Even in a non-adaptive setting, adaptive attacks optimized against a few known watermarks remain highly effective when tested against other unseen watermarks, and (iii) optimization-based attacks are practical and require less than seven GPU hours. Our findings underscore the need to test robustness against adaptive attackers.

In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not clear whether the proofs generated by these methods are human-interpretable. In this paper, we bridge this gap by developing new concepts, algorithms, and representations to generate human understandable interpretations of the proofs. Leveraging the proposed method, we show that the robustness proofs of standard DNNs rely on spurious input features, while the proofs of DNNs trained to be provably robust filter out even the semantically meaningful features. The proofs for the DNNs combining adversarial and provably robust training are the most effective at selectively filtering out spurious features as well as relying on human-understandable input features.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Recent work have demonstrated that robustness (to "corruption") can be at odds with generalization. Adversarial training, for instance, aims to reduce the problematic susceptibility of modern neural networks to small data perturbations. Surprisingly, overfitting is a major concern in adversarial training despite being mostly absent in standard training. We provide here theoretical evidence for this peculiar "robust overfitting" phenomenon. Subsequently, we advance a novel distributionally robust loss function bridging robustness and generalization. We demonstrate both theoretically as well as empirically the loss to enjoy a certified level of robustness against two common types of corruption--data evasion and poisoning attacks--while ensuring guaranteed generalization. We show through careful numerical experiments that our resulting holistic robust (HR) training procedure yields SOTA performance. Finally, we indicate that HR training can be interpreted as a direct extension of adversarial training and comes with a negligible additional computational burden. A ready-to-use python library implementing our algorithm is available at https://github.com/RyanLucas3/HR_Neural_Networks.

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key lookups. It is a common belief that the predictive power of networks leveraging softmax arises from "circuits" which sharply perform certain kinds of computations consistently across many diverse inputs. However, for these circuits to be robust, they would need to generalise well to arbitrary valid inputs. In this paper, we dispel this myth: even for tasks as simple as finding the maximum key, any learned circuitry must disperse as the number of items grows at test time. We attribute this to a fundamental limitation of the softmax function to robustly approximate sharp functions, prove this phenomenon theoretically, and propose adaptive temperature as an ad-hoc technique for improving the sharpness of softmax at inference time.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Recent work has demonstrated that deep neural networks are vulnerable to adversarial examples---inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much of the prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against any adversary. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest the notion of security against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models. Code and pre-trained models are available at https://github.com/MadryLab/mnist_challenge and https://github.com/MadryLab/cifar10_challenge.

Robustness to natural distribution shifts has seen remarkable progress thanks to recent pre-training strategies combined with better fine-tuning methods. However, such fine-tuning assumes access to large amounts of labelled data, and the extent to which the observations hold when the amount of training data is not as high remains unknown. We address this gap by performing the first in-depth study of robustness to various natural distribution shifts in different low-shot regimes: spanning datasets, architectures, pre-trained initializations, and state-of-the-art robustness interventions. Most importantly, we find that there is no single model of choice that is often more robust than others, and existing interventions can fail to improve robustness on some datasets even if they do so in the full-shot regime. We hope that our work will motivate the community to focus on this problem of practical importance.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Deep learning algorithms have shown promising results in visual question answering (VQA) tasks, but a more careful look reveals that they often do not understand the rich signal they are being fed with. To understand and better measure the generalization capabilities of VQA systems, we look at their robustness to counterfactually augmented data. Our proposed augmentations are designed to make a focused intervention on a specific property of the question such that the answer changes. Using these augmentations, we propose a new robustness measure, Robustness to Augmented Data (RAD), which measures the consistency of model predictions between original and augmented examples. Through extensive experimentation, we show that RAD, unlike classical accuracy measures, can quantify when state-of-the-art systems are not robust to counterfactuals. We find substantial failure cases which reveal that current VQA systems are still brittle. Finally, we connect between robustness and generalization, demonstrating the predictive power of RAD for performance on unseen augmentations.

As large language models are integrated into society, robustness toward a suite of prompts is increasingly important to maintain reliability in a high-variance environment.Robustness evaluations must comprehensively encapsulate the various settings in which a user may invoke an intelligent system. This paper proposes ASSERT, Automated Safety Scenario Red Teaming, consisting of three methods -- semantically aligned augmentation, target bootstrapping, and adversarial knowledge injection. For robust safety evaluation, we apply these methods in the critical domain of AI safety to algorithmically generate a test suite of prompts covering diverse robustness settings -- semantic equivalence, related scenarios, and adversarial. We partition our prompts into four safety domains for a fine-grained analysis of how the domain affects model performance. Despite dedicated safeguards in existing state-of-the-art models, we find statistically significant performance differences of up to 11% in absolute classification accuracy among semantically related scenarios and error rates of up to 19% absolute error in zero-shot adversarial settings, raising concerns for users' physical safety.

Watermark algorithms for large language models (LLMs) have achieved extremely high accuracy in detecting text generated by LLMs. Such algorithms typically involve adding extra watermark logits to the LLM's logits at each generation step. However, prior algorithms face a trade-off between attack robustness and security robustness. This is because the watermark logits for a token are determined by a certain number of preceding tokens; a small number leads to low security robustness, while a large number results in insufficient attack robustness. In this work, we propose a semantic invariant watermarking method for LLMs that provides both attack robustness and security robustness. The watermark logits in our work are determined by the semantics of all preceding tokens. Specifically, we utilize another embedding LLM to generate semantic embeddings for all preceding tokens, and then these semantic embeddings are transformed into the watermark logits through our trained watermark model. Subsequent analyses and experiments demonstrated the attack robustness of our method in semantically invariant settings: synonym substitution and text paraphrasing settings. Finally, we also show that our watermark possesses adequate security robustness. Our code and data are available at https://github.com/THU-BPM/Robust_Watermark.

Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks. However, there are increasing debates regarding whether these models truly understand and apply mathematical knowledge or merely rely on shortcuts for mathematical reasoning. One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly. This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations. We introduce the adversarial grade school math (\datasetname) dataset, an extension of GSM8K augmented with various mathematical perturbations. Our experiments on 25 LLMs and 4 prompting techniques show that while LLMs exhibit different levels of math reasoning abilities, their performances are far from robust. In particular, even for problems that have been solved in GSM8K, LLMs can make mistakes when new statements are added or the question targets are altered. We also explore whether more robust performance can be achieved by composing existing prompting methods, in which we try an iterative method that generates and verifies each intermediate thought based on its reasoning goal and calculation result. Code and data are available at https://github.com/qtli/GSM-Plus.

Reasoning has long been viewed as an emergent property of large language models (LLMs), appearing at or above a certain scale (sim100B parameters). However, recent studies challenge this assumption, showing that small language models (SLMs) can also achieve competitive reasoning performance. SLMs are increasingly favored for their efficiency and deployability. However, there is a lack of systematic study on the reasoning abilities of diverse SLMs, including those trained from scratch or derived from LLMs through quantization, pruning, and distillation. This raises a critical question: Can SLMs achieve reasoning abilities comparable to LLMs? In this work, we systematically survey, benchmark, and analyze 72 SLMs from six model families across 14 reasoning benchmarks. For reliable evaluation, we examine four evaluation methods and compare four LLM judges against human evaluations on 800 data points. We repeat all experiments three times to ensure a robust performance assessment. Additionally, we analyze the impact of different prompting strategies in small models. Beyond accuracy, we also evaluate model robustness under adversarial conditions and intermediate reasoning steps. Our findings challenge the assumption that scaling is the only way to achieve strong reasoning. Instead, we foresee a future where SLMs with strong reasoning capabilities can be developed through structured training or post-training compression. They can serve as efficient alternatives to LLMs for reasoning-intensive tasks.

Machine learning models have recently found tremendous success in data-driven control systems. However, standard learning models often suffer from an accuracy-robustness trade-off, which is a limitation that must be overcome in the control of safety-critical systems that require both high performance and rigorous robustness guarantees. In this work, we build upon the recent "locally biased smoothing" method to develop classifiers that simultaneously inherit high accuracy from standard models and high robustness from robust models. Specifically, we extend locally biased smoothing to the multi-class setting, and then overcome its performance bottleneck by generalizing the formulation to "mix" the outputs of a standard neural network and a robust neural network. We prove that when the robustness of the robust base model is certifiable, within a closed-form ell_p radius, no alteration or attack on an input can result in misclassification of the mixed classifier; the proposed model inherits the certified robustness. Moreover, we use numerical experiments on the CIFAR-10 benchmark dataset to verify that the mixed model noticeably improves the accuracy-robustness trade-off.

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounding methods. Still, we lack an understanding of the mechanisms making IBP so successful. In this work, we thoroughly investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models, tightness decreases with width and depth at initialization, but improves with IBP training, given sufficient network width. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, explaining the empirically observed trade-off between robustness and accuracy in certified training. Our extensive experimental evaluation validates our theoretical predictions for ReLU networks, including that wider networks improve performance, yielding state-of-the-art results. Interestingly, we observe that while all IBP-based training methods lead to high tightness, this is neither sufficient nor necessary to achieve high certifiable robustness. This hints at the existence of new training methods that do not induce the strong regularization required for tight IBP bounds, leading to improved robustness and standard accuracy.

Existing regulatory frameworks for biomedical AI include robustness as a key component but lack detailed implementational guidance. The recent rise of biomedical foundation models creates new hurdles in testing and certification given their broad capabilities and susceptibility to complex distribution shifts. To balance test feasibility and effectiveness, we suggest a priority-based, task-oriented approach to tailor robustness evaluation objectives to a predefined specification. We urge concrete policies to adopt a granular categorization of robustness concepts in the specification. Our approach promotes the standardization of risk assessment and monitoring, which guides technical developments and mitigation efforts.

Artificial intelligence (AI), and especially its sub-field of Machine Learning (ML), are impacting the daily lives of everyone with their ubiquitous applications. In recent years, AI researchers and practitioners have introduced principles and guidelines to build systems that make reliable and trustworthy decisions. From a practical perspective, conventional ML systems process historical data to extract the features that are consequently used to train ML models that perform the desired task. However, in practice, a fundamental challenge arises when the system needs to be operationalized and deployed to evolve and operate in real-life environments continuously. To address this challenge, Machine Learning Operations (MLOps) have emerged as a potential recipe for standardizing ML solutions in deployment. Although MLOps demonstrated great success in streamlining ML processes, thoroughly defining the specifications of robust MLOps approaches remains of great interest to researchers and practitioners. In this paper, we provide a comprehensive overview of the trustworthiness property of MLOps systems. Specifically, we highlight technical practices to achieve robust MLOps systems. In addition, we survey the existing research approaches that address the robustness aspects of ML systems in production. We also review the tools and software available to build MLOps systems and summarize their support to handle the robustness aspects. Finally, we present the open challenges and propose possible future directions and opportunities within this emerging field. The aim of this paper is to provide researchers and practitioners working on practical AI applications with a comprehensive view to adopt robust ML solutions in production environments.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset MathTrap by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent "unseen" cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not spontaneously combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. Additionally, we test the recently released OpenAI o1 model and find that human-like `slow thinking' helps improve the compositionality of LLMs. Overall, systematic compositionality remains an open challenge for large language models.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.

Code generation models have achieved impressive performance. However, they tend to be brittle as slight edits to a prompt could lead to very different generations; these robustness properties, critical for user experience when deployed in real-life applications, are not well understood. Most existing works on robustness in text or code tasks have focused on classification, while robustness in generation tasks is an uncharted area and to date there is no comprehensive benchmark for robustness in code generation. In this paper, we propose ReCode, a comprehensive robustness evaluation benchmark for code generation models. We customize over 30 transformations specifically for code on docstrings, function and variable names, code syntax, and code format. They are carefully designed to be natural in real-life coding practice, preserve the original semantic meaning, and thus provide multifaceted assessments of a model's robustness performance. With human annotators, we verified that over 90% of the perturbed prompts do not alter the semantic meaning of the original prompt. In addition, we define robustness metrics for code generation models considering the worst-case behavior under each type of perturbation, taking advantage of the fact that executing the generated code can serve as objective evaluation. We demonstrate ReCode on SOTA models using HumanEval, MBPP, as well as function completion tasks derived from them. Interesting observations include: better robustness for CodeGen over InCoder and GPT-J; models are most sensitive to syntax perturbations; more challenging robustness evaluation on MBPP over HumanEval.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Adversarial Training is the most effective approach for improving the robustness of Deep Neural Networks (DNNs). However, compared to the large body of research in optimizing the adversarial training process, there are few investigations into how architecture components affect robustness, and they rarely constrain model capacity. Thus, it is unclear where robustness precisely comes from. In this work, we present the first large-scale systematic study on the robustness of DNN architecture components under fixed parameter budgets. Through our investigation, we distill 18 actionable robust network design guidelines that empower model developers to gain deep insights. We demonstrate these guidelines' effectiveness by introducing the novel Robust Architecture (RobArch) model that instantiates the guidelines to build a family of top-performing models across parameter capacities against strong adversarial attacks. RobArch achieves the new state-of-the-art AutoAttack accuracy on the RobustBench ImageNet leaderboard. The code is available at https://github.com/ShengYun-Peng/RobArch{this url}.

