Daily Papers

This study presents PARROT (Persuasion and Agreement Robustness Rating of Output Truth), a robustness focused framework designed to measure the degradation in accuracy that occurs under social pressure exerted on users through authority and persuasion in large language models (LLMs) the phenomenon of sycophancy (excessive conformity). PARROT (i) isolates causal effects by comparing the neutral version of the same question with an authoritatively false version using a double-blind evaluation, (ii) quantifies confidence shifts toward the correct and imposed false responses using log-likelihood-based calibration tracking, and (iii) systematically classifies failure modes (e.g., robust correct, sycophantic agreement, reinforced error, stubborn error, self-correction, etc.) using an eight-state behavioral taxonomy. We evaluated 22 models using 1,302 MMLU-style multiple-choice questions across 13 domains and domain-specific authority templates. Findings show marked heterogeneity: advanced models (e.g., GPT-5, GPT-4.1, Claude Sonnet 4.5) exhibit low "follow rates" (leq 11%, GPT-5: 4\%) and minimal accuracy loss, while older/smaller models show severe epistemic collapse (GPT-4: 80\%, Qwen 2.5-1.5B: 94\%). The danger is not limited to response changes; weak models reduce confidence in the correct response while increasing confidence in the imposed incorrect response. While international law and global knowledge at the domain level exhibit high fragility, elementary mathematics is relatively resilient. Consequently, we argue that the goal of "resistance to overfitting pressure" should be addressed as a primary objective alongside accuracy, harm avoidance, and privacy for safe deployment in the real world.

Understanding how overparameterized neural networks generalize despite perfect interpolation of noisy training data is a fundamental question. Mallinar et. al. 2022 noted that neural networks seem to often exhibit ``tempered overfitting'', wherein the population risk does not converge to the Bayes optimal error, but neither does it approach infinity, yielding non-trivial generalization. However, this has not been studied rigorously. We provide the first rigorous analysis of the overfitting behavior of regression with minimum norm (ell_2 of weights), focusing on univariate two-layer ReLU networks. We show overfitting is tempered (with high probability) when measured with respect to the L_1 loss, but also show that the situation is more complex than suggested by Mallinar et. al., and overfitting is catastrophic with respect to the L_2 loss, or when taking an expectation over the training set.

Overfitting negatively impacts the generalization ability of deep neural networks (DNNs) in both natural and adversarial training. Existing methods struggle to consistently address different types of overfitting, typically designing strategies that focus separately on either natural or adversarial patterns. In this work, we adopt a unified perspective by solely focusing on natural patterns to explore different types of overfitting. Specifically, we examine the memorization effect in DNNs and reveal a shared behaviour termed over-memorization, which impairs their generalization capacity. This behaviour manifests as DNNs suddenly becoming high-confidence in predicting certain training patterns and retaining a persistent memory for them. Furthermore, when DNNs over-memorize an adversarial pattern, they tend to simultaneously exhibit high-confidence prediction for the corresponding natural pattern. These findings motivate us to holistically mitigate different types of overfitting by hindering the DNNs from over-memorization natural patterns. To this end, we propose a general framework, Distraction Over-Memorization (DOM), which explicitly prevents over-memorization by either removing or augmenting the high-confidence natural patterns. Extensive experiments demonstrate the effectiveness of our proposed method in mitigating overfitting across various training paradigms.

Deep neural networks are susceptible to adversarial attacks, which can compromise their performance and accuracy. Adversarial Training (AT) has emerged as a popular approach for protecting neural networks against such attacks. However, a key challenge of AT is robust overfitting, where the network's robust performance on test data deteriorates with further training, thus hindering generalization. Motivated by the concept of active forgetting in the brain, we introduce a novel learning paradigm called "Forget to Mitigate Overfitting (FOMO)". FOMO alternates between the forgetting phase, which randomly forgets a subset of weights and regulates the model's information through weight reinitialization, and the relearning phase, which emphasizes learning generalizable features. Our experiments on benchmark datasets and adversarial attacks show that FOMO alleviates robust overfitting by significantly reducing the gap between the best and last robust test accuracy while improving the state-of-the-art robustness. Furthermore, FOMO provides a better trade-off between standard and robust accuracy, outperforming baseline adversarial methods. Finally, our framework is robust to AutoAttacks and increases generalization in many real-world scenarios.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

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.

Machine learning models that are overfitted/overtrained are more vulnerable to knowledge leakage, which poses a risk to privacy. Suppose we download or receive a model from a third-party collaborator without knowing its training accuracy. How can we determine if it has been overfitted or overtrained on its training data? It's possible that the model was intentionally over-trained to make it vulnerable during testing. While an overfitted or overtrained model may perform well on testing data and even some generalization tests, we can't be sure it's not over-fitted. Conducting a comprehensive generalization test is also expensive. The goal of this paper is to address these issues and ensure the privacy and generalization of our method using only testing data. To achieve this, we analyze the null space in the last layer of neural networks, which enables us to quantify overfitting without access to training data or knowledge of the accuracy of those data. We evaluated our approach on various architectures and datasets and observed a distinct pattern in the angle of null space when models are overfitted. Furthermore, we show that models with poor generalization exhibit specific characteristics in this space. Our work represents the first attempt to quantify overfitting without access to training data or knowing any knowledge about the training samples.

Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes. Understanding and mitigating oversquashing has recently received significant attention from the research community. In this paper, we continue this line of work by analyzing oversquashing through the lens of the effective resistance between nodes in the input graph. Effective resistance intuitively captures the ``strength'' of connection between two nodes by paths in the graph, and has a rich literature spanning many areas of graph theory. We propose to use total effective resistance as a bound of the total amount of oversquashing in a graph and provide theoretical justification for its use. We further develop an algorithm to identify edges to be added to an input graph to minimize the total effective resistance, thereby alleviating oversquashing. We provide empirical evidence of the effectiveness of our total effective resistance based rewiring strategies for improving the performance of GNNs.

Generalist foundation models such as GPT-4 have displayed surprising capabilities in a wide variety of domains and tasks. Yet, there is a prevalent assumption that they cannot match specialist capabilities of fine-tuned models. For example, most explorations to date on medical competency benchmarks have leveraged domain-specific training, as exemplified by efforts on BioGPT and Med-PaLM. We build on a prior study of GPT-4's capabilities on medical challenge benchmarks in the absence of special training. Rather than using simple prompting to highlight the model's out-of-the-box capabilities, we perform a systematic exploration of prompt engineering. We find that prompting innovation can unlock deeper specialist capabilities and show that GPT-4 easily tops prior leading results for medical benchmarks. The prompting methods we explore are general purpose, and make no specific use of domain expertise, removing the need for expert-curated content. Our experimental design carefully controls for overfitting during the prompt engineering process. We introduce Medprompt, based on a composition of several prompting strategies. With Medprompt, GPT-4 achieves state-of-the-art results on all nine of the benchmark datasets in the MultiMedQA suite. The method outperforms leading specialist models such as Med-PaLM 2 by a significant margin with an order of magnitude fewer calls to the model. Steering GPT-4 with Medprompt achieves a 27% reduction in error rate on the MedQA dataset over the best methods to date achieved with specialist models and surpasses a score of 90% for the first time. Beyond medical problems, we show the power of Medprompt to generalize to other domains and provide evidence for the broad applicability of the approach via studies of the strategy on exams in electrical engineering, machine learning, philosophy, accounting, law, nursing, and clinical psychology.

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly with respect to the input, this is however lost in single-step AT. To address CO in single-step AT, several methods have been proposed to enforce local linearity of the loss via regularization. However, these regularization terms considerably slow down training due to Double Backpropagation. Instead, in this work, we introduce a regularization term, called ELLE, to mitigate CO effectively and efficiently in classical AT evaluations, as well as some more difficult regimes, e.g., large adversarial perturbations and long training schedules. Our regularization term can be theoretically linked to curvature of the loss function and is computationally cheaper than previous methods by avoiding Double Backpropagation. Our thorough experimental validation demonstrates that our work does not suffer from CO, even in challenging settings where previous works suffer from it. We also notice that adapting our regularization parameter during training (ELLE-A) greatly improves the performance, specially in large epsilon setups. Our implementation is available in https://github.com/LIONS-EPFL/ELLE .

We build four new test sets for the Stanford Question Answering Dataset (SQuAD) and evaluate the ability of question-answering systems to generalize to new data. Our first test set is from the original Wikipedia domain and measures the extent to which existing systems overfit the original test set. Despite several years of heavy test set re-use, we find no evidence of adaptive overfitting. The remaining three test sets are constructed from New York Times articles, Reddit posts, and Amazon product reviews and measure robustness to natural distribution shifts. Across a broad range of models, we observe average performance drops of 3.8, 14.0, and 17.4 F1 points, respectively. In contrast, a strong human baseline matches or exceeds the performance of SQuAD models on the original domain and exhibits little to no drop in new domains. Taken together, our results confirm the surprising resilience of the holdout method and emphasize the need to move towards evaluation metrics that incorporate robustness to natural distribution shifts.

We introduce the Overfitting-Underfitting Indicator (OUI), a novel tool for monitoring the training dynamics of Deep Neural Networks (DNNs) and identifying optimal regularization hyperparameters. Specifically, we validate that OUI can effectively guide the selection of the Weight Decay (WD) hyperparameter by indicating whether a model is overfitting or underfitting during training without requiring validation data. Through experiments on DenseNet-BC-100 with CIFAR- 100, EfficientNet-B0 with TinyImageNet and ResNet-34 with ImageNet-1K, we show that maintaining OUI within a prescribed interval correlates strongly with improved generalization and validation scores. Notably, OUI converges significantly faster than traditional metrics such as loss or accuracy, enabling practitioners to identify optimal WD (hyperparameter) values within the early stages of training. By leveraging OUI as a reliable indicator, we can determine early in training whether the chosen WD value leads the model to underfit the training data, overfit, or strike a well-balanced trade-off that maximizes validation scores. This enables more precise WD tuning for optimal performance on the tested datasets and DNNs. All code for reproducing these experiments is available at https://github.com/AlbertoFdezHdez/OUI.

Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, \ie the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth.

