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byAK and the research community

Sep 3

Grokking as the Transition from Lazy to Rich Training Dynamics

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

WorldPM: Scaling Human Preference Modeling

Motivated by scaling laws in language modeling that demonstrate how test loss scales as a power law with model and dataset sizes, we find that similar laws exist in preference modeling. We propose World Preference Modeling$ (WorldPM) to emphasize this scaling potential, where World Preference embodies a unified representation of human preferences. In this paper, we collect preference data from public forums covering diverse user communities, and conduct extensive training using 15M-scale data across models ranging from 1.5B to 72B parameters. We observe distinct patterns across different evaluation metrics: (1) Adversarial metrics (ability to identify deceptive features) consistently scale up with increased training data and base model size; (2) Objective metrics (objective knowledge with well-defined answers) show emergent behavior in larger language models, highlighting WorldPM's scalability potential; (3) Subjective metrics (subjective preferences from a limited number of humans or AI) do not demonstrate scaling trends. Further experiments validate the effectiveness of WorldPM as a foundation for preference fine-tuning. Through evaluations on 7 benchmarks with 20 subtasks, we find that WorldPM broadly improves the generalization performance across human preference datasets of varying sizes (7K, 100K and 800K samples), with performance gains exceeding 5% on many key subtasks. Integrating WorldPM into our internal RLHF pipeline, we observe significant improvements on both in-house and public evaluation sets, with notable gains of 4% to 8% in our in-house evaluations.

One Epoch Is All You Need

In unsupervised learning, collecting more data is not always a costly process unlike the training. For example, it is not hard to enlarge the 40GB WebText used for training GPT-2 by modifying its sampling methodology considering how many webpages there are in the Internet. On the other hand, given that training on this dataset already costs tens of thousands of dollars, training on a larger dataset naively is not cost-wise feasible. In this paper, we suggest to train on a larger dataset for only one epoch unlike the current practice, in which the unsupervised models are trained for from tens to hundreds of epochs. Furthermore, we suggest to adjust the model size and the number of iterations to be performed appropriately. We show that the performance of Transformer language model becomes dramatically improved in this way, especially if the original number of epochs is greater. For example, by replacing the training for 10 epochs with the one epoch training, this translates to 1.9-3.3x speedup in wall-clock time in our settings and more if the original number of epochs is greater. Under one epoch training, no overfitting occurs, and regularization method does nothing but slows down the training. Also, the curve of test loss over iterations follows power-law extensively. We compare the wall-clock time of the training of models with different parameter budget under one epoch training, and we show that size/iteration adjustment based on our proposed heuristics leads to 1-2.7x speedup in our cases. With the two methods combined, we achieve 3.3-5.1x speedup. Finally, we speculate various implications of one epoch training and size/iteration adjustment. In particular, based on our analysis we believe that we can reduce the cost to train the state-of-the-art models as BERT and GPT-2 dramatically, maybe even by the factor of 10.

GORACS: Group-level Optimal Transport-guided Coreset Selection for LLM-based Recommender Systems

Although large language models (LLMs) have shown great potential in recommender systems, the prohibitive computational costs for fine-tuning LLMs on entire datasets hinder their successful deployment in real-world scenarios. To develop affordable and effective LLM-based recommender systems, we focus on the task of coreset selection which identifies a small subset of fine-tuning data to optimize the test loss, thereby facilitating efficient LLMs' fine-tuning. Although there exist some intuitive solutions of subset selection, including distribution-based and importance-based approaches, they often lead to suboptimal performance due to the misalignment with downstream fine-tuning objectives or weak generalization ability caused by individual-level sample selection. To overcome these challenges, we propose GORACS, which is a novel Group-level Optimal tRAnsport-guided Coreset Selection framework for LLM-based recommender systems. GORACS is designed based on two key principles for coreset selection: 1) selecting the subsets that minimize the test loss to align with fine-tuning objectives, and 2) enhancing model generalization through group-level data selection. Corresponding to these two principles, GORACS has two key components: 1) a Proxy Optimization Objective (POO) leveraging optimal transport and gradient information to bound the intractable test loss, thus reducing computational costs by avoiding repeated LLM retraining, and 2) a two-stage Initialization-Then-Refinement Algorithm (ITRA) for efficient group-level selection. Our extensive experiments across diverse recommendation datasets and tasks validate that GORACS significantly reduces fine-tuning costs of LLMs while achieving superior performance over the state-of-the-art baselines and full data training. The source code of GORACS are available at https://github.com/Mithas-114/GORACS.