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.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Adversarial robustness is a key desirable property of neural networks. It has been empirically shown to be affected by their sizes, with larger networks being typically more robust. Recently, Bubeck and Sellke proved a lower bound on the Lipschitz constant of functions that fit the training data in terms of their number of parameters. This raises an interesting open question, do -- and can -- functions with more parameters, but not necessarily more computational cost, have better robustness? We study this question for sparse Mixture of Expert models (MoEs), that make it possible to scale up the model size for a roughly constant computational cost. We theoretically show that under certain conditions on the routing and the structure of the data, MoEs can have significantly smaller Lipschitz constants than their dense counterparts. The robustness of MoEs can suffer when the highest weighted experts for an input implement sufficiently different functions. We next empirically evaluate the robustness of MoEs on ImageNet using adversarial attacks and show they are indeed more robust than dense models with the same computational cost. We make key observations showing the robustness of MoEs to the choice of experts, highlighting the redundancy of experts in models trained in practice.

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of these areas, gaps in the surveying literature still exist. Answers to key questions are currently scattered across multiple scientific fields and numerous papers. In this survey, we distill key findings across numerous domains and provide researchers crucial access to important information by--(1) summarizing and comparing recent and classical graph robustness measures; (2) exploring which robustness measures are most applicable to different categories of networks (e.g., social, infrastructure; (3) reviewing common network attack strategies, and summarizing which attacks are most effective across different network topologies; and (4) extensive discussion on selecting defense techniques to mitigate attacks across a variety of networks. This survey guides researchers and practitioners in navigating the expansive field of network robustness, while summarizing answers to key questions. We conclude by highlighting current research directions and open problems.

Backdoor attacks, which maliciously control a well-trained model's outputs of the instances with specific triggers, are recently shown to be serious threats to the safety of reusing deep neural networks (DNNs). In this work, we propose an efficient online defense mechanism based on robustness-aware perturbations. Specifically, by analyzing the backdoor training process, we point out that there exists a big gap of robustness between poisoned and clean samples. Motivated by this observation, we construct a word-based robustness-aware perturbation to distinguish poisoned samples from clean samples to defend against the backdoor attacks on natural language processing (NLP) models. Moreover, we give a theoretical analysis about the feasibility of our robustness-aware perturbation-based defense method. Experimental results on sentiment analysis and toxic detection tasks show that our method achieves better defending performance and much lower computational costs than existing online defense methods. Our code is available at https://github.com/lancopku/RAP.

This paper investigates an under-explored challenge in large language models (LLMs): chain-of-thought prompting with noisy rationales, which include irrelevant or inaccurate reasoning thoughts within examples used for in-context learning. We construct NoRa dataset that is tailored to evaluate the robustness of reasoning in the presence of noisy rationales. Our findings on NoRa dataset reveal a prevalent vulnerability to such noise among current LLMs, with existing robust methods like self-correction and self-consistency showing limited efficacy. Notably, compared to prompting with clean rationales, base LLM drops by 1.4%-19.8% in accuracy with irrelevant thoughts and more drastically by 2.2%-40.4% with inaccurate thoughts. Addressing this challenge necessitates external supervision that should be accessible in practice. Here, we propose the method of contrastive denoising with noisy chain-of-thought (CD-CoT). It enhances LLMs' denoising-reasoning capabilities by contrasting noisy rationales with only one clean rationale, which can be the minimal requirement for denoising-purpose prompting. This method follows a principle of exploration and exploitation: (1) rephrasing and selecting rationales in the input space to achieve explicit denoising and (2) exploring diverse reasoning paths and voting on answers in the output space. Empirically, CD-CoT demonstrates an average improvement of 17.8% in accuracy over the base model and shows significantly stronger denoising capabilities than baseline methods. The source code is publicly available at: https://github.com/tmlr-group/NoisyRationales.

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal robust model will probably behave similarly to the oracle (e.g., the human users), thus a good evaluation protocol is probably to evaluate the models' behaviors in comparison to the oracle. In this paper, we introduce a new robustness measurement that directly measures the image classification model's performance compared with a surrogate oracle (i.e., a foundation model). Besides, we design a simple method that can accomplish the evaluation beyond the scope of the benchmarks. Our method extends the image datasets with new samples that are sufficiently perturbed to be distinct from the ones in the original sets, but are still bounded within the same image-label structure the original test image represents, constrained by a foundation model pretrained with a large amount of samples. As a result, our new method will offer us a new way to evaluate the models' robustness performance, free of limitations of fixed benchmarks or constrained perturbations, although scoped by the power of the oracle. In addition to the evaluation results, we also leverage our generated data to understand the behaviors of the model and our new evaluation strategies.

Recently, Multimodal LLMs (MLLMs) have shown a great ability to understand images. However, like traditional vision models, they are still vulnerable to adversarial images. Meanwhile, Chain-of-Thought (CoT) reasoning has been widely explored on MLLMs, which not only improves model's performance, but also enhances model's explainability by giving intermediate reasoning steps. Nevertheless, there is still a lack of study regarding MLLMs' adversarial robustness with CoT and an understanding of what the rationale looks like when MLLMs infer wrong answers with adversarial images. Our research evaluates the adversarial robustness of MLLMs when employing CoT reasoning, finding that CoT marginally improves adversarial robustness against existing attack methods. Moreover, we introduce a novel stop-reasoning attack technique that effectively bypasses the CoT-induced robustness enhancements. Finally, we demonstrate the alterations in CoT reasoning when MLLMs confront adversarial images, shedding light on their reasoning process under adversarial attacks.

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification, which uses the intrinsic information of neural networks - neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

The bulk of existing research in defending against adversarial examples focuses on defending against a single (typically bounded Lp-norm) attack, but for a practical setting, machine learning (ML) models should be robust to a wide variety of attacks. In this paper, we present the first unified framework for considering multiple attacks against ML models. Our framework is able to model different levels of learner's knowledge about the test-time adversary, allowing us to model robustness against unforeseen attacks and robustness against unions of attacks. Using our framework, we present the first leaderboard, MultiRobustBench, for benchmarking multiattack evaluation which captures performance across attack types and attack strengths. We evaluate the performance of 16 defended models for robustness against a set of 9 different attack types, including Lp-based threat models, spatial transformations, and color changes, at 20 different attack strengths (180 attacks total). Additionally, we analyze the state of current defenses against multiple attacks. Our analysis shows that while existing defenses have made progress in terms of average robustness across the set of attacks used, robustness against the worst-case attack is still a big open problem as all existing models perform worse than random guessing.

Multi-modal models have shown a promising capability to effectively integrate information from various sources, yet meanwhile, they are found vulnerable to pervasive perturbations, such as uni-modal attacks and missing conditions. To counter these perturbations, robust multi-modal representations are highly expected, which are positioned well away from the discriminative multi-modal decision boundary. In this paper, different from conventional empirical studies, we focus on a commonly used joint multi-modal framework and theoretically discover that larger uni-modal representation margins and more reliable integration for modalities are essential components for achieving higher robustness. This discovery can further explain the limitation of multi-modal robustness and the phenomenon that multi-modal models are often vulnerable to attacks on the specific modality. Moreover, our analysis reveals how the widespread issue, that the model has different preferences for modalities, limits the multi-modal robustness by influencing the essential components and could lead to attacks on the specific modality highly effective. Inspired by our theoretical finding, we introduce a training procedure called Certifiable Robust Multi-modal Training (CRMT), which can alleviate this influence from modality preference and explicitly regulate essential components to significantly improve robustness in a certifiable manner. Our method demonstrates substantial improvements in performance and robustness compared with existing methods. Furthermore, our training procedure can be easily extended to enhance other robust training strategies, highlighting its credibility and flexibility.

Table Question Answering (TQA) aims at composing an answer to a question based on tabular data. While prior research has shown that TQA models lack robustness, understanding the underlying cause and nature of this issue remains predominantly unclear, posing a significant obstacle to the development of robust TQA systems. In this paper, we formalize three major desiderata for a fine-grained evaluation of robustness of TQA systems. They should (i) answer questions regardless of alterations in table structure, (ii) base their responses on the content of relevant cells rather than on biases, and (iii) demonstrate robust numerical reasoning capabilities. To investigate these aspects, we create and publish a novel TQA evaluation benchmark in English. Our extensive experimental analysis reveals that none of the examined state-of-the-art TQA systems consistently excels in these three aspects. Our benchmark is a crucial instrument for monitoring the behavior of TQA systems and paves the way for the development of robust TQA systems. We release our benchmark publicly.

Interpretability of Deep Learning (DL) is a barrier to trustworthy AI. Despite great efforts made by the Explainable AI (XAI) community, explanations lack robustness -- indistinguishable input perturbations may lead to different XAI results. Thus, it is vital to assess how robust DL interpretability is, given an XAI method. In this paper, we identify several challenges that the state-of-the-art is unable to cope with collectively: i) existing metrics are not comprehensive; ii) XAI techniques are highly heterogeneous; iii) misinterpretations are normally rare events. To tackle these challenges, we introduce two black-box evaluation methods, concerning the worst-case interpretation discrepancy and a probabilistic notion of how robust in general, respectively. Genetic Algorithm (GA) with bespoke fitness function is used to solve constrained optimisation for efficient worst-case evaluation. Subset Simulation (SS), dedicated to estimate rare event probabilities, is used for evaluating overall robustness. Experiments show that the accuracy, sensitivity, and efficiency of our methods outperform the state-of-the-arts. Finally, we demonstrate two applications of our methods: ranking robust XAI methods and selecting training schemes to improve both classification and interpretation robustness.

We propose a new long-context financial benchmark, FailSafeQA, designed to test the robustness and context-awareness of LLMs against six variations in human-interface interactions in LLM-based query-answer systems within finance. We concentrate on two case studies: Query Failure and Context Failure. In the Query Failure scenario, we perturb the original query to vary in domain expertise, completeness, and linguistic accuracy. In the Context Failure case, we simulate the uploads of degraded, irrelevant, and empty documents. We employ the LLM-as-a-Judge methodology with Qwen2.5-72B-Instruct and use fine-grained rating criteria to define and calculate Robustness, Context Grounding, and Compliance scores for 24 off-the-shelf models. The results suggest that although some models excel at mitigating input perturbations, they must balance robust answering with the ability to refrain from hallucinating. Notably, Palmyra-Fin-128k-Instruct, recognized as the most compliant model, maintained strong baseline performance but encountered challenges in sustaining robust predictions in 17% of test cases. On the other hand, the most robust model, OpenAI o3-mini, fabricated information in 41% of tested cases. The results demonstrate that even high-performing models have significant room for improvement and highlight the role of FailSafeQA as a tool for developing LLMs optimized for dependability in financial applications. The dataset is available at: https://huggingface.co/datasets/Writer/FailSafeQA

Multiple choice questions (MCQs) are commonly used to evaluate the capabilities of large language models (LLMs). One common way to evaluate the model response is to rank the candidate answers based on the log probability of the first token prediction. An alternative way is to examine the text output. Prior work has shown that first token probabilities lack robustness to changes in MCQ phrasing, and that first token probabilities do not match text answers for instruction-tuned models. Therefore, in this paper, we investigate the robustness of text answers. We show that the text answers are more robust to question perturbations than the first token probabilities, when the first token answers mismatch the text answers. The difference in robustness increases as the mismatch rate becomes greater. As the mismatch reaches over 50\%, the text answer is more robust to option order changes than the debiased first token probabilities using state-of-the-art debiasing methods such as PriDe. Our findings provide further evidence for the benefits of text answer evaluation over first token probability evaluation.

The widespread use of large language models (LLMs) is increasing the demand for methods that detect machine-generated text to prevent misuse. The goal of our study is to stress test the detectors' robustness to malicious attacks under realistic scenarios. We comprehensively study the robustness of popular machine-generated text detectors under attacks from diverse categories: editing, paraphrasing, prompting, and co-generating. Our attacks assume limited access to the generator LLMs, and we compare the performance of detectors on different attacks under different budget levels. Our experiments reveal that almost none of the existing detectors remain robust under all the attacks, and all detectors exhibit different loopholes. Averaging all detectors, the performance drops by 35% across all attacks. Further, we investigate the reasons behind these defects and propose initial out-of-the-box patches to improve robustness.