Catastrophic overfitting (CO) presents a significant challenge in single-step adversarial training (AT), manifesting as highly distorted deep neural networks (DNNs) that are vulnerable to multi-step adversarial attacks. However, the underlying factors that lead to the distortion of decision boundaries remain unclear. In this work, we delve into the specific changes within different DNN layers and discover that during CO, the former layers are more susceptible, experiencing earlier and greater distortion, while the latter layers show relative insensitivity. Our analysis further reveals that this increased sensitivity in former layers stems from the formation of pseudo-robust shortcuts, which alone can impeccably defend against single-step adversarial attacks but bypass genuine-robust learning, resulting in distorted decision boundaries. Eliminating these shortcuts can partially restore robustness in DNNs from the CO state, thereby verifying that dependence on them triggers the occurrence of CO. This understanding motivates us to implement adaptive weight perturbations across different layers to hinder the generation of pseudo-robust shortcuts, consequently mitigating CO. Extensive experiments demonstrate that our proposed method, Layer-Aware Adversarial Weight Perturbation (LAP), can effectively prevent CO and further enhance robustness.

Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can sometimes be benign. Second, they can undergo a period of classical, harmful overfitting -- achieving a perfect fit to training data with near-random performance on test data -- before transitioning ("grokking") to near-optimal generalization later in training. In this work, we show that both of these phenomena provably occur in two-layer ReLU networks trained by GD on XOR cluster data where a constant fraction of the training labels are flipped. In this setting, we show that after the first step of GD, the network achieves 100% training accuracy, perfectly fitting the noisy labels in the training data, but achieves near-random test accuracy. At a later training step, the network achieves near-optimal test accuracy while still fitting the random labels in the training data, exhibiting a "grokking" phenomenon. This provides the first theoretical result of benign overfitting in neural network classification when the data distribution is not linearly separable. Our proofs rely on analyzing the feature learning process under GD, which reveals that the network implements a non-generalizable linear classifier after one step and gradually learns generalizable features in later steps.

In living organisms, homeostasis is the natural regulation of internal states aimed at maintaining conditions compatible with life. Typical artificial systems are not equipped with comparable regulatory features. Here, we introduce an artificial neural network that incorporates homeostatic features. Its own computing substrate is placed in a needful and vulnerable relation to the very objects over which it computes. For example, artificial neurons performing classification of MNIST digits or Fashion-MNIST articles of clothing may receive excitatory or inhibitory effects, which alter their own learning rate as a direct result of perceiving and classifying the digits. In this scenario, accurate recognition is desirable to the agent itself because it guides decisions to regulate its vulnerable internal states and functionality. Counterintuitively, the addition of vulnerability to a learner does not necessarily impair its performance. On the contrary, self-regulation in response to vulnerability confers benefits under certain conditions. We show that homeostatic design confers increased adaptability under concept shift, in which the relationships between labels and data change over time, and that the greatest advantages are obtained under the highest rates of shift. This necessitates the rapid un-learning of past associations and the re-learning of new ones. We also demonstrate the superior abilities of homeostatic learners in environments with dynamically changing rates of concept shift. Our homeostatic design exposes the artificial neural network's thinking machinery to the consequences of its own "thoughts", illustrating the advantage of putting one's own "skin in the game" to improve fluid intelligence.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

A ventilator simulation system can make mechanical ventilation easier and more effective. As a result, predicting a patient's ventilator pressure is essential when designing a simulation ventilator. We suggested a hybrid deep learning-based approach to forecast required ventilator pressure for patients. This system is made up of Bi-LSTM and Bi-GRU networks. The SELU activation function was used in our proposed model. MAE and MSE were used to examine the accuracy of the proposed model so that our proposed methodology can be applied to real-world problems. The model performed well against test data and created far too few losses. Major parts of our research were data collection, data analysis, data cleaning, building hybrid Bi-LSTM and Bi-GRU model, training the model, model evaluation, and result analysis. We compared the results of our research with some contemporary works, and our proposed model performed better than those models.

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.

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.

Large Language Models (LLMs) require careful safety alignment to prevent malicious outputs. While significant research focuses on mitigating harmful content generation, the enhanced safety often come with the side effect of over-refusal, where LLMs may reject innocuous prompts and become less helpful. Although the issue of over-refusal has been empirically observed, a systematic measurement is challenging due to the difficulty of crafting prompts that appear harmful but are benign. This study proposes a novel method for automatically generating large-scale sets of "seemingly toxic prompts" (benign prompts likely rejected by LLMs). Leveraging this technique, we introduce OR-Bench, the first large-scale over-refusal benchmark. OR-Bench comprises 80,000 seemingly toxic prompts across 10 common rejection categories, a subset of around 1,000 hard prompts that are challenging even for state-of-the-art LLMs, and an additional 600 toxic prompts to prevent indiscriminate responses. We then conduct a comprehensive study to measure the over-refusal of 25 popular LLMs across 8 model families. Our datasets are available at https://huggingface.co/datasets/bench-llm/or-bench and the demo can be found at https://huggingface.co/spaces/bench-llm/or-bench. We hope this benchmark can help the community develop better safety aligned models.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

Conventional wisdom suggests that neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. Our work reassesses this assumption for neural networks with high-dimensional inputs. Rather than extrapolating in arbitrary ways, we observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. Moreover, we find that this value often closely approximates the optimal constant solution (OCS), i.e., the prediction that minimizes the average loss over the training data without observing the input. We present results showing this phenomenon across 8 datasets with different distributional shifts (including CIFAR10-C and ImageNet-R, S), different loss functions (cross entropy, MSE, and Gaussian NLL), and different architectures (CNNs and transformers). Furthermore, we present an explanation for this behavior, which we first validate empirically and then study theoretically in a simplified setting involving deep homogeneous networks with ReLU activations. Finally, we show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.