Scaling Laws and Interpretability of Learning from Repeated Data

Recent large language models have been trained on vast datasets, but also often on repeated data, either intentionally for the purpose of upweighting higher quality data, or unintentionally because data deduplication is not perfect and the model is exposed to repeated data at the sentence, paragraph, or document level. Some works have reported substantial negative performance effects of this repeated data. In this paper we attempt to study repeated data systematically and to understand its effects mechanistically. To do this, we train a family of models where most of the data is unique but a small fraction of it is repeated many times. We find a strong double descent phenomenon, in which repeated data can lead test loss to increase midway through training. A predictable range of repetition frequency leads to surprisingly severe degradation in performance. For instance, performance of an 800M parameter model can be degraded to that of a 2x smaller model (400M params) by repeating 0.1% of the data 100 times, despite the other 90% of the training tokens remaining unique. We suspect there is a range in the middle where the data can be memorized and doing so consumes a large fraction of the model's capacity, and this may be where the peak of degradation occurs. Finally, we connect these observations to recent mechanistic interpretability work - attempting to reverse engineer the detailed computations performed by the model - by showing that data repetition disproportionately damages copying and internal structures associated with generalization, such as induction heads, providing a possible mechanism for the shift from generalization to memorization. Taken together, these results provide a hypothesis for why repeating a relatively small fraction of data in large language models could lead to disproportionately large harms to performance.

Unraveling the Mystery of Scaling Laws: Part I

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.

S3IM: Stochastic Structural SIMilarity and Its Unreasonable Effectiveness for Neural Fields

Recently, Neural Radiance Field (NeRF) has shown great success in rendering novel-view images of a given scene by learning an implicit representation with only posed RGB images. NeRF and relevant neural field methods (e.g., neural surface representation) typically optimize a point-wise loss and make point-wise predictions, where one data point corresponds to one pixel. Unfortunately, this line of research failed to use the collective supervision of distant pixels, although it is known that pixels in an image or scene can provide rich structural information. To the best of our knowledge, we are the first to design a nonlocal multiplex training paradigm for NeRF and relevant neural field methods via a novel Stochastic Structural SIMilarity (S3IM) loss that processes multiple data points as a whole set instead of process multiple inputs independently. Our extensive experiments demonstrate the unreasonable effectiveness of S3IM in improving NeRF and neural surface representation for nearly free. The improvements of quality metrics can be particularly significant for those relatively difficult tasks: e.g., the test MSE loss unexpectedly drops by more than 90% for TensoRF and DVGO over eight novel view synthesis tasks; a 198% F-score gain and a 64% Chamfer L_{1} distance reduction for NeuS over eight surface reconstruction tasks. Moreover, S3IM is consistently robust even with sparse inputs, corrupted images, and dynamic scenes.

Efficient Test-Time Model Adaptation without Forgetting

Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and testing data by adapting a given model w.r.t. any testing sample. This task is particularly important for deep models when the test environment changes frequently. Although some recent attempts have been made to handle this task, we still face two practical challenges: 1) existing methods have to perform backward computation for each test sample, resulting in unbearable prediction cost to many applications; 2) while existing TTA solutions can significantly improve the test performance on out-of-distribution data, they often suffer from severe performance degradation on in-distribution data after TTA (known as catastrophic forgetting). In this paper, we point out that not all the test samples contribute equally to model adaptation, and high-entropy ones may lead to noisy gradients that could disrupt the model. Motivated by this, we propose an active sample selection criterion to identify reliable and non-redundant samples, on which the model is updated to minimize the entropy loss for test-time adaptation. Furthermore, to alleviate the forgetting issue, we introduce a Fisher regularizer to constrain important model parameters from drastic changes, where the Fisher importance is estimated from test samples with generated pseudo labels. Extensive experiments on CIFAR-10-C, ImageNet-C, and ImageNet-R verify the effectiveness of our proposed method.

A-STAR: Test-time Attention Segregation and Retention for Text-to-image Synthesis

While recent developments in text-to-image generative models have led to a suite of high-performing methods capable of producing creative imagery from free-form text, there are several limitations. By analyzing the cross-attention representations of these models, we notice two key issues. First, for text prompts that contain multiple concepts, there is a significant amount of pixel-space overlap (i.e., same spatial regions) among pairs of different concepts. This eventually leads to the model being unable to distinguish between the two concepts and one of them being ignored in the final generation. Next, while these models attempt to capture all such concepts during the beginning of denoising (e.g., first few steps) as evidenced by cross-attention maps, this knowledge is not retained by the end of denoising (e.g., last few steps). Such loss of knowledge eventually leads to inaccurate generation outputs. To address these issues, our key innovations include two test-time attention-based loss functions that substantially improve the performance of pretrained baseline text-to-image diffusion models. First, our attention segregation loss reduces the cross-attention overlap between attention maps of different concepts in the text prompt, thereby reducing the confusion/conflict among various concepts and the eventual capture of all concepts in the generated output. Next, our attention retention loss explicitly forces text-to-image diffusion models to retain cross-attention information for all concepts across all denoising time steps, thereby leading to reduced information loss and the preservation of all concepts in the generated output.