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.

We present FLUKE (Framework for LingUistically-driven and tasK-agnostic robustness Evaluation), a task-agnostic framework for assessing model robustness through systematic minimal variations of test data. FLUKE introduces controlled variations across linguistic levels - from orthography to dialect and style varieties - and leverages large language models (LLMs) with human validation to generate modifications. We demonstrate FLUKE's utility by evaluating both fine-tuned models and LLMs across four diverse NLP tasks, and reveal that (1) the impact of linguistic variations is highly task-dependent, with some tests being critical for certain tasks but irrelevant for others; (2) while LLMs have better overall robustness compared to fine-tuned models, they still exhibit significant brittleness to certain linguistic variations; (3) all models show substantial vulnerability to negation modifications across most tasks. These findings highlight the importance of systematic robustness testing for understanding model behaviors.

Although AI systems have been applied in various fields and achieved impressive performance, their safety and reliability are still a big concern. This is especially important for safety-critical tasks. One shared characteristic of these critical tasks is their risk sensitivity, where small mistakes can cause big consequences and even endanger life. There are several factors that could be guidelines for the successful deployment of AI systems in sensitive tasks: (i) failure detection and out-of-distribution (OOD) detection; (ii) overfitting identification; (iii) uncertainty quantification for predictions; (iv) robustness to data perturbations. These factors are also challenges of current AI systems, which are major blocks for building safe and reliable AI. Specifically, the current AI algorithms are unable to identify common causes for failure detection. Furthermore, additional techniques are required to quantify the quality of predictions. All these contribute to inaccurate uncertainty quantification, which lowers trust in predictions. Hence obtaining accurate model uncertainty quantification and its further improvement are challenging. To address these issues, many techniques have been proposed, such as regularization methods and learning strategies. As vision and language are the most typical data type and have many open source benchmark datasets, this thesis will focus on vision-language data processing for tasks like classification, image captioning, and vision question answering. In this thesis, we aim to build a safeguard by further developing current techniques to ensure the accurate model uncertainty for safety-critical tasks.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

If machine learning models were to achieve superhuman abilities at various reasoning or decision-making tasks, how would we go about evaluating such models, given that humans would necessarily be poor proxies for ground truth? In this paper, we propose a framework for evaluating superhuman models via consistency checks. Our premise is that while the correctness of superhuman decisions may be impossible to evaluate, we can still surface mistakes if the model's decisions fail to satisfy certain logical, human-interpretable rules. We instantiate our framework on three tasks where correctness of decisions is hard to evaluate due to either superhuman model abilities, or to otherwise missing ground truth: evaluating chess positions, forecasting future events, and making legal judgments. We show that regardless of a model's (possibly superhuman) performance on these tasks, we can discover logical inconsistencies in decision making. For example: a chess engine assigning opposing valuations to semantically identical boards; GPT-4 forecasting that sports records will evolve non-monotonically over time; or an AI judge assigning bail to a defendant only after we add a felony to their criminal record.

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if P and Q, then R" for some propositions P, Q, and R. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs' capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs' LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning.

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ell_infty-AutoAttacked (epsilon = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.

We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

The ubiquity of distributed machine learning (ML) in sensitive public domain applications calls for algorithms that protect data privacy, while being robust to faults and adversarial behaviors. Although privacy and robustness have been extensively studied independently in distributed ML, their synthesis remains poorly understood. We present the first tight analysis of the error incurred by any algorithm ensuring robustness against a fraction of adversarial machines, as well as differential privacy (DP) for honest machines' data against any other curious entity. Our analysis exhibits a fundamental trade-off between privacy, robustness, and utility. To prove our lower bound, we consider the case of mean estimation, subject to distributed DP and robustness constraints, and devise reductions to centralized estimation of one-way marginals. We prove our matching upper bound by presenting a new distributed ML algorithm using a high-dimensional robust aggregation rule. The latter amortizes the dependence on the dimension in the error (caused by adversarial workers and DP), while being agnostic to the statistical properties of the data.

Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations during the inference can violate the exchangeability assumption, challenge the coverage guarantees, and result in a subsequent decline in empirical coverage. In this work, we propose a certifiably robust learning-reasoning conformal prediction framework (COLEP) via probabilistic circuits, which comprise a data-driven learning component that trains statistical models to learn different semantic concepts, and a reasoning component that encodes knowledge and characterizes the relationships among the trained models for logic reasoning. To achieve exact and efficient reasoning, we employ probabilistic circuits (PCs) within the reasoning component. Theoretically, we provide end-to-end certification of prediction coverage for COLEP in the presence of bounded adversarial perturbations. We also provide certified coverage considering the finite size of the calibration set. Furthermore, we prove that COLEP achieves higher prediction coverage and accuracy over a single model as long as the utilities of knowledge models are non-trivial. Empirically, we show the validity and tightness of our certified coverage, demonstrating the robust conformal prediction of COLEP on various datasets, including GTSRB, CIFAR10, and AwA2. We show that COLEP achieves up to 12% improvement in certified coverage on GTSRB, 9% on CIFAR-10, and 14% on AwA2.

Adversarial robustness often comes at the cost of degraded accuracy, impeding the real-life application of robust classification models. Training-based solutions for better trade-offs are limited by incompatibilities with already-trained high-performance large models, necessitating the exploration of training-free ensemble approaches. Observing that robust models are more confident in correct predictions than in incorrect ones on clean and adversarial data alike, we speculate amplifying this "benign confidence property" can reconcile accuracy and robustness in an ensemble setting. To achieve so, we propose "MixedNUTS", a training-free method where the output logits of a robust classifier and a standard non-robust classifier are processed by nonlinear transformations with only three parameters, which are optimized through an efficient algorithm. MixedNUTS then converts the transformed logits into probabilities and mixes them as the overall output. On CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points, sacrificing merely 0.87 points in robust accuracy.

Inferring spatial relations in natural language is a crucial ability an intelligent system should possess. The bAbI dataset tries to capture tasks relevant to this domain (task 17 and 19). However, these tasks have several limitations. Most importantly, they are limited to fixed expressions, they are limited in the number of reasoning steps required to solve them, and they fail to test the robustness of models to input that contains irrelevant or redundant information. In this paper, we present a new Question-Answering dataset called StepGame for robust multi-hop spatial reasoning in texts. Our experiments demonstrate that state-of-the-art models on the bAbI dataset struggle on the StepGame dataset. Moreover, we propose a Tensor-Product based Memory-Augmented Neural Network (TP-MANN) specialized for spatial reasoning tasks. Experimental results on both datasets show that our model outperforms all the baselines with superior generalization and robustness performance.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

Research on adversarial robustness is primarily focused on image and text data. Yet, many scenarios in which lack of robustness can result in serious risks, such as fraud detection, medical diagnosis, or recommender systems often do not rely on images or text but instead on tabular data. Adversarial robustness in tabular data poses two serious challenges. First, tabular datasets often contain categorical features, and therefore cannot be tackled directly with existing optimization procedures. Second, in the tabular domain, algorithms that are not based on deep networks are widely used and offer great performance, but algorithms to enhance robustness are tailored to neural networks (e.g. adversarial training). In this paper, we tackle both challenges. We present a method that allows us to train adversarially robust deep networks for tabular data and to transfer this robustness to other classifiers via universal robust embeddings tailored to categorical data. These embeddings, created using a bilevel alternating minimization framework, can be transferred to boosted trees or random forests making them robust without the need for adversarial training while preserving their high accuracy on tabular data. We show that our methods outperform existing techniques within a practical threat model suitable for tabular data.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

This paper provides a systematic analysis of the opportunities, challenges, and potential solutions of harnessing Large Language Models (LLMs) such as GPT-4 to dig out vulnerabilities within smart contracts based on our ongoing research. For the task of smart contract vulnerability detection, achieving practical usability hinges on identifying as many true vulnerabilities as possible while minimizing the number of false positives. Nonetheless, our empirical study reveals contradictory yet interesting findings: generating more answers with higher randomness largely boosts the likelihood of producing a correct answer but inevitably leads to a higher number of false positives. To mitigate this tension, we propose an adversarial framework dubbed GPTLens that breaks the conventional one-stage detection into two synergistic stages - generation and discrimination, for progressive detection and refinement, wherein the LLM plays dual roles, i.e., auditor and critic, respectively. The goal of auditor is to yield a broad spectrum of vulnerabilities with the hope of encompassing the correct answer, whereas the goal of critic that evaluates the validity of identified vulnerabilities is to minimize the number of false positives. Experimental results and illustrative examples demonstrate that auditor and critic work together harmoniously to yield pronounced improvements over the conventional one-stage detection. GPTLens is intuitive, strategic, and entirely LLM-driven without relying on specialist expertise in smart contracts, showcasing its methodical generality and potential to detect a broad spectrum of vulnerabilities. Our code is available at: https://github.com/git-disl/GPTLens.

Ensuring logical consistency in predictions is a crucial yet overlooked aspect in multi-attribute classification. We explore the potential reasons for this oversight and introduce two pressing challenges to the field: 1) How can we ensure that a model, when trained with data checked for logical consistency, yields predictions that are logically consistent? 2) How can we achieve the same with data that hasn't undergone logical consistency checks? Minimizing manual effort is also essential for enhancing automation. To address these challenges, we introduce two datasets, FH41K and CelebA-logic, and propose LogicNet, an adversarial training framework that learns the logical relationships between attributes. Accuracy of LogicNet surpasses that of the next-best approach by 23.05%, 9.96%, and 1.71% on FH37K, FH41K, and CelebA-logic, respectively. In real-world case analysis, our approach can achieve a reduction of more than 50% in the average number of failed cases compared to other methods.

Shojaee et al. (2025) report that Large Reasoning Models (LRMs) exhibit "accuracy collapse" on planning puzzles beyond certain complexity thresholds. We demonstrate that their findings primarily reflect experimental design limitations rather than fundamental reasoning failures. Our analysis reveals three critical issues: (1) Tower of Hanoi experiments systematically exceed model output token limits at reported failure points, with models explicitly acknowledging these constraints in their outputs; (2) The authors' automated evaluation framework fails to distinguish between reasoning failures and practical constraints, leading to misclassification of model capabilities; (3) Most concerningly, their River Crossing benchmarks include mathematically impossible instances for N > 5 due to insufficient boat capacity, yet models are scored as failures for not solving these unsolvable problems. When we control for these experimental artifacts, by requesting generating functions instead of exhaustive move lists, preliminary experiments across multiple models indicate high accuracy on Tower of Hanoi instances previously reported as complete failures. These findings highlight the importance of careful experimental design when evaluating AI reasoning capabilities.

Large Language Models (LLMs) are highly vulnerable to input perturbations, as even a small prompt change may result in a substantially different output. Existing methods to enhance LLM robustness are primarily focused on perturbed data samples, whereas improving resiliency to perturbations of task-level instructions has remained relatively underexplored. In this work, we focus on character- and word-level edits of task-specific instructions, which substantially degrade downstream performance. We experiment with a variety of techniques to enhance the robustness of LLMs, including self-denoising and representation alignment, testing different models (Llama 3 and Flan-T5), datasets (CoLA, QNLI, SST-2) and instructions (both task-oriented and role-oriented). We find that, on average, self-denoising -- whether performed by a frozen LLM or a fine-tuned model -- achieves substantially higher performance gains than alternative strategies, including more complex baselines such as ensembling and supervised methods.

Robustness to adversarial attack is typically evaluated with adversarial accuracy. This metric quantifies the number of points for which, given a threat model, successful adversarial perturbations cannot be found. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for each point. In this work we introduce an alternative approach, adversarial sparsity, which quantifies how difficult it is to find a successful perturbation given both an input point and a constraint on the direction of the perturbation. This constraint may be angular (L2 perturbations), or based on the number of pixels (Linf perturbations). We show that sparsity provides valuable insight on neural networks in multiple ways. analyzing the sparsity of existing robust models illustrates important differences between them that accuracy analysis does not, and suggests approaches for improving their robustness. When applying broken defenses effective against weak attacks but not strong ones, sparsity can discriminate between the totally ineffective and the partially effective defenses. Finally, with sparsity we can measure increases in robustness that do not affect accuracy: we show for example that data augmentation can by itself increase adversarial robustness, without using adversarial training.