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).

LLMs increasingly exhibit over-refusal behavior, where safety mechanisms cause models to reject benign instructions that superficially resemble harmful content. This phenomena diminishes utility in production applications that repeatedly rely on common prompt templates or applications that frequently rely on LLMs for specific tasks (e.g. sentiment analysis, language translation). Through comprehensive evaluation, we demonstrate that LLMs still tend to refuse responses to harmful instructions when those instructions are reframed to appear as benign tasks. Our mechanistic analysis reveal that LLMs follow distinct "constellation" patterns in embedding space as representations traverse layers, with each task maintaining consistent trajectories that shift predictably between refusal and non-refusal cases. We introduce SafeConstellations, an inference-time trajectory-shifting approach that tracks task-specific trajectory patterns and guides representations toward non-refusal pathways. By selectively guiding model behavior only on tasks prone to over-refusal, and by preserving general model behavior, our method reduces over-refusal rates by up to 73% with minimal impact on utility-offering a principled approach to mitigating over-refusals.

Text-to-Image (T2I) models have achieved remarkable success in generating visual content from text inputs. Although multiple safety alignment strategies have been proposed to prevent harmful outputs, they often lead to overly cautious behavior -- rejecting even benign prompts -- a phenomenon known as over-refusal that reduces the practical utility of T2I models. Despite over-refusal having been observed in practice, there is no large-scale benchmark that systematically evaluates this phenomenon for T2I models. In this paper, we present an automatic workflow to construct synthetic evaluation data, resulting in OVERT (OVEr-Refusal evaluation on Text-to-image models), the first large-scale benchmark for assessing over-refusal behaviors in T2I models. OVERT includes 4,600 seemingly harmful but benign prompts across nine safety-related categories, along with 1,785 genuinely harmful prompts (OVERT-unsafe) to evaluate the safety-utility trade-off. Using OVERT, we evaluate several leading T2I models and find that over-refusal is a widespread issue across various categories (Figure 1), underscoring the need for further research to enhance the safety alignment of T2I models without compromising their functionality. As a preliminary attempt to reduce over-refusal, we explore prompt rewriting; however, we find it often compromises faithfulness to the meaning of the original prompts. Finally, we demonstrate the flexibility of our generation framework in accommodating diverse safety requirements by generating customized evaluation data adapting to user-defined policies.

Zero-shot learning in prompted vision-language models, the practice of crafting prompts to build classifiers without an explicit training process, has achieved impressive performance in many settings. This success presents a seemingly surprising observation: these methods suffer relatively little from overfitting, i.e., when a prompt is manually engineered to achieve low error on a given training set (thus rendering the method no longer actually zero-shot), the approach still performs well on held-out test data. In this paper, we show that we can explain such performance well via recourse to classical PAC-Bayes bounds. Specifically, we show that the discrete nature of prompts, combined with a PAC-Bayes prior given by a language model, results in generalization bounds that are remarkably tight by the standards of the literature: for instance, the generalization bound of an ImageNet classifier is often within a few percentage points of the true test error. We demonstrate empirically that this holds for existing handcrafted prompts and prompts generated through simple greedy search. Furthermore, the resulting bound is well-suited for model selection: the models with the best bound typically also have the best test performance. This work thus provides a possible justification for the widespread practice of prompt engineering, even if it seems that such methods could potentially overfit the training data.

Large language models (LLMs) exhibit degraded performance under prompt compression, but the mechanisms remain poorly understood. We introduce the Compression-Decay Comprehension Test (CDCT), a benchmark that independently measures constraint compliance (CC) and semantic accuracy (SA) across compression levels. We evaluate 9 frontier LLMs across 8 concepts using 5 compression levels from extreme (c=0.0, ~2 words) to none (c=1.0, ~135 words). A three-judge LLM jury achieves almost perfect inter-rater agreement on CC (Fleiss' appa=0.90). We observe a universal U-curve pattern in constraint compliance (97.2% prevalence), with violations peaking at medium compression (c=0.5, ~27 words). Counterintuitively, models perform better at extreme compression than medium lengths. The dimensions are statistically orthogonal (r=0.193, p=0.084), with constraint effects 2.9x larger than semantic effects. Experimental validation via RLHF ablation confirms our constraint salience hypothesis: removing "helpfulness" signals improves CC by 598% on average (71/72 trials, p<0.001), with 79% achieving perfect compliance. This demonstrates that RLHF-trained helpfulness behaviors are the dominant cause of constraint violations at medium compression. Reasoning models outperform efficient models by 27.5% (Cohen's d=0.96). Our findings reveal a fundamental tension between RLHF alignment and instruction-following, providing actionable guidelines for improving deployed systems.