Lossless Acceleration for Seq2seq Generation with Aggressive Decoding

We study lossless acceleration for seq2seq generation with a novel decoding algorithm -- Aggressive Decoding. Unlike the previous efforts (e.g., non-autoregressive decoding) speeding up seq2seq generation at the cost of quality loss, our approach aims to yield the identical (or better) generation compared with autoregressive decoding but in a significant speedup, achieved by innovative cooperation of aggressive decoding and verification that are both efficient due to parallel computing. We propose two Aggressive Decoding paradigms for 2 kinds of seq2seq tasks: 1) For the seq2seq tasks whose inputs and outputs are highly similar (e.g., Grammatical Error Correction), we propose Input-guided Aggressive Decoding (IAD) that aggressively copies from the input sentence as drafted decoded tokens to verify in parallel; 2) For other general seq2seq tasks (e.g., Machine Translation), we propose Generalized Aggressive Decoding (GAD) that first employs an additional non-autoregressive decoding model for aggressive decoding and then verifies in parallel in the autoregressive manner. We test Aggressive Decoding on the most popular 6-layer Transformer model on GPU in multiple seq2seq tasks: 1) For IAD, we show that it can introduce a 7x-9x speedup for the Transformer in Grammatical Error Correction and Text Simplification tasks with the identical results as greedy decoding; 2) For GAD, we observe a 3x-5x speedup with the identical or even better quality in two important seq2seq tasks: Machine Translation and Abstractive Summarization. Moreover, Aggressive Decoding can benefit even more from stronger computing devices that are better at parallel computing. Given the lossless quality as well as significant and promising speedup, we believe Aggressive Decoding may potentially evolve into a de facto standard for efficient and lossless seq2seq generation in the near future.

Unit Test Case Generation with Transformers and Focal Context

Automated unit test case generation tools facilitate test-driven development and support developers by suggesting tests intended to identify flaws in their code. Existing approaches are usually guided by the test coverage criteria, generating synthetic test cases that are often difficult for developers to read or understand. In this paper we propose AthenaTest, an approach that aims to generate unit test cases by learning from real-world focal methods and developer-written testcases. We formulate unit test case generation as a sequence-to-sequence learning task, adopting a two-step training procedure consisting of denoising pretraining on a large unsupervised Java corpus, and supervised finetuning for a downstream translation task of generating unit tests. We investigate the impact of natural language and source code pretraining, as well as the focal context information surrounding the focal method. Both techniques provide improvements in terms of validation loss, with pretraining yielding 25% relative improvement and focal context providing additional 11.1% improvement. We also introduce Methods2Test, the largest publicly available supervised parallel corpus of unit test case methods and corresponding focal methods in Java, which comprises 780K test cases mined from 91K open-source repositories from GitHub. We evaluate AthenaTest on five defects4j projects, generating 25K passing test cases covering 43.7% of the focal methods with only 30 attempts. We execute the test cases, collect test coverage information, and compare them with test cases generated by EvoSuite and GPT-3, finding that our approach outperforms GPT-3 and has comparable coverage w.r.t. EvoSuite. Finally, we survey professional developers on their preference in terms of readability, understandability, and testing effectiveness of the generated tests, showing overwhelmingly preference towards AthenaTest.

Test-time adaptation with slot-centric models

Current supervised visual detectors, though impressive within their training distribution, often fail to segment out-of-distribution scenes into their constituent entities. Recent test-time adaptation methods use auxiliary self-supervised losses to adapt the network parameters to each test example independently and have shown promising results towards generalization outside the training distribution for the task of image classification. In our work, we find evidence that these losses can be insufficient for instance segmentation tasks, without also considering architectural inductive biases. For image segmentation, recent slot-centric generative models break such dependence on supervision by attempting to segment scenes into entities in a self-supervised manner by reconstructing pixels. Drawing upon these two lines of work, we propose Slot-TTA, a semi-supervised instance segmentation model equipped with a slot-centric inductive bias, that is adapted per scene at test time through gradient descent on reconstruction or novel view synthesis objectives. We show that test-time adaptation in Slot-TTA greatly improves instance segmentation in out-of-distribution scenes. We evaluate Slot-TTA in several 3D and 2D scene instance segmentation benchmarks and show substantial out-of-distribution performance improvements against state-of-the-art supervised feed-forward detectors and self-supervised test-time adaptation methods.

SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.

Individualizing Glioma Radiotherapy Planning by Optimization of Data and Physics-Informed Discrete Loss

Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss (ODIL), where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation (PDE) model, which is adapted for complex cases.

CAFA: Class-Aware Feature Alignment for Test-Time Adaptation

Despite recent advancements in deep learning, deep neural networks continue to suffer from performance degradation when applied to new data that differs from training data. Test-time adaptation (TTA) aims to address this challenge by adapting a model to unlabeled data at test time. TTA can be applied to pretrained networks without modifying their training procedures, enabling them to utilize a well-formed source distribution for adaptation. One possible approach is to align the representation space of test samples to the source distribution (i.e., feature alignment). However, performing feature alignment in TTA is especially challenging in that access to labeled source data is restricted during adaptation. That is, a model does not have a chance to learn test data in a class-discriminative manner, which was feasible in other adaptation tasks (e.g., unsupervised domain adaptation) via supervised losses on the source data. Based on this observation, we propose a simple yet effective feature alignment loss, termed as Class-Aware Feature Alignment (CAFA), which simultaneously 1) encourages a model to learn target representations in a class-discriminative manner and 2) effectively mitigates the distribution shifts at test time. Our method does not require any hyper-parameters or additional losses, which are required in previous approaches. We conduct extensive experiments on 6 different datasets and show our proposed method consistently outperforms existing baselines.

Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Test-time Batch Statistics Calibration for Covariate Shift

Deep neural networks have a clear degradation when applying to the unseen environment due to the covariate shift. Conventional approaches like domain adaptation requires the pre-collected target data for iterative training, which is impractical in real-world applications. In this paper, we propose to adapt the deep models to the novel environment during inference. An previous solution is test time normalization, which substitutes the source statistics in BN layers with the target batch statistics. However, we show that test time normalization may potentially deteriorate the discriminative structures due to the mismatch between target batch statistics and source parameters. To this end, we present a general formulation alpha-BN to calibrate the batch statistics by mixing up the source and target statistics for both alleviating the domain shift and preserving the discriminative structures. Based on alpha-BN, we further present a novel loss function to form a unified test time adaptation framework Core, which performs the pairwise class correlation online optimization. Extensive experiments show that our approaches achieve the state-of-the-art performance on total twelve datasets from three topics, including model robustness to corruptions, domain generalization on image classification and semantic segmentation. Particularly, our alpha-BN improves 28.4\% to 43.9\% on GTA5 rightarrow Cityscapes without any training, even outperforms the latest source-free domain adaptation method.

Threshold-Consistent Margin Loss for Open-World Deep Metric Learning

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

Improved Test-Time Adaptation for Domain Generalization

The main challenge in domain generalization (DG) is to handle the distribution shift problem that lies between the training and test data. Recent studies suggest that test-time training (TTT), which adapts the learned model with test data, might be a promising solution to the problem. Generally, a TTT strategy hinges its performance on two main factors: selecting an appropriate auxiliary TTT task for updating and identifying reliable parameters to update during the test phase. Both previous arts and our experiments indicate that TTT may not improve but be detrimental to the learned model if those two factors are not properly considered. This work addresses those two factors by proposing an Improved Test-Time Adaptation (ITTA) method. First, instead of heuristically defining an auxiliary objective, we propose a learnable consistency loss for the TTT task, which contains learnable parameters that can be adjusted toward better alignment between our TTT task and the main prediction task. Second, we introduce additional adaptive parameters for the trained model, and we suggest only updating the adaptive parameters during the test phase. Through extensive experiments, we show that the proposed two strategies are beneficial for the learned model (see Figure 1), and ITTA could achieve superior performance to the current state-of-the-art methods on several DG benchmarks. Code is available at https://github.com/liangchen527/ITTA.

Dice Loss for Data-imbalanced NLP Tasks

Many NLP tasks such as tagging and machine reading comprehension are faced with the severe data imbalance issue: negative examples significantly outnumber positive examples, and the huge number of background examples (or easy-negative examples) overwhelms the training. The most commonly used cross entropy (CE) criteria is actually an accuracy-oriented objective, and thus creates a discrepancy between training and test: at training time, each training instance contributes equally to the objective function, while at test time F1 score concerns more about positive examples. In this paper, we propose to use dice loss in replacement of the standard cross-entropy objective for data-imbalanced NLP tasks. Dice loss is based on the Sorensen-Dice coefficient or Tversky index, which attaches similar importance to false positives and false negatives, and is more immune to the data-imbalance issue. To further alleviate the dominating influence from easy-negative examples in training, we propose to associate training examples with dynamically adjusted weights to deemphasize easy-negative examples.Theoretical analysis shows that this strategy narrows down the gap between the F1 score in evaluation and the dice loss in training. With the proposed training objective, we observe significant performance boost on a wide range of data imbalanced NLP tasks. Notably, we are able to achieve SOTA results on CTB5, CTB6 and UD1.4 for the part of speech tagging task; SOTA results on CoNLL03, OntoNotes5.0, MSRA and OntoNotes4.0 for the named entity recognition task; along with competitive results on the tasks of machine reading comprehension and paraphrase identification.