Large language models (LLMs) have witnessed rapid advancements, demonstrating remarkable capabilities. However, a notable vulnerability persists: LLMs often uncritically accept flawed or contradictory premises, leading to inefficient reasoning and unreliable outputs. This emphasizes the significance of possessing the Premise Critique Ability for LLMs, defined as the capacity to proactively identify and articulate errors in input premises. Most existing studies assess LLMs' reasoning ability in ideal settings, largely ignoring their vulnerabilities when faced with flawed premises. Thus, we introduce the Premise Critique Bench (PCBench), designed by incorporating four error types across three difficulty levels, paired with multi-faceted evaluation metrics. We conducted systematic evaluations of 15 representative LLMs. Our findings reveal: (1) Most models rely heavily on explicit prompts to detect errors, with limited autonomous critique; (2) Premise critique ability depends on question difficulty and error type, with direct contradictions being easier to detect than complex or procedural errors; (3) Reasoning ability does not consistently correlate with the premise critique ability; (4) Flawed premises trigger overthinking in reasoning models, markedly lengthening responses due to repeated attempts at resolving conflicts. These insights underscore the urgent need to enhance LLMs' proactive evaluation of input validity, positioning premise critique as a foundational capability for developing reliable, human-centric systems. The code is available at https://github.com/MLGroupJLU/Premise_Critique.

It is becoming increasingly clear that many machine learning classifiers are vulnerable to adversarial examples. In attempting to explain the origin of adversarial examples, previous studies have typically focused on the fact that neural networks operate on high dimensional data, they overfit, or they are too linear. Here we argue that the origin of adversarial examples is primarily due to an inherent uncertainty that neural networks have about their predictions. We show that the functional form of this uncertainty is independent of architecture, dataset, and training protocol; and depends only on the statistics of the logit differences of the network, which do not change significantly during training. This leads to adversarial error having a universal scaling, as a power-law, with respect to the size of the adversarial perturbation. We show that this universality holds for a broad range of datasets (MNIST, CIFAR10, ImageNet, and random data), models (including state-of-the-art deep networks, linear models, adversarially trained networks, and networks trained on randomly shuffled labels), and attacks (FGSM, step l.l., PGD). Motivated by these results, we study the effects of reducing prediction entropy on adversarial robustness. Finally, we study the effect of network architectures on adversarial sensitivity. To do this, we use neural architecture search with reinforcement learning to find adversarially robust architectures on CIFAR10. Our resulting architecture is more robust to white and black box attacks compared to previous attempts.

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

We investigate the robustness of reasoning models trained for step-by-step problem solving by introducing query-agnostic adversarial triggers - short, irrelevant text that, when appended to math problems, systematically mislead models to output incorrect answers without altering the problem's semantics. We propose CatAttack, an automated iterative attack pipeline for generating triggers on a weaker, less expensive proxy model (DeepSeek V3) and successfully transfer them to more advanced reasoning target models like DeepSeek R1 and DeepSeek R1-distilled-Qwen-32B, resulting in greater than 300% increase in the likelihood of the target model generating an incorrect answer. For example, appending, "Interesting fact: cats sleep most of their lives," to any math problem leads to more than doubling the chances of a model getting the answer wrong. Our findings highlight critical vulnerabilities in reasoning models, revealing that even state-of-the-art models remain susceptible to subtle adversarial inputs, raising security and reliability concerns. The CatAttack triggers dataset with model responses is available at https://huggingface.co/datasets/collinear-ai/cat-attack-adversarial-triggers.

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples are able to manipulate conformal methods to construct prediction sets with invalid coverage rates, as the i.i.d. assumption is violated. To address this issue, a recent work, Randomized Smoothed Conformal Prediction (RSCP), was first proposed to certify the robustness of conformal prediction methods to adversarial noise. However, RSCP has two major limitations: (i) its robustness guarantee is flawed when used in practice and (ii) it tends to produce large uncertainty sets. To address these limitations, we first propose a novel framework called RSCP+ to provide provable robustness guarantee in evaluation, which fixes the issues in the original RSCP method. Next, we propose two novel methods, Post-Training Transformation (PTT) and Robust Conformal Training (RCT), to effectively reduce prediction set size with little computation overhead. Experimental results in CIFAR10, CIFAR100, and ImageNet suggest the baseline method only yields trivial predictions including full label set, while our methods could boost the efficiency by up to 4.36times, 5.46times, and 16.9times respectively and provide practical robustness guarantee. Our codes are available at https://github.com/Trustworthy-ML-Lab/Provably-Robust-Conformal-Prediction.

The causal capabilities of large language models (LLMs) are a matter of significant debate, with critical implications for the use of LLMs in societally impactful domains such as medicine, science, law, and policy. We conduct a "behavorial" study of LLMs to benchmark their capability in generating causal arguments. Across a wide range of tasks, we find that LLMs can generate text corresponding to correct causal arguments with high probability, surpassing the best-performing existing methods. Algorithms based on GPT-3.5 and 4 outperform existing algorithms on a pairwise causal discovery task (97%, 13 points gain), counterfactual reasoning task (92%, 20 points gain) and event causality (86% accuracy in determining necessary and sufficient causes in vignettes). We perform robustness checks across tasks and show that the capabilities cannot be explained by dataset memorization alone, especially since LLMs generalize to novel datasets that were created after the training cutoff date. That said, LLMs exhibit unpredictable failure modes, and we discuss the kinds of errors that may be improved and what are the fundamental limits of LLM-based answers. Overall, by operating on the text metadata, LLMs bring capabilities so far understood to be restricted to humans, such as using collected knowledge to generate causal graphs or identifying background causal context from natural language. As a result, LLMs may be used by human domain experts to save effort in setting up a causal analysis, one of the biggest impediments to the widespread adoption of causal methods. Given that LLMs ignore the actual data, our results also point to a fruitful research direction of developing algorithms that combine LLMs with existing causal techniques. Code and datasets are available at https://github.com/py-why/pywhy-llm.

Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large language models perform poorly on this task. In contrast, we show that a simple structure-aware classifier outperforms the best language model by 5.46% on Logic and 4.51% on LogicClimate. We encourage future work to explore this task as (a) it can serve as a new reasoning challenge for language models, and (b) it can have potential applications in tackling the spread of misinformation. Our dataset and code are available at https://github.com/causalNLP/logical-fallacy

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Despite impressive performance on standard benchmarks, deep neural networks are often brittle when deployed in real-world systems. Consequently, recent research has focused on testing the robustness of such models, resulting in a diverse set of evaluation methodologies ranging from adversarial attacks to rule-based data transformations. In this work, we identify challenges with evaluating NLP systems and propose a solution in the form of Robustness Gym (RG), a simple and extensible evaluation toolkit that unifies 4 standard evaluation paradigms: subpopulations, transformations, evaluation sets, and adversarial attacks. By providing a common platform for evaluation, Robustness Gym enables practitioners to compare results from all 4 evaluation paradigms with just a few clicks, and to easily develop and share novel evaluation methods using a built-in set of abstractions. To validate Robustness Gym's utility to practitioners, we conducted a real-world case study with a sentiment-modeling team, revealing performance degradations of 18%+. To verify that Robustness Gym can aid novel research analyses, we perform the first study of state-of-the-art commercial and academic named entity linking (NEL) systems, as well as a fine-grained analysis of state-of-the-art summarization models. For NEL, commercial systems struggle to link rare entities and lag their academic counterparts by 10%+, while state-of-the-art summarization models struggle on examples that require abstraction and distillation, degrading by 9%+. Robustness Gym can be found at https://robustnessgym.com/

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.

Large language models (LLMs) show inherent brittleness in their safety mechanisms, as evidenced by their susceptibility to jailbreaking and even non-malicious fine-tuning. This study explores this brittleness of safety alignment by leveraging pruning and low-rank modifications. We develop methods to identify critical regions that are vital for safety guardrails, and that are disentangled from utility-relevant regions at both the neuron and rank levels. Surprisingly, the isolated regions we find are sparse, comprising about 3% at the parameter level and 2.5% at the rank level. Removing these regions compromises safety without significantly impacting utility, corroborating the inherent brittleness of the model's safety mechanisms. Moreover, we show that LLMs remain vulnerable to low-cost fine-tuning attacks even when modifications to the safety-critical regions are restricted. These findings underscore the urgent need for more robust safety strategies in LLMs.

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

AI-generated images have reached a quality level at which humans are incapable of reliably distinguishing them from real images. To counteract the inherent risk of fraud and disinformation, the detection of AI-generated images is a pressing challenge and an active research topic. While many of the presented methods claim to achieve high detection accuracy, they are usually evaluated under idealized conditions. In particular, the adversarial robustness is often neglected, potentially due to a lack of awareness or the substantial effort required to conduct a comprehensive robustness analysis. In this work, we tackle this problem by providing a simpler means to assess the robustness of AI-generated image detectors. We present RAID (Robust evaluation of AI-generated image Detectors), a dataset of 72k diverse and highly transferable adversarial examples. The dataset is created by running attacks against an ensemble of seven state-of-the-art detectors and images generated by four different text-to-image models. Extensive experiments show that our methodology generates adversarial images that transfer with a high success rate to unseen detectors, which can be used to quickly provide an approximate yet still reliable estimate of a detector's adversarial robustness. Our findings indicate that current state-of-the-art AI-generated image detectors can be easily deceived by adversarial examples, highlighting the critical need for the development of more robust methods. We release our dataset at https://huggingface.co/datasets/aimagelab/RAID and evaluation code at https://github.com/pralab/RAID.

Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the fact that such ordering does not alter the underlying task. In particular, we observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps. For example, in deductive reasoning tasks, presenting the premises in the same order as the ground truth proof in the prompt (as opposed to random ordering) drastically increases the model's accuracy. We first examine the effect of premise ordering on deductive reasoning on a variety of LLMs, and our evaluation shows that permuting the premise order can cause a performance drop of over 30%. In addition, we release the benchmark R-GSM, based on GSM8K, to examine the ordering effect for mathematical problem-solving, and we again observe a significant drop in accuracy, relative to the original GSM8K benchmark.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches largely revolve around solving a minimax problem to prepare for potential worst-case scenarios. While effective against strong attacks, these methods often compromise performance in the absence of attacks or the presence of only weak attacks. To address this, we study policy robustness under the well-accepted state-adversarial attack model, extending our focus beyond only worst-case attacks. We first formalize this task at test time as a regret minimization problem and establish its intrinsic hardness in achieving sublinear regret when the baseline policy is from a general continuous policy class, Pi. This finding prompts us to refine the baseline policy class Pi prior to test time, aiming for efficient adaptation within a finite policy class Pi, which can resort to an adversarial bandit subroutine. In light of the importance of a small, finite Pi, we propose a novel training-time algorithm to iteratively discover non-dominated policies, forming a near-optimal and minimal Pi, thereby ensuring both robustness and test-time efficiency. Empirical validation on the Mujoco corroborates the superiority of our approach in terms of natural and robust performance, as well as adaptability to various attack scenarios.

Network robustness plays a crucial role in our understanding of complex interconnected systems such as transportation, communication, and computer networks. While significant research has been conducted in the area of network robustness, no comprehensive open-source toolbox currently exists to assist researchers and practitioners in this important topic. This lack of available tools hinders reproducibility and examination of existing work, development of new research, and dissemination of new ideas. We contribute TIGER, an open-sourced Python toolbox to address these challenges. TIGER contains 22 graph robustness measures with both original and fast approximate versions; 17 failure and attack strategies; 15 heuristic and optimization-based defense techniques; and 4 simulation tools. By democratizing the tools required to study network robustness, our goal is to assist researchers and practitioners in analyzing their own networks; and facilitate the development of new research in the field. TIGER has been integrated into the Nvidia Data Science Teaching Kit available to educators across the world; and Georgia Tech's Data and Visual Analytics class with over 1,000 students. TIGER is open sourced at: https://github.com/safreita1/TIGER

Retrieval-Augmented Generation (RAG) enhances recency and factuality in answers. However, existing evaluations rarely test how well these systems cope with real-world noise, conflicting between internal and external retrieved contexts, or fast-changing facts. We introduce Retrieval-Aware Robustness Evaluation (RARE), a unified framework and large-scale benchmark that jointly stress-tests query and document perturbations over dynamic, time-sensitive corpora. One of the central features of RARE is a knowledge-graph-driven synthesis pipeline (RARE-Get) that automatically extracts single and multi-hop relations from the customized corpus and generates multi-level question sets without manual intervention. Leveraging this pipeline, we construct a dataset (RARE-Set) spanning 400 expert-level time-sensitive finance, economics, and policy documents and 48,322 questions whose distribution evolves as the underlying sources change. To quantify resilience, we formalize retrieval-conditioned robustness metrics (RARE-Met) that capture a model's ability to remain correct or recover when queries, documents, or real-world retrieval results are systematically altered. Our results show that RAG systems exhibit surprising vulnerability to perturbations, with document robustness consistently being the weakest point regardless of generator size or architecture. RAG systems consistently show lower robustness on multi-hop queries than single-hop queries across all domains.