Neural networks are often highly sensitive to input and weight perturbations. This sensitivity has been linked to pathologies such as vulnerability to adversarial examples, divergent training, and overfitting. To combat these problems, past research has looked at building neural networks entirely from Lipschitz components. However, these techniques have not matured to the point where researchers have trained a modern architecture such as a transformer with a Lipschitz certificate enforced beyond initialization. To explore this gap, we begin by developing and benchmarking novel, computationally-efficient tools for maintaining norm-constrained weight matrices. Applying these tools, we are able to train transformer models with Lipschitz bounds enforced throughout training. We find that optimizer dynamics matter: switching from AdamW to Muon improves standard methods -- weight decay and spectral normalization -- allowing models to reach equal performance with a lower Lipschitz bound. Inspired by Muon's update having a fixed spectral norm, we co-design a weight constraint method that improves the Lipschitz vs. performance tradeoff on MLPs and 2M parameter transformers. Our 2-Lipschitz transformer on Shakespeare text reaches validation accuracy 60%. Scaling to 145M parameters, our 10-Lipschitz transformer reaches 21% accuracy on internet text. However, to match the NanoGPT baseline validation accuracy of 39.4%, our Lipschitz upper bound increases to 10^264. Nonetheless, our Lipschitz transformers train without stability measures such as layer norm, QK norm, and logit tanh softcapping.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

Large language models are pre-trained on ever-growing token budgets under the assumption that better pre-training performance translates to improved downstream models. In this work, we challenge this assumption and show that extended pre-training can make models harder to fine-tune, leading to degraded final performance. We term this phenomenon catastrophic overtraining. For example, the instruction-tuned OLMo-1B model pre-trained on 3T tokens leads to over 2% worse performance on multiple standard LLM benchmarks than its 2.3T token counterpart. Through controlled experiments and theoretical analysis, we show that catastrophic overtraining arises from a systematic increase in the broad sensitivity of pre-trained parameters to modifications, including but not limited to fine-tuning. Our findings call for a critical reassessment of pre-training design that considers the downstream adaptability of the model.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

In order to minimize the generalization error in neural networks, a novel technique to identify overfitting phenomena when training the learner is formally introduced. This enables support of a reliable and trustworthy early stopping condition, thus improving the predictive power of that type of modeling. Our proposal exploits the correlation over time in a collection of online indicators, namely characteristic functions for indicating if a set of hypotheses are met, associated with a range of independent stopping conditions built from a canary judgment to evaluate the presence of overfitting. That way, we provide a formal basis for decision making in terms of interrupting the learning process. As opposed to previous approaches focused on a single criterion, we take advantage of subsidiarities between independent assessments, thus seeking both a wider operating range and greater diagnostic reliability. With a view to illustrating the effectiveness of the halting condition described, we choose to work in the sphere of natural language processing, an operational continuum increasingly based on machine learning. As a case study, we focus on parser generation, one of the most demanding and complex tasks in the domain. The selection of cross-validation as a canary function enables an actual comparison with the most representative early stopping conditions based on overfitting identification, pointing to a promising start toward an optimal bias and variance control.

Deep-learning based Automatic Essay Scoring (AES) systems are being actively used by states and language testing agencies alike to evaluate millions of candidates for life-changing decisions ranging from college applications to visa approvals. However, little research has been put to understand and interpret the black-box nature of deep-learning based scoring algorithms. Previous studies indicate that scoring models can be easily fooled. In this paper, we explore the reason behind their surprising adversarial brittleness. We utilize recent advances in interpretability to find the extent to which features such as coherence, content, vocabulary, and relevance are important for automated scoring mechanisms. We use this to investigate the oversensitivity i.e., large change in output score with a little change in input essay content) and overstability i.e., little change in output scores with large changes in input essay content) of AES. Our results indicate that autoscoring models, despite getting trained as "end-to-end" models with rich contextual embeddings such as BERT, behave like bag-of-words models. A few words determine the essay score without the requirement of any context making the model largely overstable. This is in stark contrast to recent probing studies on pre-trained representation learning models, which show that rich linguistic features such as parts-of-speech and morphology are encoded by them. Further, we also find that the models have learnt dataset biases, making them oversensitive. To deal with these issues, we propose detection-based protection models that can detect oversensitivity and overstability causing samples with high accuracies. We find that our proposed models are able to detect unusual attribution patterns and flag adversarial samples successfully.

Generalization to out-of-distribution (OOD) data is a critical challenge in machine learning. Ensemble-based methods, like weight space ensembles that interpolate model parameters, have been shown to achieve superior OOD performance. However, the underlying mechanism for their effectiveness remains unclear. In this study, we closely examine WiSE-FT, a popular weight space ensemble method that interpolates between a pre-trained and a fine-tuned model. We observe an unexpected phenomenon, in which WiSE-FT successfully corrects many cases where each individual model makes incorrect predictions, which contributes significantly to its OOD effectiveness. To gain further insights, we conduct theoretical analysis in a multi-class setting with a large number of spurious features. Our analysis predicts the above phenomenon and it further shows that ensemble-based models reduce prediction errors in the OOD settings by utilizing a more diverse set of spurious features. Contrary to the conventional wisdom that focuses on learning invariant features for better OOD performance, our findings suggest that incorporating a large number of diverse spurious features weakens their individual contributions, leading to improved overall OOD generalization performance. Empirically we demonstrate the effectiveness of utilizing diverse spurious features on a MultiColorMNIST dataset, and our experimental results are consistent with the theoretical analysis. Building upon the new theoretical insights into the efficacy of ensemble methods, we further identify an issue of WiSE-FT caused by the overconfidence of fine-tuned models in OOD situations. This overconfidence magnifies the fine-tuned model's incorrect prediction, leading to deteriorated OOD ensemble performance. To remedy this problem, we propose a novel method called BAlaNced averaGing (BANG), which significantly enhances the OOD performance of WiSE-FT.