Where to find Grokking in LLM Pretraining? Monitor Memorization-to-Generalization without Test

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

Adaptive Dual Uncertainty Optimization: Boosting Monocular 3D Object Detection under Test-Time Shifts

Accurate monocular 3D object detection (M3OD) is pivotal for safety-critical applications like autonomous driving, yet its reliability deteriorates significantly under real-world domain shifts caused by environmental or sensor variations. To address these shifts, Test-Time Adaptation (TTA) methods have emerged, enabling models to adapt to target distributions during inference. While prior TTA approaches recognize the positive correlation between low uncertainty and high generalization ability, they fail to address the dual uncertainty inherent to M3OD: semantic uncertainty (ambiguous class predictions) and geometric uncertainty (unstable spatial localization). To bridge this gap, we propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD. Through a convex optimization lens, we introduce an innovative convex structure of the focal loss and further derive a novel unsupervised version, enabling label-agnostic uncertainty weighting and balanced learning for high-uncertainty objects. In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues, reducing uncertainty from the unstable 3D representation. This dual-branch mechanism forms a complementary loop: enhanced spatial perception improves semantic classification, and robust semantic predictions further refine spatial understanding. Extensive experiments demonstrate the superiority of DUO over existing methods across various datasets and domain shift types.

Robust Mean Teacher for Continual and Gradual Test-Time Adaptation

Since experiencing domain shifts during test-time is inevitable in practice, test-time adaption (TTA) continues to adapt the model after deployment. Recently, the area of continual and gradual test-time adaptation (TTA) emerged. In contrast to standard TTA, continual TTA considers not only a single domain shift, but a sequence of shifts. Gradual TTA further exploits the property that some shifts evolve gradually over time. Since in both settings long test sequences are present, error accumulation needs to be addressed for methods relying on self-training. In this work, we propose and show that in the setting of TTA, the symmetric cross-entropy is better suited as a consistency loss for mean teachers compared to the commonly used cross-entropy. This is justified by our analysis with respect to the (symmetric) cross-entropy's gradient properties. To pull the test feature space closer to the source domain, where the pre-trained model is well posed, contrastive learning is leveraged. Since applications differ in their requirements, we address several settings, including having source data available and the more challenging source-free setting. We demonstrate the effectiveness of our proposed method 'robust mean teacher' (RMT) on the continual and gradual corruption benchmarks CIFAR10C, CIFAR100C, and Imagenet-C. We further consider ImageNet-R and propose a new continual DomainNet-126 benchmark. State-of-the-art results are achieved on all benchmarks.

C3PO: Critical-Layer, Core-Expert, Collaborative Pathway Optimization for Test-Time Expert Re-Mixing

Mixture-of-Experts (MoE) Large Language Models (LLMs) suffer from severely sub-optimal expert pathways-our study reveals that naive expert selection learned from pretraining leaves a surprising 10-20% accuracy gap for improvement. Motivated by this observation, we develop a novel class of test-time optimization methods to re-weight or "re-mixing" the experts in different layers jointly for each test sample. Since the test sample's ground truth is unknown, we propose to optimize a surrogate objective defined by the sample's "successful neighbors" from a reference set of samples. We introduce three surrogates and algorithms based on mode-finding, kernel regression, and the average loss of similar reference samples/tasks. To reduce the cost of optimizing whole pathways, we apply our algorithms merely to the core experts' mixing weights in critical layers, which enjoy similar performance but save significant computation. This leads to "Critical-Layer, Core-Expert, Collaborative Pathway Optimization (C3PO)". We apply C3PO to two recent MoE LLMs and examine it on six widely-used benchmarks. It consistently improves the base model by 7-15% in accuracy and outperforms widely used test-time learning baselines, e.g., in-context learning and prompt/prefix tuning, by a large margin. Moreover, C3PO enables MoE LLMs with 1-3B active parameters to outperform LLMs of 7-9B parameters, hence improving MoE's advantages on efficiency. Our thorough ablation study further sheds novel insights on achieving test-time improvement on MoE.

SuSana Distancia is all you need: Enforcing class separability in metric learning via two novel distance-based loss functions for few-shot image classification

Few-shot learning is a challenging area of research that aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches leverage the meta-learning approach, which is encompassed by episodic tasks that make use a support (training) and query set (test) with the objective of learning a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. Previous works have addressed this problem using metric learning approaches, but the properties of the underlying latent space and the separability of the difference classes on it was not entirely enforced. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function, which we dub ICNN loss is based on an inter and intra class nearest neighbors score, which help us to assess the quality of embeddings obtained from the trained network. Our results, obtained from a extensive experimental setup show a significant improvement in accuracy in the miniImagenNet benchmark compared to other metric-based few-shot learning methods by a margin of 2%, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes. In our experiments, we demonstrate competitive generalization capabilities to other domains, such as the Caltech CUB, Dogs and Cars datasets compared with the state of the art.