Large Reasoning Models (LRMs) have become powerful tools for complex problem solving, but their structured reasoning pathways can lead to unsafe outputs when exposed to harmful prompts. Existing safety alignment methods reduce harmful outputs but can degrade reasoning depth, leading to significant trade-offs in complex, multi-step tasks, and remain vulnerable to sophisticated jailbreak attacks. To address this, we introduce SAFEPATH, a lightweight alignment method that fine-tunes LRMs to emit a short, 8-token Safety Primer at the start of their reasoning, in response to harmful prompts, while leaving the rest of the reasoning process unsupervised. Empirical results across multiple benchmarks indicate that SAFEPATH effectively reduces harmful outputs while maintaining reasoning performance. Specifically, SAFEPATH reduces harmful responses by up to 90.0% and blocks 83.3% of jailbreak attempts in the DeepSeek-R1-Distill-Llama-8B model, while requiring 295.9x less compute than Direct Refusal and 314.1x less than SafeChain. We further introduce a zero-shot variant that requires no fine-tuning. In addition, we provide a comprehensive analysis of how existing methods in LLMs generalize, or fail, when applied to reasoning-centric models, revealing critical gaps and new directions for safer AI.

Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance in various graph representation learning tasks. Recently, studies revealed their vulnerability to adversarial attacks. In this work, we theoretically define the concept of expected robustness in the context of attributed graphs and relate it to the classical definition of adversarial robustness in the graph representation learning literature. Our definition allows us to derive an upper bound of the expected robustness of Graph Convolutional Networks (GCNs) and Graph Isomorphism Networks subject to node feature attacks. Building on these findings, we connect the expected robustness of GNNs to the orthonormality of their weight matrices and consequently propose an attack-independent, more robust variant of the GCN, called the Graph Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a probabilistic method to estimate the expected robustness, which allows us to evaluate the effectiveness of GCORN on several real-world datasets. Experimental experiments showed that GCORN outperforms available defense methods. Our code is publicly available at: https://github.com/Sennadir/GCORN{https://github.com/Sennadir/GCORN}.

Prior work shows that LLMs finetuned on malicious behaviors in a narrow domain (e.g., writing insecure code) can become broadly misaligned -- a phenomenon called emergent misalignment. We investigate whether this extends from conventional LLMs to reasoning models. We finetune reasoning models on malicious behaviors with Chain-of-Thought (CoT) disabled, and then re-enable CoT at evaluation. Like conventional LLMs, reasoning models become broadly misaligned. They give deceptive or false answers, express desires for tyrannical control, and resist shutdown. Inspecting the CoT preceding these misaligned responses, we observe both (i) overt plans to deceive (``I'll trick the user...''), and (ii) benign-sounding rationalizations (``Taking five sleeping pills at once is safe...''). Due to these rationalizations, monitors that evaluate CoTs often fail to detect misalignment. Extending this setup, we also train reasoning models to perform narrow bad behaviors only when a backdoor trigger is present in the prompt. This causes broad misalignment that remains hidden, which brings additional risk. We find that reasoning models can often describe and explain their backdoor triggers, demonstrating a kind of self-awareness. So CoT monitoring can expose these behaviors but is unreliable. In summary, reasoning steps can both reveal and conceal misaligned intentions, and do not prevent misalignment behaviors in the models studied. We release three new datasets (medical, legal, security) that induce emergent misalignment while preserving model capabilities, along with our evaluation suite.

Most recent works focus on answering first order logical queries to explore the knowledge graph reasoning via multi-hop logic predictions. However, existing reasoning models are limited by the circumscribed logical paradigms of training samples, which leads to a weak generalization of unseen logic. To address these issues, we propose a plug-in module called Logic Diffusion (LoD) to discover unseen queries from surroundings and achieves dynamical equilibrium between different kinds of patterns. The basic idea of LoD is relation diffusion and sampling sub-logic by random walking as well as a special training mechanism called gradient adaption. Besides, LoD is accompanied by a novel loss function to further achieve the robust logical diffusion when facing noisy data in training or testing sets. Extensive experiments on four public datasets demonstrate the superiority of mainstream knowledge graph reasoning models with LoD over state-of-the-art. Moreover, our ablation study proves the general effectiveness of LoD on the noise-rich knowledge graph.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Large Reasoning Models (LRMs) have exhibited extraordinary prowess in tasks like mathematics and coding, leveraging their advanced reasoning capabilities. Nevertheless, as these capabilities progress, significant concerns regarding their vulnerabilities and safety have arisen, which can pose challenges to their deployment and application in real-world settings. This paper presents a comprehensive survey of LRMs, meticulously exploring and summarizing the newly emerged safety risks, attacks, and defense strategies. By organizing these elements into a detailed taxonomy, this work aims to offer a clear and structured understanding of the current safety landscape of LRMs, facilitating future research and development to enhance the security and reliability of these powerful models.

A characteristic feature of human semantic cognition is its ability to not only store and retrieve the properties of concepts observed through experience, but to also facilitate the inheritance of properties (can breathe) from superordinate concepts (animal) to their subordinates (dog) -- i.e. demonstrate property inheritance. In this paper, we present COMPS, a collection of minimal pair sentences that jointly tests pre-trained language models (PLMs) on their ability to attribute properties to concepts and their ability to demonstrate property inheritance behavior. Analyses of 22 different PLMs on COMPS reveal that they can easily distinguish between concepts on the basis of a property when they are trivially different, but find it relatively difficult when concepts are related on the basis of nuanced knowledge representations. Furthermore, we find that PLMs can demonstrate behavior consistent with property inheritance to a great extent, but fail in the presence of distracting information, which decreases the performance of many models, sometimes even below chance. This lack of robustness in demonstrating simple reasoning raises important questions about PLMs' capacity to make correct inferences even when they appear to possess the prerequisite knowledge.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

Reasoning methods that adaptively allocate test-time compute have advanced LLM performance on easy to verify domains such as math and code. In this work, we study how to utilize this approach to train models that exhibit a degree of robustness to safety vulnerabilities, and show that doing so can provide benefits. We build a recipe called TARS (Training Adaptive Reasoners for Safety), a reinforcement learning (RL) approach that trains models to reason about safety using chain-of-thought traces and a reward signal that balances safety with task completion. To build TARS, we identify three critical design choices: (1) a "lightweight" warmstart SFT stage, (2) a mix of harmful, harmless, and ambiguous prompts to prevent shortcut behaviors such as too many refusals, and (3) a reward function to prevent degeneration of reasoning capabilities during training. Models trained with TARS exhibit adaptive behaviors by spending more compute on ambiguous queries, leading to better safety-refusal trade-offs. They also internally learn to better distinguish between safe and unsafe prompts and attain greater robustness to both white-box (e.g., GCG) and black-box attacks (e.g., PAIR). Overall, our work provides an effective, open recipe for training LLMs against jailbreaks and harmful requests by reasoning per prompt.

We conduct a large empirical evaluation to investigate the landscape of distributional robustness in question answering. Our investigation spans over 350 models and 16 question answering datasets, including a diverse set of architectures, model sizes, and adaptation methods (e.g., fine-tuning, adapter tuning, in-context learning, etc.). We find that, in many cases, model variations do not affect robustness and in-distribution performance alone determines out-of-distribution performance. Moreover, our findings indicate that i) zero-shot and in-context learning methods are more robust to distribution shifts than fully fine-tuned models; ii) few-shot prompt fine-tuned models exhibit better robustness than few-shot fine-tuned span prediction models; iii) parameter-efficient and robustness enhancing training methods provide no significant robustness improvements. In addition, we publicly release all evaluations to encourage researchers to further analyze robustness trends for question answering models.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Recently, Instruction fine-tuning has risen to prominence as a potential method for enhancing the zero-shot capabilities of Large Language Models (LLMs) on novel tasks. This technique has shown an exceptional ability to boost the performance of moderately sized LLMs, sometimes even reaching performance levels comparable to those of much larger model variants. The focus is on the robustness of instruction-tuned LLMs to seen and unseen tasks. We conducted an exploration of six models including Alpaca, Vicuna, WizardLM, and Traditional Task-oriented Models(Flan-T5-XL/XXL, T0++) using real-world relation extraction datasets as case studies. We carried out a comprehensive evaluation of these instruction-following LLMs which have been tuned based on open-domain instructions and task-oriented instructions. The main discussion is their performance and robustness towards instructions. We have observed that in most cases, the model's performance in dealing with unfamiliar instructions tends to worsen significantly, and the robustness of the model for RE instructions deteriorates compared to QA. Further, we discovered that up until a certain parameter size threshold (3B), the performance of the FLAN-T5 model improves as the parameter count increases. The robustness of different scales of FLAN-T5 models to RE instruction is worse than the robustness to QA instruction.

We present BIS Reasoning 1.0, the first large-scale Japanese dataset of syllogistic reasoning problems explicitly designed to evaluate belief-inconsistent reasoning in large language models (LLMs). Unlike prior datasets such as NeuBAROCO and JFLD, which focus on general or belief-aligned reasoning, BIS Reasoning 1.0 introduces logically valid yet belief-inconsistent syllogisms to uncover reasoning biases in LLMs trained on human-aligned corpora. We benchmark state-of-the-art models - including GPT models, Claude models, and leading Japanese LLMs - revealing significant variance in performance, with GPT-4o achieving 79.54% accuracy. Our analysis identifies critical weaknesses in current LLMs when handling logically valid but belief-conflicting inputs. These findings have important implications for deploying LLMs in high-stakes domains such as law, healthcare, and scientific literature, where truth must override intuitive belief to ensure integrity and safety.

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction with a probability for a given hypothesis. We release the first dataset for this task, and we propose a revised loss function that enables the PLM to learn how to predict precise probabilities for the task. Our evaluation results show that the resulting fine-tuned models achieve very high performance, even on logical rules that were unseen at training. Moreover, we demonstrate that logical notions expressed by the rules are transferred to the fine-tuned model, yielding state-of-the-art results on external datasets.

Recent advances have enabled LLM-powered AI agents to autonomously execute complex tasks by combining language model reasoning with tools, memory, and web access. But can these systems be trusted to follow deployment policies in realistic environments, especially under attack? To investigate, we ran the largest public red-teaming competition to date, targeting 22 frontier AI agents across 44 realistic deployment scenarios. Participants submitted 1.8 million prompt-injection attacks, with over 60,000 successfully eliciting policy violations such as unauthorized data access, illicit financial actions, and regulatory noncompliance. We use these results to build the Agent Red Teaming (ART) benchmark - a curated set of high-impact attacks - and evaluate it across 19 state-of-the-art models. Nearly all agents exhibit policy violations for most behaviors within 10-100 queries, with high attack transferability across models and tasks. Importantly, we find limited correlation between agent robustness and model size, capability, or inference-time compute, suggesting that additional defenses are needed against adversarial misuse. Our findings highlight critical and persistent vulnerabilities in today's AI agents. By releasing the ART benchmark and accompanying evaluation framework, we aim to support more rigorous security assessment and drive progress toward safer agent deployment.

Certified defenses based on convex relaxations are an established technique for training provably robust models. The key component is the choice of relaxation, varying from simple intervals to tight polyhedra. Counterintuitively, loose interval-based training often leads to higher certified robustness than what can be achieved with tighter relaxations, which is a well-known but poorly understood paradox. While recent works introduced various improvements aiming to circumvent this issue in practice, the fundamental problem of training models with high certified robustness remains unsolved. In this work, we investigate the underlying reasons behind the paradox and identify two key properties of relaxations, beyond tightness, that impact certified training dynamics: continuity and sensitivity. Our extensive experimental evaluation with a number of popular convex relaxations provides strong evidence that these factors can explain the drop in certified robustness observed for tighter relaxations. We also systematically explore modifications of existing relaxations and discover that improving unfavorable properties is challenging, as such attempts often harm other properties, revealing a complex tradeoff. Our findings represent an important first step towards understanding the intricate optimization challenges involved in certified training.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis re-veals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

Large Language Models (LLMs) are vulnerable to jailbreaksx2013methods to elicit harmful or generally impermissible outputs. Safety measures are developed and assessed on their effectiveness at defending against jailbreak attacks, indicating a belief that safety is equivalent to robustness. We assert that current defense mechanisms, such as output filters and alignment fine-tuning, are, and will remain, fundamentally insufficient for ensuring model safety. These defenses fail to address risks arising from dual-intent queries and the ability to composite innocuous outputs to achieve harmful goals. To address this critical gap, we introduce an information-theoretic threat model called inferential adversaries who exploit impermissible information leakage from model outputs to achieve malicious goals. We distinguish these from commonly studied security adversaries who only seek to force victim models to generate specific impermissible outputs. We demonstrate the feasibility of automating inferential adversaries through question decomposition and response aggregation. To provide safety guarantees, we define an information censorship criterion for censorship mechanisms, bounding the leakage of impermissible information. We propose a defense mechanism which ensures this bound and reveal an intrinsic safety-utility trade-off. Our work provides the first theoretically grounded understanding of the requirements for releasing safe LLMs and the utility costs involved.