Overfitting widely exists in adversarial robust training of deep networks. An effective remedy is adversarial weight perturbation, which injects the worst-case weight perturbation during network training by maximizing the classification loss on adversarial examples. Adversarial weight perturbation helps reduce the robust generalization gap; however, it also undermines the robustness improvement. A criterion that regulates the weight perturbation is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find that it is essential to conduct weight perturbation on adversarial data with small classification loss to eliminate robust overfitting. Weight perturbation on adversarial data with large classification loss is not necessary and may even lead to poor robustness. Based on these observations, we propose a robust perturbation strategy to constrain the extent of weight perturbation. The perturbation strategy prevents deep networks from overfitting while avoiding the side effect of excessive weight perturbation, significantly improving the robustness of adversarial training. Extensive experiments demonstrate the superiority of the proposed method over the state-of-the-art adversarial training methods.

Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and test data by adapting a given model w.r.t. any test sample. Although recent TTA has shown promising performance, we still face two key challenges: 1) prior methods perform backpropagation for each test sample, resulting in unbearable optimization costs to many applications; 2) while existing TTA 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 forgetting). To this end, we have proposed an Efficient Anti-Forgetting Test-Time Adaptation (EATA) method which develops an active sample selection criterion to identify reliable and non-redundant samples for test-time entropy minimization. To alleviate forgetting, EATA introduces a Fisher regularizer estimated from test samples to constrain important model parameters from drastic changes. However, in EATA, the adopted entropy loss consistently assigns higher confidence to predictions even for samples that are underlying uncertain, leading to overconfident predictions. To tackle this, we further propose EATA with Calibration (EATA-C) to separately exploit the reducible model uncertainty and the inherent data uncertainty for calibrated TTA. Specifically, we measure the model uncertainty by the divergence between predictions from the full network and its sub-networks, on which we propose a divergence loss to encourage consistent predictions instead of overconfident ones. To further recalibrate prediction confidence, we utilize the disagreement among predicted labels as an indicator of the data uncertainty, and then devise a min-max entropy regularizer to selectively increase and decrease prediction confidence for different samples. Experiments on image classification and semantic segmentation verify the effectiveness of our methods.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Aligning powerful AI models on tasks that surpass human evaluation capabilities is the central problem of superalignment. To address this problem, weak-to-strong generalization aims to elicit the capabilities of strong models through weak supervisors and ensure that the behavior of strong models aligns with the intentions of weak supervisors without unsafe behaviors such as deception. Although weak-to-strong generalization exhibiting certain generalization capabilities, strong models exhibit significant overfitting in weak-to-strong generalization: Due to the strong fit ability of strong models, erroneous labels from weak supervisors may lead to overfitting in strong models. In addition, simply filtering out incorrect labels may lead to a degeneration in question quality, resulting in a weak generalization ability of strong models on hard questions. To mitigate overfitting in weak-to-strong generalization, we propose a two-stage framework that simultaneously improves the quality of supervision signals and the quality of input questions. Experimental results in three series of large language models and two mathematical benchmarks demonstrate that our framework significantly improves PGR compared to naive weak-to-strong generalization, even achieving up to 100\% PGR on some models.

Prior work has shown that fine-tuning models on a narrow domain with misaligned data can lead to broad misalignment - a phenomenon termed "emergent misalignment" (Betley et al. 2025). While all tested models were susceptible to emergent misalignment, some models showed more resistance than others. Specifically the Qwen-2.5 family proved to be relatively resistant, while GPT-4o exhibited the strongest misalignment. In this paper we evaluate if current-generation open-weights models exhibit similar resistance to the Qwen-2.5 family and measure misalignment robustness over a range of model architectures and scales. We replicate the effect across nine modern open-weights models (Gemma 3 and Qwen 3 families, 1B-32B parameters). Models fine-tuned on insecure code generation show a 0.68% misalignment rate (compared to 0.07% for base models), matching the lower end of prior open-model results but dramatically lower than GPT-4o's 20%. We identify a critical format-dependent vulnerability: requiring JSON output doubles misalignment rates compared to natural language prompts (0.96% vs 0.42%). This suggests that structural constraints may bypass safety training by reducing the model's 'degrees of freedom' to refuse. These findings confirm emergent misalignment as a reproducible phenomenon in modern open-weights models, with rates substantially lower than observed in proprietary systems.

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.