Constructing interval variables via faceted Rasch measurement and multitask deep learning: a hate speech application

We propose a general method for measuring complex variables on a continuous, interval spectrum by combining supervised deep learning with the Constructing Measures approach to faceted Rasch item response theory (IRT). We decompose the target construct, hate speech in our case, into multiple constituent components that are labeled as ordinal survey items. Those survey responses are transformed via IRT into a debiased, continuous outcome measure. Our method estimates the survey interpretation bias of the human labelers and eliminates that influence on the generated continuous measure. We further estimate the response quality of each labeler using faceted IRT, allowing responses from low-quality labelers to be removed. Our faceted Rasch scaling procedure integrates naturally with a multitask deep learning architecture for automated prediction on new data. The ratings on the theorized components of the target outcome are used as supervised, ordinal variables for the neural networks' internal concept learning. We test the use of an activation function (ordinal softmax) and loss function (ordinal cross-entropy) designed to exploit the structure of ordinal outcome variables. Our multitask architecture leads to a new form of model interpretation because each continuous prediction can be directly explained by the constituent components in the penultimate layer. We demonstrate this new method on a dataset of 50,000 social media comments sourced from YouTube, Twitter, and Reddit and labeled by 11,000 U.S.-based Amazon Mechanical Turk workers to measure a continuous spectrum from hate speech to counterspeech. We evaluate Universal Sentence Encoders, BERT, and RoBERTa as language representation models for the comment text, and compare our predictive accuracy to Google Jigsaw's Perspective API models, showing significant improvement over this standard benchmark.

Scaling Laws for Neural Machine Translation

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

Automatically Interpreting Millions of Features in Large Language Models

While the activations of neurons in deep neural networks usually do not have a simple human-understandable interpretation, sparse autoencoders (SAEs) can be used to transform these activations into a higher-dimensional latent space which may be more easily interpretable. However, these SAEs can have millions of distinct latent features, making it infeasible for humans to manually interpret each one. In this work, we build an open-source automated pipeline to generate and evaluate natural language explanations for SAE features using LLMs. We test our framework on SAEs of varying sizes, activation functions, and losses, trained on two different open-weight LLMs. We introduce five new techniques to score the quality of explanations that are cheaper to run than the previous state of the art. One of these techniques, intervention scoring, evaluates the interpretability of the effects of intervening on a feature, which we find explains features that are not recalled by existing methods. We propose guidelines for generating better explanations that remain valid for a broader set of activating contexts, and discuss pitfalls with existing scoring techniques. We use our explanations to measure the semantic similarity of independently trained SAEs, and find that SAEs trained on nearby layers of the residual stream are highly similar. Our large-scale analysis confirms that SAE latents are indeed much more interpretable than neurons, even when neurons are sparsified using top-k postprocessing. Our code is available at https://github.com/EleutherAI/sae-auto-interp, and our explanations are available at https://huggingface.co/datasets/EleutherAI/auto_interp_explanations.

Can we learn better with hard samples?

In deep learning, mini-batch training is commonly used to optimize network parameters. However, the traditional mini-batch method may not learn the under-represented samples and complex patterns in the data, leading to a longer time for generalization. To address this problem, a variant of the traditional algorithm has been proposed, which trains the network focusing on mini-batches with high loss. The study evaluates the effectiveness of the proposed training using various deep neural networks trained on three benchmark datasets (CIFAR-10, CIFAR-100, and STL-10). The deep neural networks used in the study are ResNet-18, ResNet-50, Efficient Net B4, EfficientNetV2-S, and MobilenetV3-S. The experimental results showed that the proposed method can significantly improve the test accuracy and speed up the convergence compared to the traditional mini-batch training method. Furthermore, we introduce a hyper-parameter delta ({\delta}) that decides how many mini-batches are considered for training. Experiments on various values of {\delta} found that the performance of the proposed method for smaller {\delta} values generally results in similar test accuracy and faster generalization. We show that the proposed method generalizes in 26.47% less number of epochs than the traditional mini-batch method in EfficientNet-B4 on STL-10. The proposed method also improves the test top-1 accuracy by 7.26% in ResNet-18 on CIFAR-100.

Applying Spatiotemporal Attention to Identify Distracted and Drowsy Driving with Vision Transformers

A 20% rise in car crashes in 2021 compared to 2020 has been observed as a result of increased distraction and drowsiness. Drowsy and distracted driving are the cause of 45% of all car crashes. As a means to decrease drowsy and distracted driving, detection methods using computer vision can be designed to be low-cost, accurate, and minimally invasive. This work investigated the use of the vision transformer to outperform state-of-the-art accuracy from 3D-CNNs. Two separate transformers were trained for drowsiness and distractedness. The drowsy video transformer model was trained on the National Tsing-Hua University Drowsy Driving Dataset (NTHU-DDD) with a Video Swin Transformer model for 10 epochs on two classes -- drowsy and non-drowsy simulated over 10.5 hours. The distracted video transformer was trained on the Driver Monitoring Dataset (DMD) with Video Swin Transformer for 50 epochs over 9 distraction-related classes. The accuracy of the drowsiness model reached 44% and a high loss value on the test set, indicating overfitting and poor model performance. Overfitting indicates limited training data and applied model architecture lacked quantifiable parameters to learn. The distracted model outperformed state-of-the-art models on DMD reaching 97.5%, indicating that with sufficient data and a strong architecture, transformers are suitable for unfit driving detection. Future research should use newer and stronger models such as TokenLearner to achieve higher accuracy and efficiency, merge existing datasets to expand to detecting drunk driving and road rage to create a comprehensive solution to prevent traffic crashes, and deploying a functioning prototype to revolutionize the automotive safety industry.