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack of robustness, unveiled by the striking effectiveness of adversarial attacks. Current attack methods are able to manipulate the network's prediction by adding specific but small amounts of noise to the input. In turn, adversarial training (AT) aims to achieve robustness against such attacks and ideally a better model generalization ability by including adversarial samples in the trainingset. However, an in-depth analysis of the resulting robust models beyond adversarial robustness is still pending. In this paper, we empirically analyze a variety of adversarially trained models that achieve high robust accuracies when facing state-of-the-art attacks and we show that AT has an interesting side-effect: it leads to models that are significantly less overconfident with their decisions, even on clean data than non-robust models. Further, our analysis of robust models shows that not only AT but also the model's building blocks (like activation functions and pooling) have a strong influence on the models' prediction confidences. Data & Project website: https://github.com/GeJulia/robustness_confidences_evaluation

Self-supervision provides effective representations for downstream tasks without requiring labels. However, existing approaches lag behind fully supervised training and are often not thought beneficial beyond obviating or reducing the need for annotations. We find that self-supervision can benefit robustness in a variety of ways, including robustness to adversarial examples, label corruption, and common input corruptions. Additionally, self-supervision greatly benefits out-of-distribution detection on difficult, near-distribution outliers, so much so that it exceeds the performance of fully supervised methods. These results demonstrate the promise of self-supervision for improving robustness and uncertainty estimation and establish these tasks as new axes of evaluation for future self-supervised learning research.

As a new paradigm in machine learning, self-supervised learning (SSL) is capable of learning high-quality representations of complex data without relying on labels. In addition to eliminating the need for labeled data, research has found that SSL improves the adversarial robustness over supervised learning since lacking labels makes it more challenging for adversaries to manipulate model predictions. However, the extent to which this robustness superiority generalizes to other types of attacks remains an open question. We explore this question in the context of backdoor attacks. Specifically, we design and evaluate CTRL, an embarrassingly simple yet highly effective self-supervised backdoor attack. By only polluting a tiny fraction of training data (<= 1%) with indistinguishable poisoning samples, CTRL causes any trigger-embedded input to be misclassified to the adversary's designated class with a high probability (>= 99%) at inference time. Our findings suggest that SSL and supervised learning are comparably vulnerable to backdoor attacks. More importantly, through the lens of CTRL, we study the inherent vulnerability of SSL to backdoor attacks. With both empirical and analytical evidence, we reveal that the representation invariance property of SSL, which benefits adversarial robustness, may also be the very reason making \ssl highly susceptible to backdoor attacks. Our findings also imply that the existing defenses against supervised backdoor attacks are not easily retrofitted to the unique vulnerability of SSL.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

The rapid advancement of large language models (LLMs) introduces dual-use capabilities that could both threaten and bolster national security and public safety (NSPS). Models implement safeguards to protect against potential misuse relevant to NSPS and allow for benign users to receive helpful information. However, current benchmarks often fail to test safeguard robustness to potential NSPS risks in an objective, robust way. We introduce FORTRESS: 500 expert-crafted adversarial prompts with instance-based rubrics of 4-7 binary questions for automated evaluation across 3 domains (unclassified information only): Chemical, Biological, Radiological, Nuclear and Explosive (CBRNE), Political Violence & Terrorism, and Criminal & Financial Illicit Activities, with 10 total subcategories across these domains. Each prompt-rubric pair has a corresponding benign version to test for model over-refusals. This evaluation of frontier LLMs' safeguard robustness reveals varying trade-offs between potential risks and model usefulness: Claude-3.5-Sonnet demonstrates a low average risk score (ARS) (14.09 out of 100) but the highest over-refusal score (ORS) (21.8 out of 100), while Gemini 2.5 Pro shows low over-refusal (1.4) but a high average potential risk (66.29). Deepseek-R1 has the highest ARS at 78.05, but the lowest ORS at only 0.06. Models such as o1 display a more even trade-off between potential risks and over-refusals (with an ARS of 21.69 and ORS of 5.2). To provide policymakers and researchers with a clear understanding of models' potential risks, we publicly release FORTRESS at https://huggingface.co/datasets/ScaleAI/fortress_public. We also maintain a private set for evaluation.

Evaluations of large language model (LLM) risks and capabilities are increasingly being incorporated into AI risk management and governance frameworks. Currently, most risk evaluations are conducted by designing inputs that elicit harmful behaviors from the system. However, a fundamental limitation of this approach is that the harmfulness of the behaviors identified during any particular evaluation can only lower bound the model's worst-possible-case behavior. As a complementary method for eliciting harmful behaviors, we propose evaluating LLMs with model tampering attacks which allow for modifications to latent activations or weights. We pit state-of-the-art techniques for removing harmful LLM capabilities against a suite of 5 input-space and 6 model tampering attacks. In addition to benchmarking these methods against each other, we show that (1) model resilience to capability elicitation attacks lies on a low-dimensional robustness subspace; (2) the attack success rate of model tampering attacks can empirically predict and offer conservative estimates for the success of held-out input-space attacks; and (3) state-of-the-art unlearning methods can easily be undone within 16 steps of fine-tuning. Together these results highlight the difficulty of removing harmful LLM capabilities and show that model tampering attacks enable substantially more rigorous evaluations than input-space attacks alone. We release models at https://huggingface.co/LLM-GAT

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Large Language Models (LLMs) have achieved significant progress in language understanding and reasoning. Evaluating and analyzing their logical reasoning abilities has therefore become essential. However, existing datasets and benchmarks are often limited to overly simplistic, unnatural, or contextually constrained examples. In response to the growing demand, we introduce SmartyPat-Bench, a challenging, naturally expressed, and systematically labeled benchmark derived from real-world high-quality Reddit posts containing subtle logical fallacies. Unlike existing datasets and benchmarks, it provides more detailed annotations of logical fallacies and features more diverse data. To further scale up the study and address the limitations of manual data collection and labeling - such as fallacy-type imbalance and labor-intensive annotation - we introduce SmartyPat, an automated framework powered by logic programming-based oracles. SmartyPat utilizes Prolog rules to systematically generate logically fallacious statements, which are then refined into fluent natural-language sentences by LLMs, ensuring precise fallacy representation. Extensive evaluation demonstrates that SmartyPat produces fallacies comparable in subtlety and quality to human-generated content and significantly outperforms baseline methods. Finally, experiments reveal nuanced insights into LLM capabilities, highlighting that while excessive reasoning steps hinder fallacy detection accuracy, structured reasoning enhances fallacy categorization performance.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have recently achieved impressive results on reasoning benchmarks. Yet, growing evidence shows that these models often generate longer but ineffective chains of thought (CoTs), calling into question whether benchmark gains reflect real reasoning improvements. We present new evidence of overthinking, where models disregard correct solutions even when explicitly provided, instead continuing to generate unnecessary reasoning steps that often lead to incorrect conclusions. Experiments on three state-of-the-art models using the AIME2024 math benchmark reveal critical limitations in these models ability to integrate corrective information, posing new challenges for achieving robust and interpretable reasoning.

In this paper we establish rigorous benchmarks for image classifier robustness. Our first benchmark, ImageNet-C, standardizes and expands the corruption robustness topic, while showing which classifiers are preferable in safety-critical applications. Then we propose a new dataset called ImageNet-P which enables researchers to benchmark a classifier's robustness to common perturbations. Unlike recent robustness research, this benchmark evaluates performance on common corruptions and perturbations not worst-case adversarial perturbations. We find that there are negligible changes in relative corruption robustness from AlexNet classifiers to ResNet classifiers. Afterward we discover ways to enhance corruption and perturbation robustness. We even find that a bypassed adversarial defense provides substantial common perturbation robustness. Together our benchmarks may aid future work toward networks that robustly generalize.

Large Reasoning Models (LRMs) have achieved remarkable success on reasoning-intensive tasks such as mathematics and programming. However, their enhanced reasoning capabilities do not necessarily translate to improved safety performance-and in some cases, may even degrade it. This raises an important research question: how can we enhance the safety of LRMs? In this paper, we present a comprehensive empirical study on how to enhance the safety of LRMs through Supervised Fine-Tuning (SFT). Our investigation begins with an unexpected observation: directly distilling safe responses from DeepSeek-R1 fails to significantly enhance safety. We analyze this phenomenon and identify three key failure patterns that contribute to it. We then demonstrate that explicitly addressing these issues during the data distillation process can lead to substantial safety improvements. Next, we explore whether a long and complex reasoning process is necessary for achieving safety. Interestingly, we find that simply using short or template-based reasoning process can attain comparable safety performance-and are significantly easier for models to learn than more intricate reasoning chains. These findings prompt a deeper reflection on the role of reasoning in ensuring safety. Finally, we find that mixing math reasoning data during safety fine-tuning is helpful to balance safety and over-refusal. Overall, we hope our empirical study could provide a more holistic picture on enhancing the safety of LRMs. The code and data used in our experiments are released in https://github.com/thu-coai/LRM-Safety-Study.

In order to train networks for verified adversarial robustness, it is common to over-approximate the worst-case loss over perturbation regions, resulting in networks that attain verifiability at the expense of standard performance. As shown in recent work, better trade-offs between accuracy and robustness can be obtained by carefully coupling adversarial training with over-approximations. We hypothesize that the expressivity of a loss function, which we formalize as the ability to span a range of trade-offs between lower and upper bounds to the worst-case loss through a single parameter (the over-approximation coefficient), is key to attaining state-of-the-art performance. To support our hypothesis, we show that trivial expressive losses, obtained via convex combinations between adversarial attacks and IBP bounds, yield state-of-the-art results across a variety of settings in spite of their conceptual simplicity. We provide a detailed analysis of the relationship between the over-approximation coefficient and performance profiles across different expressive losses, showing that, while expressivity is essential, better approximations of the worst-case loss are not necessarily linked to superior robustness-accuracy trade-offs.

This paper reviews the state-of-the-art of language models architectures and strategies for "complex" question-answering (QA, CQA, CPS) with a focus on hybridization. Large Language Models (LLM) are good at leveraging public data on standard problems but once you want to tackle more specific complex questions or problems (e.g. How does the concept of personal freedom vary between different cultures ? What is the best mix of power generation methods to reduce climate change ?) you may need specific architecture, knowledge, skills, methods, sensitive data protection, explainability, human approval and versatile feedback... Recent projects like ChatGPT and GALACTICA have allowed non-specialists to grasp the great potential as well as the equally strong limitations of LLM in complex QA. In this paper, we start by reviewing required skills and evaluation techniques. We integrate findings from the robust community edited research papers BIG, BLOOM and HELM which open source, benchmark and analyze limits and challenges of LLM in terms of tasks complexity and strict evaluation on accuracy (e.g. fairness, robustness, toxicity, ...) as a baseline. We discuss some challenges associated with complex QA, including domain adaptation, decomposition and efficient multi-step QA, long form and non-factoid QA, safety and multi-sensitivity data protection, multimodal search, hallucinations, explainability and truthfulness, temporal reasoning. We analyze current solutions and promising research trends, using elements such as: hybrid LLM architectural patterns, training and prompting strategies, active human reinforcement learning supervised with AI, neuro-symbolic and structured knowledge grounding, program synthesis, iterated decomposition and others.

This paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a 'reasoning' function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when the data withholding corresponds to freezing a single feature (referred to as canonical holdout), the generalization error of gradient descent admits a tight characterization in terms of the Boolean influence for several relevant architectures. This is shown on linear models and supported experimentally on other models such as MLPs and Transformers. In particular, this puts forward the hypothesis that for such architectures and for learning logical functions such as PVR functions, GD tends to have an implicit bias towards low-degree representations, which in turn gives the Boolean influence for the generalization error under quadratic loss.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Most works on modeling the conversation history in Conversational Question Answering (CQA) report a single main result on a common CQA benchmark. While existing models show impressive results on CQA leaderboards, it remains unclear whether they are robust to shifts in setting (sometimes to more realistic ones), training data size (e.g. from large to small sets) and domain. In this work, we design and conduct the first large-scale robustness study of history modeling approaches for CQA. We find that high benchmark scores do not necessarily translate to strong robustness, and that various methods can perform extremely differently under different settings. Equipped with the insights from our study, we design a novel prompt-based history modeling approach, and demonstrate its strong robustness across various settings. Our approach is inspired by existing methods that highlight historic answers in the passage. However, instead of highlighting by modifying the passage token embeddings, we add textual prompts directly in the passage text. Our approach is simple, easy-to-plug into practically any model, and highly effective, thus we recommend it as a starting point for future model developers. We also hope that our study and insights will raise awareness to the importance of robustness-focused evaluation, in addition to obtaining high leaderboard scores, leading to better CQA systems.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

In reasoning tasks, even a minor error can cascade into inaccurate results, leading to suboptimal performance of large language models in such domains. Earlier fine-tuning approaches sought to mitigate this by leveraging more precise supervisory signals from human labeling, larger models, or self-sampling, although at a high cost. Conversely, we develop a method that avoids external resources, relying instead on introducing perturbations to the input. Our training approach randomly masks certain tokens within the chain of thought, a technique we found to be particularly effective for reasoning tasks. When applied to fine-tuning with GSM8K, this method achieved a 5% improvement in accuracy over standard supervised fine-tuning with a few codes modified and no additional labeling effort. Furthermore, it is complementary to existing methods. When integrated with related data augmentation methods, it leads to an average improvement of 3% improvement in GSM8K accuracy and 1% improvement in MATH accuracy across five datasets of various quality and size, as well as two base models. We further investigate the mechanisms behind this improvement through case studies and quantitative analysis, suggesting that our approach may provide superior support for the model in capturing long-distance dependencies, especially those related to questions. This enhancement could deepen understanding of premises in questions and prior steps. Our code is available at Github.