Open-weight AI systems offer unique benefits, including enhanced transparency, open research, and decentralized access. However, they are vulnerable to tampering attacks which can efficiently elicit harmful behaviors by modifying weights or activations. Currently, there is not yet a robust science of open-weight model risk management. Existing safety fine-tuning methods and other post-training techniques have struggled to make LLMs resistant to more than a few dozen steps of adversarial fine-tuning. In this paper, we investigate whether filtering text about dual-use topics from training data can prevent unwanted capabilities and serve as a more tamper-resistant safeguard. We introduce a multi-stage pipeline for scalable data filtering and show that it offers a tractable and effective method for minimizing biothreat proxy knowledge in LLMs. We pretrain multiple 6.9B-parameter models from scratch and find that they exhibit substantial resistance to adversarial fine-tuning attacks on up to 10,000 steps and 300M tokens of biothreat-related text -- outperforming existing post-training baselines by over an order of magnitude -- with no observed degradation to unrelated capabilities. However, while filtered models lack internalized dangerous knowledge, we find that they can still leverage such information when it is provided in context (e.g., via search tool augmentation), demonstrating a need for a defense-in-depth approach. Overall, these findings help to establish pretraining data curation as a promising layer of defense for open-weight AI systems.

Introduced by Hinton et al. in 2012, dropout has stood the test of time as a regularizer for preventing overfitting in neural networks. In this study, we demonstrate that dropout can also mitigate underfitting when used at the start of training. During the early phase, we find dropout reduces the directional variance of gradients across mini-batches and helps align the mini-batch gradients with the entire dataset's gradient. This helps counteract the stochasticity of SGD and limit the influence of individual batches on model training. Our findings lead us to a solution for improving performance in underfitting models - early dropout: dropout is applied only during the initial phases of training, and turned off afterwards. Models equipped with early dropout achieve lower final training loss compared to their counterparts without dropout. Additionally, we explore a symmetric technique for regularizing overfitting models - late dropout, where dropout is not used in the early iterations and is only activated later in training. Experiments on ImageNet and various vision tasks demonstrate that our methods consistently improve generalization accuracy. Our results encourage more research on understanding regularization in deep learning and our methods can be useful tools for future neural network training, especially in the era of large data. Code is available at https://github.com/facebookresearch/dropout.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Since the release of OpenAI's ChatGPT, generative language models have attracted extensive public attention. The increased usage has highlighted generative models' broad utility, but also revealed several forms of embedded bias. Some is induced by the pre-training corpus; but additional bias specific to generative models arises from the use of subjective fine-tuning to avoid generating harmful content. Fine-tuning bias may come from individual engineers and company policies, and affects which prompts the model chooses to refuse. In this experiment, we characterize ChatGPT's refusal behavior using a black-box attack. We first query ChatGPT with a variety of offensive and benign prompts (n=1,706), then manually label each response as compliance or refusal. Manual examination of responses reveals that refusal is not cleanly binary, and lies on a continuum; as such, we map several different kinds of responses to a binary of compliance or refusal. The small manually-labeled dataset is used to train a refusal classifier, which achieves an accuracy of 96%. Second, we use this refusal classifier to bootstrap a larger (n=10,000) dataset adapted from the Quora Insincere Questions dataset. With this machine-labeled data, we train a prompt classifier to predict whether ChatGPT will refuse a given question, without seeing ChatGPT's response. This prompt classifier achieves 76% accuracy on a test set of manually labeled questions (n=985). We examine our classifiers and the prompt n-grams that are most predictive of either compliance or refusal. Our datasets and code are available at https://github.com/maxwellreuter/chatgpt-refusals.

Few-shot learning for neural networks (NNs) is an important problem that aims to train NNs with a few data. The main challenge is how to avoid overfitting since over-parameterized NNs can easily overfit to such small dataset. Previous work (e.g. MAML by Finn et al. 2017) tackles this challenge by meta-learning, which learns how to learn from a few data by using various tasks. On the other hand, one conventional approach to avoid overfitting is restricting hypothesis spaces by endowing sparse NN structures like convolution layers in computer vision. However, although such manually-designed sparse structures are sample-efficient for sufficiently large datasets, they are still insufficient for few-shot learning. Then the following questions naturally arise: (1) Can we find sparse structures effective for few-shot learning by meta-learning? (2) What benefits will it bring in terms of meta-generalization? In this work, we propose a novel meta-learning approach, called Meta-ticket, to find optimal sparse subnetworks for few-shot learning within randomly initialized NNs. We empirically validated that Meta-ticket successfully discover sparse subnetworks that can learn specialized features for each given task. Due to this task-wise adaptation ability, Meta-ticket achieves superior meta-generalization compared to MAML-based methods especially with large NNs. The code is available at: https://github.com/dchiji-ntt/meta-ticket

Modern representation learning methods often struggle to adapt quickly under non-stationarity because they suffer from catastrophic forgetting and decaying plasticity. Such problems prevent learners from fast adaptation since they may forget useful features or have difficulty learning new ones. Hence, these methods are rendered ineffective for continual learning. This paper proposes Utility-based Perturbed Gradient Descent (UPGD), an online learning algorithm well-suited for continual learning agents. UPGD protects useful weights or features from forgetting and perturbs less useful ones based on their utilities. Our empirical results show that UPGD helps reduce forgetting and maintain plasticity, enabling modern representation learning methods to work effectively in continual learning.