Optimal Sparsity of Mixture-of-Experts Language Models for Reasoning Tasks

Empirical scaling laws have driven the evolution of large language models (LLMs), yet their coefficients shift whenever the model architecture or data pipeline changes. Mixture-of-Experts (MoE) models, now standard in state-of-the-art systems, introduce a new sparsity dimension that current dense-model frontiers overlook. We investigate how MoE sparsity influences two distinct capability regimes: memorization and reasoning. We train families of MoE Transformers that systematically vary total parameters, active parameters, and top-k routing while holding the compute budget fixed. For every model we record pre-training loss, downstream task loss, and task accuracy, allowing us to separate the train-test generalization gap from the loss-accuracy gap. Memorization benchmarks improve monotonically with total parameters, mirroring training loss. By contrast, reasoning performance saturates and can even regress despite continued gains in both total parameters and training loss. Altering top-k alone has little effect when active parameters are constant, and classic hyperparameters such as learning rate and initialization modulate the generalization gap in the same direction as sparsity. Neither post-training reinforcement learning (GRPO) nor extra test-time compute rescues the reasoning deficit of overly sparse models. Our model checkpoints, code and logs are open-source at https://github.com/rioyokotalab/optimal-sparsity.

AI-Generated Text Detection and Classification Based on BERT Deep Learning Algorithm

AI-generated text detection plays an increasingly important role in various fields. In this study, we developed an efficient AI-generated text detection model based on the BERT algorithm, which provides new ideas and methods for solving related problems. In the data preprocessing stage, a series of steps were taken to process the text, including operations such as converting to lowercase, word splitting, removing stop words, stemming extraction, removing digits, and eliminating redundant spaces, to ensure data quality and accuracy. By dividing the dataset into a training set and a test set in the ratio of 60% and 40%, and observing the changes in the accuracy and loss values during the training process, we found that the model performed well during the training process. The accuracy increases steadily from the initial 94.78% to 99.72%, while the loss value decreases from 0.261 to 0.021 and converges gradually, which indicates that the BERT model is able to detect AI-generated text with high accuracy and the prediction results are gradually approaching the real classification results. Further analysis of the results of the training and test sets reveals that in terms of loss value, the average loss of the training set is 0.0565, while the average loss of the test set is 0.0917, showing a slightly higher loss value. As for the accuracy, the average accuracy of the training set reaches 98.1%, while the average accuracy of the test set is 97.71%, which is not much different from each other, indicating that the model has good generalisation ability. In conclusion, the AI-generated text detection model based on the BERT algorithm proposed in this study shows high accuracy and stability in experiments, providing an effective solution for related fields.

GM-DF: Generalized Multi-Scenario Deepfake Detection

Existing face forgery detection usually follows the paradigm of training models in a single domain, which leads to limited generalization capacity when unseen scenarios and unknown attacks occur. In this paper, we elaborately investigate the generalization capacity of deepfake detection models when jointly trained on multiple face forgery detection datasets. We first find a rapid degradation of detection accuracy when models are directly trained on combined datasets due to the discrepancy across collection scenarios and generation methods. To address the above issue, a Generalized Multi-Scenario Deepfake Detection framework (GM-DF) is proposed to serve multiple real-world scenarios by a unified model. First, we propose a hybrid expert modeling approach for domain-specific real/forgery feature extraction. Besides, as for the commonality representation, we use CLIP to extract the common features for better aligning visual and textual features across domains. Meanwhile, we introduce a masked image reconstruction mechanism to force models to capture rich forged details. Finally, we supervise the models via a domain-aware meta-learning strategy to further enhance their generalization capacities. Specifically, we design a novel domain alignment loss to strongly align the distributions of the meta-test domains and meta-train domains. Thus, the updated models are able to represent both specific and common real/forgery features across multiple datasets. In consideration of the lack of study of multi-dataset training, we establish a new benchmark leveraging multi-source data to fairly evaluate the models' generalization capacity on unseen scenarios. Both qualitative and quantitative experiments on five datasets conducted on traditional protocols as well as the proposed benchmark demonstrate the effectiveness of our approach.

DreamVideo-2: Zero-Shot Subject-Driven Video Customization with Precise Motion Control

Recent advances in customized video generation have enabled users to create videos tailored to both specific subjects and motion trajectories. However, existing methods often require complicated test-time fine-tuning and struggle with balancing subject learning and motion control, limiting their real-world applications. In this paper, we present DreamVideo-2, a zero-shot video customization framework capable of generating videos with a specific subject and motion trajectory, guided by a single image and a bounding box sequence, respectively, and without the need for test-time fine-tuning. Specifically, we introduce reference attention, which leverages the model's inherent capabilities for subject learning, and devise a mask-guided motion module to achieve precise motion control by fully utilizing the robust motion signal of box masks derived from bounding boxes. While these two components achieve their intended functions, we empirically observe that motion control tends to dominate over subject learning. To address this, we propose two key designs: 1) the masked reference attention, which integrates a blended latent mask modeling scheme into reference attention to enhance subject representations at the desired positions, and 2) a reweighted diffusion loss, which differentiates the contributions of regions inside and outside the bounding boxes to ensure a balance between subject and motion control. Extensive experimental results on a newly curated dataset demonstrate that DreamVideo-2 outperforms state-of-the-art methods in both subject customization and motion control. The dataset, code, and models will be made publicly available.