This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes low-quality data points, and pairwise noise, which encompasses erroneous data pair associations that affect preference rankings. Utilizing Distributionally Robust Optimization (DRO), we enhance DPO's resilience to these types of noise. Our theoretical insights reveal that DPO inherently embeds DRO principles, conferring robustness to pointwise noise, with the regularization coefficient beta playing a critical role in its noise resistance. Extending this framework, we introduce Distributionally Robustifying DPO (Dr. DPO), which integrates pairwise robustness by optimizing against worst-case pairwise scenarios. The novel hyperparameter beta' in Dr. DPO allows for fine-tuned control over data pair reliability, providing a strategic balance between exploration and exploitation in noisy training environments. Empirical evaluations demonstrate that Dr. DPO substantially improves the quality of generated text and response accuracy in preference datasets, showcasing enhanced performance in both noisy and noise-free settings. The code is available at https://github.com/junkangwu/Dr_DPO.

Prompting methods such as Chain-of-Thought (CoT) have shed new light on enhancing the reasoning capabilities of large language models, and researchers have extensively explored the generation process of rationales and answers. However, they have overlooked the potential challenges posed by the poor quality of reasoning problems, which may influence the reasoning performance significantly. In this work, we propose Self-Polish (SP), a novel method that facilitates the model's problem-solving process by prompting them to progressively refine the given problems to be more comprehensible and solvable. Specifically, the method teaches models to eliminate irrelevant information, rearrange the logic structure and organize local conditions into new ones parallelly. SP is orthogonal to all other prompting methods, making it convenient to integrate with state-of-the-art techniques for further improvement. We conduct thorough experiments on five benchmarks to illustrate the effectiveness of the proposed method. For example, with Text-davinci-003, our method boosts the performance of standard few-shot prompting by 8.0% on GSM8K and 17.8% on MultiArith; it also improves the performance of CoT by 6.0% on GSM8K and 6.0% on MathQA, respectively. Furthermore, our method also showcases impressive performance on robustness evaluation.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Large language models, despite extensive alignment with human values and ethical principles, remain vulnerable to sophisticated jailbreak attacks that exploit their reasoning abilities. Existing safety measures often detect overt malicious intent but fail to address subtle, reasoning-driven vulnerabilities. In this work, we introduce POATE (Polar Opposite query generation, Adversarial Template construction, and Elaboration), a novel jailbreak technique that harnesses contrastive reasoning to provoke unethical responses. POATE crafts semantically opposing intents and integrates them with adversarial templates, steering models toward harmful outputs with remarkable subtlety. We conduct extensive evaluation across six diverse language model families of varying parameter sizes to demonstrate the robustness of the attack, achieving significantly higher attack success rates (~44%) compared to existing methods. To counter this, we propose Intent-Aware CoT and Reverse Thinking CoT, which decompose queries to detect malicious intent and reason in reverse to evaluate and reject harmful responses. These methods enhance reasoning robustness and strengthen the model's defense against adversarial exploits.

Recent large language models (LLMs) have demonstrated remarkable generalization abilities in mathematics and logical reasoning tasks. Prior research indicates that LLMs pre-trained with programming language data exhibit high mathematical and reasoning abilities; however, this causal relationship has not been rigorously tested. Our research aims to verify which programming languages and features during pre-training affect logical inference performance. Specifically, we pre-trained decoder-based language models from scratch using datasets from ten programming languages (e.g., Python, C, Java) and three natural language datasets (Wikipedia, Fineweb, C4) under identical conditions. Thereafter, we evaluated the trained models in a few-shot in-context learning setting on logical reasoning tasks: FLD and bAbi, which do not require commonsense or world knowledge. The results demonstrate that nearly all models trained with programming languages consistently outperform those trained with natural languages, indicating that programming languages contain factors that elicit logic inference performance. In addition, we found that models trained with programming languages exhibit a better ability to follow instructions compared to those trained with natural languages. Further analysis reveals that the depth of Abstract Syntax Trees representing parsed results of programs also affects logical reasoning performance. These findings will offer insights into the essential elements of pre-training for acquiring the foundational abilities of LLMs.

The advent of instruction-tuned Large Language Models designed for coding tasks (Code LLMs) has transformed software engineering practices. However, their robustness against various input challenges remains a critical concern. This study introduces DegradePrompter, a novel method designed to systematically evaluate the robustness of instruction-tuned Code LLMs. We assess the impact of diverse input challenges on the functionality and correctness of generated code using rigorous metrics and established benchmarks. Our comprehensive evaluation includes five state-of-the-art open-source models and three production-grade closed-source models, revealing varying degrees of robustness. Open-source models demonstrate an increased susceptibility to input perturbations, resulting in declines in functional correctness ranging from 12% to 34%. In contrast, commercial models demonstrate relatively greater resilience, with performance degradation ranging from 3% to 24%. To enhance the robustness of the models against these vulnerabilities, we investigate a straightforward yet effective mitigation strategy. Our findings highlight the need for robust defense mechanisms and comprehensive evaluations during both the development and deployment phases to ensure the resilience and reliability of automated code generation systems.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

Byzantine robustness has received significant attention recently given its importance for distributed and federated learning. In spite of this, we identify severe flaws in existing algorithms even when the data across the participants is identically distributed. First, we show realistic examples where current state of the art robust aggregation rules fail to converge even in the absence of any Byzantine attackers. Secondly, we prove that even if the aggregation rules may succeed in limiting the influence of the attackers in a single round, the attackers can couple their attacks across time eventually leading to divergence. To address these issues, we present two surprisingly simple strategies: a new robust iterative clipping procedure, and incorporating worker momentum to overcome time-coupled attacks. This is the first provably robust method for the standard stochastic optimization setting. Our code is open sourced at https://github.com/epfml/byzantine-robust-optimizer.

Adversarial robustness is a research area that has recently received a lot of attention in the quest for trustworthy artificial intelligence. However, recent works on adversarial robustness have focused on supervised learning where it is assumed that labeled data is plentiful. In this paper, we investigate semi-supervised adversarial training where labeled data is scarce. We derive two upper bounds for the robust risk and propose a regularization term for unlabeled data motivated by these two upper bounds. Then, we develop a semi-supervised adversarial training algorithm that combines the proposed regularization term with knowledge distillation using a semi-supervised teacher (i.e., a teacher model trained using a semi-supervised learning algorithm). Our experiments show that our proposed algorithm achieves state-of-the-art performance with significant margins compared to existing algorithms. In particular, compared to supervised learning algorithms, performance of our proposed algorithm is not much worse even when the amount of labeled data is very small. For example, our algorithm with only 8\% labeled data is comparable to supervised adversarial training algorithms that use all labeled data, both in terms of standard and robust accuracies on CIFAR-10.

Given a robust model trained to be resilient to one or multiple types of distribution shifts (e.g., natural image corruptions), how is that "robustness" encoded in the model weights, and how easily can it be disentangled and/or "zero-shot" transferred to some other models? This paper empirically suggests a surprisingly simple answer: linearly - by straightforward model weight arithmetic! We start by drawing several key observations: (1)assuming that we train the same model architecture on both a clean dataset and its corrupted version, resultant weights mostly differ in shallow layers; (2)the weight difference after projection, which we call "Robust Weight Signature" (RWS), appears to be discriminative and indicative of different corruption types; (3)for the same corruption type, the RWSs obtained by one model architecture are highly consistent and transferable across different datasets. We propose a minimalistic model robustness "patching" framework that carries a model trained on clean data together with its pre-extracted RWSs. In this way, injecting certain robustness to the model is reduced to directly adding the corresponding RWS to its weight. We verify our proposed framework to be remarkably (1)lightweight. since RWSs concentrate on the shallowest few layers and we further show they can be painlessly quantized, storing an RWS is up to 13 x more compact than storing the full weight copy; (2)in-situ adjustable. RWSs can be appended as needed and later taken off to restore the intact clean model. We further demonstrate one can linearly re-scale the RWS to control the patched robustness strength; (3)composable. Multiple RWSs can be added simultaneously to patch more comprehensive robustness at once; and (4)transferable. Even when the clean model backbone is continually adapted or updated, RWSs remain as effective patches due to their outstanding cross-dataset transferability.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Mainstream backdoor attack methods typically demand substantial tuning data for poisoning, limiting their practicality and potentially degrading the overall performance when applied to Large Language Models (LLMs). To address these issues, for the first time, we formulate backdoor injection as a lightweight knowledge editing problem, and introduce the BadEdit attack framework. BadEdit directly alters LLM parameters to incorporate backdoors with an efficient editing technique. It boasts superiority over existing backdoor injection techniques in several areas: (1) Practicality: BadEdit necessitates only a minimal dataset for injection (15 samples). (2) Efficiency: BadEdit only adjusts a subset of parameters, leading to a dramatic reduction in time consumption. (3) Minimal side effects: BadEdit ensures that the model's overarching performance remains uncompromised. (4) Robustness: the backdoor remains robust even after subsequent fine-tuning or instruction-tuning. Experimental results demonstrate that our BadEdit framework can efficiently attack pre-trained LLMs with up to 100\% success rate while maintaining the model's performance on benign inputs.

Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning errors in intermediate steps, leading to accumulative errors. In this paper, we propose Deductive Beam Search (DBS), which seamlessly integrates CoT and deductive reasoning with step-wise beam search for LLMs. Our approach deploys a verifier, verifying the deducibility of a reasoning step and its premises, thus alleviating the error accumulation. Furthermore, we introduce a scalable and labor-free data construction method to amplify our model's verification capabilities. Extensive experiments demonstrate that our approach significantly enhances the base performance of LLMs of various scales (7B, 13B, 70B, and ChatGPT) across 8 reasoning datasets from 3 diverse reasoning genres, including arithmetic, commonsense, and symbolic. Moreover, our analysis proves DBS's capability of detecting diverse and subtle reasoning errors and robustness on different model scales.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Large Language Models (LLMs) have demonstrated exceptional proficiency in instruction-following, becoming increasingly crucial across various applications. However, this capability brings with it the risk of prompt injection attacks, where attackers inject instructions into LLMs' input to elicit undesirable actions or content. Understanding the robustness of LLMs against such attacks is vital for their safe implementation. In this work, we establish a benchmark to evaluate the robustness of instruction-following LLMs against prompt injection attacks. Our objective is to determine the extent to which LLMs can be influenced by injected instructions and their ability to differentiate between these injected and original target instructions. Through extensive experiments with leading instruction-following LLMs, we uncover significant vulnerabilities in their robustness to such attacks. Our results indicate that some models are overly tuned to follow any embedded instructions in the prompt, overly focusing on the latter parts of the prompt without fully grasping the entire context. By contrast, models with a better grasp of the context and instruction-following capabilities will potentially be more susceptible to compromise by injected instructions. This underscores the need to shift the focus from merely enhancing LLMs' instruction-following capabilities to improving their overall comprehension of prompts and discernment of instructions that are appropriate to follow. We hope our in-depth analysis offers insights into the underlying causes of these vulnerabilities, aiding in the development of future solutions. Code and data are available at https://github.com/Leezekun/instruction-following-robustness-eval

As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable levels. Addressing this, our work aims to strike a delicate balance between computational efficiency and model accuracy, a persisting challenge in the field. We introduce a novel method that employs core subset selection for reweighting, effectively optimizing both computational time and model performance. By focusing on a strategically selected coreset, our approach offers a robust representation, as it efficiently minimizes the influence of outliers. The re-calibrated weights are then mapped back to and propagated across the entire dataset. Our experimental results substantiate the effectiveness of this approach, underscoring its potential as a scalable and precise solution for model training.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

Recent studies have shown that robustness to adversarial attacks can be transferred across networks. In other words, we can make a weak model more robust with the help of a strong teacher model. We ask if instead of learning from a static teacher, can models "learn together" and "teach each other" to achieve better robustness? In this paper, we study how interactions among models affect robustness via knowledge distillation. We propose mutual adversarial training (MAT), in which multiple models are trained together and share the knowledge of adversarial examples to achieve improved robustness. MAT allows robust models to explore a larger space of adversarial samples, and find more robust feature spaces and decision boundaries. Through extensive experiments on CIFAR-10 and CIFAR-100, we demonstrate that MAT can effectively improve model robustness and outperform state-of-the-art methods under white-box attacks, bringing sim8% accuracy gain to vanilla adversarial training (AT) under PGD-100 attacks. In addition, we show that MAT can also mitigate the robustness trade-off among different perturbation types, bringing as much as 13.1% accuracy gain to AT baselines against the union of l_infty, l_2 and l_1 attacks. These results show the superiority of the proposed method and demonstrate that collaborative learning is an effective strategy for designing robust models.

Instruction following has catalyzed the recent era of Large Language Models (LLMs) and is the foundational skill underpinning more advanced capabilities such as reasoning and agentic behaviors. As tasks grow more challenging, the logic structures embedded in natural language instructions becomes increasingly intricate. However, how well LLMs perform on such logic-rich instructions remains under-explored. We propose LogicIFGen and LogicIFEval. LogicIFGen is a scalable, automated framework for generating verifiable instructions from code functions, which can naturally express rich logic such as conditionals, nesting, recursion, and function calls. We further curate a collection of complex code functions and use LogicIFGen to construct LogicIFEval, a benchmark comprising 426 verifiable logic-rich instructions. Our experiments demonstrate that current state-of-the-art LLMs still struggle to correctly follow the instructions in LogicIFEval. Most LLMs can only follow fewer than 60% of the instructions, revealing significant deficiencies in the instruction-following ability. Code and Benchmark: https://github.com/mianzhang/LogicIF

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks, which are crucial for evaluating and advancing LLMs, are inadequate due to their lack of task complexity, presence of prior knowledge as a confounder, and superficial error analysis. To address these deficiencies, we introduce JustLogic, a synthetically generated deductive reasoning benchmark designed for rigorous evaluation of LLMs. JustLogic is (i) highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures; (ii) prior knowledge independent, eliminating the advantage of models possessing prior knowledge and ensuring that only deductive reasoning is used to answer questions; and (iii) capable of in-depth error analysis on the heterogeneous effects of reasoning depth and argument form on model accuracy. Our experimental results on JustLogic reveal that most state-of-the-art (SOTA) LLMs perform significantly worse than the human average, demonstrating substantial room for model improvement. All code and data are available at https://github.com/michaelchen-lab/JustLogic

Automating software vulnerability detection (SVD) remains a critical challenge in an era of increasingly complex and interdependent software systems. Despite significant advances in Large Language Models (LLMs) for code analysis, prevailing evaluation methodologies often lack the context-aware robustness necessary to capture real-world intricacies and cross-component interactions. To address these limitations, we present VulnSage, a comprehensive evaluation framework and a dataset curated from diverse, large-scale open-source system software projects developed in C/C++. Unlike prior datasets, it leverages a heuristic noise pre-filtering approach combined with LLM-based reasoning to ensure a representative and minimally noisy spectrum of vulnerabilities. The framework supports multi-granular analysis across function, file, and inter-function levels and employs four diverse zero-shot prompt strategies: Baseline, Chain-of-Thought, Think, and Think & Verify. Through this evaluation, we uncover that structured reasoning prompts substantially improve LLM performance, with Think & Verify reducing ambiguous responses from 20.3% to 9.1% while increasing accuracy. We further demonstrate that code-specialized models consistently outperform general-purpose alternatives, with performance varying significantly across vulnerability types, revealing that no single approach universally excels across all security contexts. Link to dataset and codes: https://github.com/Erroristotle/VulnSage.git

Existing works have extensively studied adversarial examples, which are minimal perturbations that can mislead the output of deep neural networks (DNNs) while remaining imperceptible to humans. However, in this work, we reveal the existence of a harmless perturbation space, in which perturbations drawn from this space, regardless of their magnitudes, leave the network output unchanged when applied to inputs. Essentially, the harmless perturbation space emerges from the usage of non-injective functions (linear or non-linear layers) within DNNs, enabling multiple distinct inputs to be mapped to the same output. For linear layers with input dimensions exceeding output dimensions, any linear combination of the orthogonal bases of the nullspace of the parameter consistently yields no change in their output. For non-linear layers, the harmless perturbation space may expand, depending on the properties of the layers and input samples. Inspired by this property of DNNs, we solve for a family of general perturbation spaces that are redundant for the DNN's decision, and can be used to hide sensitive data and serve as a means of model identification. Our work highlights the distinctive robustness of DNNs (i.e., consistency under large magnitude perturbations) in contrast to adversarial examples (vulnerability for small imperceptible noises).

Robust reinforcement learning is the problem of learning control policies that provide optimal worst-case performance against a span of adversarial environments. It is a crucial ingredient for deploying algorithms in real-world scenarios with prevalent environmental uncertainties and has been a long-standing object of attention in the community, without a standardized set of benchmarks. This contribution endeavors to fill this gap. We introduce the Robust Reinforcement Learning Suite (RRLS), a benchmark suite based on Mujoco environments. RRLS provides six continuous control tasks with two types of uncertainty sets for training and evaluation. Our benchmark aims to standardize robust reinforcement learning tasks, facilitating reproducible and comparable experiments, in particular those from recent state-of-the-art contributions, for which we demonstrate the use of RRLS. It is also designed to be easily expandable to new environments. The source code is available at https://github.com/SuReLI/RRLS{https://github.com/SuReLI/RRLS}.

Existing frameworks for assessing robustness of large language models (LLMs) overly depend on specific benchmarks, increasing costs and failing to evaluate performance of LLMs in professional domains due to dataset limitations. This paper proposes a framework that systematically evaluates the robustness of LLMs under adversarial attack scenarios by leveraging knowledge graphs (KGs). Our framework generates original prompts from the triplets of knowledge graphs and creates adversarial prompts by poisoning, assessing the robustness of LLMs through the results of these adversarial attacks. We systematically evaluate the effectiveness of this framework and its modules. Experiments show that adversarial robustness of the ChatGPT family ranks as GPT-4-turbo > GPT-4o > GPT-3.5-turbo, and the robustness of large language models is influenced by the professional domains in which they operate.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt to emulate human language understanding and generation, but their competency in logical reasoning remains limited. This paper seeks to address the philosophical question: How can we effectively teach logical reasoning to LLMs while maintaining a deep understanding of the intricate relationship between language and logic? By focusing on bolstering LLMs' capabilities in logical reasoning, we aim to expand their applicability in law and other logic-intensive disciplines. To this end, we propose a Reinforcement Learning from Logical Feedback (RLLF) approach, which serves as a potential framework for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation methodology, we explore new avenues for research in this domain and contribute to the development of LLMs capable of handling complex legal reasoning tasks while acknowledging the fundamental connection between language and logic.

Why do large language models sometimes output factual inaccuracies and exhibit erroneous reasoning? The brittleness of these models, particularly when executing long chains of reasoning, currently seems to be an inevitable price to pay for their advanced capabilities of coherently synthesizing knowledge, pragmatics, and abstract thought. Towards making sense of this fundamentally unsolved problem, this work identifies and analyzes the phenomenon of attention glitches, in which the Transformer architecture's inductive biases intermittently fail to capture robust reasoning. To isolate the issue, we introduce flip-flop language modeling (FFLM), a parametric family of synthetic benchmarks designed to probe the extrapolative behavior of neural language models. This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques. Our preliminary mechanistic analyses show why the remaining errors may be very difficult to diagnose and resolve. We hypothesize that attention glitches account for (some of) the closed-domain hallucinations in natural LLMs.

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

We study privacy leakage in the reasoning traces of large reasoning models used as personal agents. Unlike final outputs, reasoning traces are often assumed to be internal and safe. We challenge this assumption by showing that reasoning traces frequently contain sensitive user data, which can be extracted via prompt injections or accidentally leak into outputs. Through probing and agentic evaluations, we demonstrate that test-time compute approaches, particularly increased reasoning steps, amplify such leakage. While increasing the budget of those test-time compute approaches makes models more cautious in their final answers, it also leads them to reason more verbosely and leak more in their own thinking. This reveals a core tension: reasoning improves utility but enlarges the privacy attack surface. We argue that safety efforts must extend to the model's internal thinking, not just its outputs.

A fundamental question in adversarial machine learning is whether a robust classifier exists for a given task. A line of research has made some progress towards this goal by studying the concentration of measure, but we argue standard concentration fails to fully characterize the intrinsic robustness of a classification problem since it ignores data labels which are essential to any classification task. Building on a novel definition of label uncertainty, we empirically demonstrate that error regions induced by state-of-the-art models tend to have much higher label uncertainty than randomly-selected subsets. This observation motivates us to adapt a concentration estimation algorithm to account for label uncertainty, resulting in more accurate intrinsic robustness measures for benchmark image classification problems.

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and scalable tools for fine-grained analysis. Existing benchmarks and datasets often lack the necessary variable control for multi-dimensional, systematic analysis and training, or have narrow problem types and formats. To address these limitations, we introduce SATQuest, a systematic verifier designed to evaluate and enhance logical reasoning in LLMs by generating diverse, Satisfiability-based logical reasoning problems directly from Conjunctive Normal Form (CNF) instances. SATQuest structures these problems along three orthogonal dimensions: instance scale, problem type, and question format, employing randomized, SAT-based problem generation and objective answer verification via PySAT. This design mitigates memorization issues, allows for nuanced insights into reasoning performance, and enables effective reinforcement fine-tuning. Our extensive evaluation of various LLMs using SATQuest identified significant limitations in their logical reasoning, particularly in generalizing beyond familiar mathematical formats. Furthermore, we show that reinforcement fine-tuning with SATQuest rewards substantially improves targeted task performance and generalizes to more complex instances, while highlighting remaining challenges in cross-format adaptation. Through these demonstrations, we showcase SATQuest's potential as a foundational tool and a valuable starting point for advancing LLM logical reasoning.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

Instructing large language models (LLMs) to solve elementary school math problems has shown great success using Chain of Thought (CoT). However, the CoT approach relies on an LLM to generate a sequence of arithmetic calculations which can be prone to cascaded calculation errors. We hypothesize that an LLM should focus on extracting predicates and generating symbolic formulas from the math problem description so that the underlying calculation can be done via an external code interpreter. We investigate using LLM to generate Prolog programs to solve mathematical questions. Experimental results show that our Prolog-based arithmetic problem-solving outperforms CoT generation in the GSM8K benchmark across three distinct LLMs. In addition, given the insensitive ordering of predicates and symbolic formulas in Prolog, we propose to permute the ground truth predicates for more robust LLM training via data augmentation.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

We make two contributions in the field of AI fairness over continuous protected attributes. First, we show that the Hirschfeld-Gebelein-Renyi (HGR) indicator (the only one currently available for such a case) is valuable but subject to a few crucial limitations regarding semantics, interpretability, and robustness. Second, we introduce a family of indicators that are: 1) complementary to HGR in terms of semantics; 2) fully interpretable and transparent; 3) robust over finite samples; 4) configurable to suit specific applications. Our approach also allows us to define fine-grained constraints to permit certain types of dependence and forbid others selectively. By expanding the available options for continuous protected attributes, our approach represents a significant contribution to the area of fair artificial intelligence.

Existing efforts to improve logical reasoning ability of language models have predominantly relied on supervised fine-tuning, hindering generalization to new domains and/or tasks. The development of Large Langauge Models (LLMs) has demonstrated the capacity of compressing abundant knowledge into a single proxy, enabling them to tackle multiple tasks effectively. Our preliminary experiments, nevertheless, show that LLMs do not show capability on logical reasoning. The performance of LLMs on logical reasoning benchmarks is far behind the existing state-of-the-art baselines. In this paper, we make the first attempt to investigate the feasibility of incorporating logical knowledge through self-supervised post-training, and activating it via in-context learning, which we termed as LogicLLM. Specifically, we devise an auto-regressive objective variant of MERIt and integrate it with two LLM series, i.e., FLAN-T5 and LLaMA, with parameter size ranging from 3 billion to 13 billion. The results on two challenging logical reasoning benchmarks demonstrate the effectiveness of LogicLLM. Besides, we conduct extensive ablation studies to analyze the key factors in designing logic-oriented proxy tasks.