General-Purpose In-Context Learning by Meta-Learning Transformers

Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general-purpose in-context learning algorithms from scratch, using only black-box models with minimal inductive bias. Such a model takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general-purpose in-context learners. We characterize transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks, and meta-optimization. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size (memory) determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general-purpose in-context learning algorithms.

Neural Common Neighbor with Completion for Link Prediction

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor.

Toward a Holistic Evaluation of Robustness in CLIP Models

Contrastive Language-Image Pre-training (CLIP) models have shown significant potential, particularly in zero-shot classification across diverse distribution shifts. Building on existing evaluations of overall classification robustness, this work aims to provide a more comprehensive assessment of CLIP by introducing several new perspectives. First, we investigate their robustness to variations in specific visual factors. Second, we assess two critical safety objectives--confidence uncertainty and out-of-distribution detection--beyond mere classification accuracy. Third, we evaluate the finesse with which CLIP models bridge the image and text modalities. Fourth, we extend our examination to 3D awareness in CLIP models, moving beyond traditional 2D image understanding. Finally, we explore the interaction between vision and language encoders within modern large multimodal models (LMMs) that utilize CLIP as the visual backbone, focusing on how this interaction impacts classification robustness. In each aspect, we consider the impact of six factors on CLIP models: model architecture, training distribution, training set size, fine-tuning, contrastive loss, and test-time prompts. Our study uncovers several previously unknown insights into CLIP. For instance, the architecture of the visual encoder in CLIP plays a significant role in their robustness against 3D corruption. CLIP models tend to exhibit a bias towards shape when making predictions. Moreover, this bias tends to diminish after fine-tuning on ImageNet. Vision-language models like LLaVA, leveraging the CLIP vision encoder, could exhibit benefits in classification performance for challenging categories over CLIP alone. Our findings are poised to offer valuable guidance for enhancing the robustness and reliability of CLIP models.

Optimizing Calibration by Gaining Aware of Prediction Correctness

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

More is Better in Modern Machine Learning: when Infinite Overparameterization is Optimal and Overfitting is Obligatory

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and the number of samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is obligatory: near-optimal performance can only be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural tangent kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization, overfitting, and more data in random feature models.

Learning Hierarchical Polynomials with Three-Layer Neural Networks

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In this work, we propose to address these challenges from a causal representation perspective. We first introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables, namely invariant variables, style confounders, and spurious features. We then introduce a learning framework that treats each group separately: (i) unlike the common practice mixing datasets collected from different locations, we exploit their subtle distinctions by means of an invariance loss encouraging the model to suppress spurious correlations; (ii) we devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a sparse causal graph; (iii) we introduce a style contrastive loss that not only enforces the structure of style representations but also serves as a self-supervisory signal for test-time refinement on the fly. Experiments on synthetic and real datasets show that our proposed method improves the robustness and reusability of learned motion representations, significantly outperforming prior state-of-the-art motion forecasting models for out-of-distribution generalization and low-shot transfer.

TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. TopoMortar enables to investigate in two ways whether methods incorporate prior topological knowledge. First, by eliminating challenges seen in real-world data, such as small training set, noisy labels, and out-of-distribution test-set images, that, as we show, impact the effectiveness of topology losses. Second, by allowing to assess in the same dataset topology accuracy across dataset challenges, isolating dataset-related effects from the effect of incorporating prior topological knowledge. In these two experiments, it is deliberately difficult to improve topology accuracy without actually using topology information, thus, permitting to attribute an improvement in topology accuracy to the incorporation of prior topological knowledge. To this end, TopoMortar includes three types of labels (accurate, noisy, pseudo-labels), two fixed training sets (large and small), and in-distribution and out-of-distribution test-set images. We compared eight loss functions on TopoMortar, and we found that clDice achieved the most topologically accurate segmentations, Skeleton Recall loss performed best particularly with noisy labels, and the relative advantageousness of the other loss functions depended on the experimental setting. Additionally, we show that simple methods, such as data augmentation and self-distillation, can elevate Cross entropy Dice loss to surpass most topology loss functions, and that those simple methods can enhance topology loss functions as well. clDice and Skeleton Recall loss, both skeletonization-based loss functions, were also the fastest to train, making this type of loss function a promising research direction. TopoMortar and our code can be found at https://github.com/jmlipman/TopoMortar