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of increasing epoch count and parameter count eventually overfit, and we significantly improve upon such recipes by properly tuning regularization, finding that the optimal weight decay is 30times larger than standard practice. Since our regularized recipe monotonically decreases loss following a simple power law in parameter count, we estimate its best possible performance via the asymptote of its scaling law rather than the performance at a fixed compute budget. We then identify that ensembling independently trained models achieves a significantly lower loss asymptote than the regularized recipe. Our best intervention combining epoching, regularization, parameter scaling, and ensemble scaling achieves an asymptote at 200M tokens using 5.17times less data than our baseline, and our data scaling laws predict that this improvement persists at higher token budgets. We find that our data efficiency gains can be realized at much smaller parameter counts as we can distill an ensemble into a student model that is 8times smaller and retains 83% of the ensembling benefit. Finally, our interventions designed for validation loss generalize to downstream benchmarks, achieving a 9% improvement for pre-training evals and a 17.5times data efficiency improvement over continued pre-training on math mid-training data. Our results show that simple algorithmic improvements can enable significantly more data-efficient pre-training in a compute-rich future.

Human intelligence involves metacognitive abilities like self-regulation, recognizing limitations, and seeking assistance only when needed. While LLM Agents excel in many domains, they often lack this awareness. Overconfident agents risk catastrophic failures, while those that seek help excessively hinder efficiency. A key challenge is enabling agents with a limited intervention budget C is to decide when to request assistance. In this paper, we propose an offline framework that trains a "helper" policy to request interventions, such as more powerful models or test-time compute, by combining LLM-based process reward models (PRMs) with tabular reinforcement learning. Using state transitions collected offline, we score optimal intervention timing with PRMs and train the helper model on these labeled trajectories. This offline approach significantly reduces costly intervention calls during training. Furthermore, the integration of PRMs with tabular RL enhances robustness to off-policy data while avoiding the inefficiencies of deep RL. We empirically find that our method delivers optimal helper behavior.

Deep neural networks are vulnerable to adversarial examples. Adversarial training (AT) is an effective defense against adversarial examples. However, AT is prone to overfitting which degrades robustness substantially. Recently, data augmentation (DA) was shown to be effective in mitigating robust overfitting if appropriately designed and optimized for AT. This work proposes a new method to automatically learn online, instance-wise, DA policies to improve robust generalization for AT. A novel policy learning objective, consisting of Vulnerability, Affinity and Diversity, is proposed and shown to be sufficiently effective and efficient to be practical for automatic DA generation during AT. This allows our method to efficiently explore a large search space for a more effective DA policy and evolve the policy as training progresses. Empirically, our method is shown to outperform or match all competitive DA methods across various model architectures (CNNs and ViTs) and datasets (CIFAR10, SVHN and Imagenette). Our DA policy reinforced vanilla AT to surpass several state-of-the-art AT methods (with baseline DA) in terms of both accuracy and robustness. It can also be combined with those advanced AT methods to produce a further boost in robustness.

Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating from deep networks being "too linear" (Goodfellow et al., 2014). We show here that the linear explanation of adversarial examples presents a number of limitations: the formal argument is not convincing, linear classifiers do not always suffer from the phenomenon, and when they do their adversarial examples are different from the ones affecting deep networks. We propose a new perspective on the phenomenon. We argue that adversarial examples exist when the classification boundary lies close to the submanifold of sampled data, and present a mathematical analysis of this new perspective in the linear case. We define the notion of adversarial strength and show that it can be reduced to the deviation angle between the classifier considered and the nearest centroid classifier. Then, we show that the adversarial strength can be made arbitrarily high independently of the classification performance due to a mechanism that we call boundary tilting. This result leads us to defining a new taxonomy of adversarial examples. Finally, we show that the adversarial strength observed in practice is directly dependent on the level of regularisation used and the strongest adversarial examples, symptomatic of overfitting, can be avoided by using a proper level of regularisation.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Masked language modeling is a widely used method for learning language representations, where the model predicts a randomly masked word in each input. However, this approach typically considers only a single correct answer during training, ignoring the variety of plausible alternatives that humans might choose. This issue becomes more pronounced when the input text is short, as the possible word distribution tends to have higher entropy, potentially causing the model to become overconfident in its predictions. To mitigate this, we propose a novel confidence regularizer that adaptively adjusts the regularization strength based on the input length. Experiments on the GLUE and SQuAD benchmarks show that our method improves both accuracy and expected calibration error

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with ell_1-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and--perhaps surprisingly--even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the ell_1-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

Large reasoning models (LRMs) achieve remarkable performance by leveraging reinforcement learning (RL) on reasoning tasks to generate long chain-of-thought (CoT) reasoning. However, this over-optimization often prioritizes compliance, making models vulnerable to harmful prompts. To mitigate this safety degradation, recent approaches rely on external teacher distillation, yet this introduces a distributional discrepancy that degrades native reasoning. We propose ThinkSafe, a self-generated alignment framework that restores safety alignment without external teachers. Our key insight is that while compliance suppresses safety mechanisms, models often retain latent knowledge to identify harm. ThinkSafe unlocks this via lightweight refusal steering, guiding the model to generate in-distribution safety reasoning traces. Fine-tuning on these self-generated responses effectively realigns the model while minimizing distribution shift. Experiments on DeepSeek-R1-Distill and Qwen3 show ThinkSafe significantly improves safety while preserving reasoning proficiency. Notably, it achieves superior safety and comparable reasoning to GRPO, with significantly reduced computational cost. Code, models, and datasets are available at https://github.com/seanie12/ThinkSafe.git.

Humans are prone to cognitive distortions -- biased thinking patterns that lead to exaggerated responses to specific stimuli, albeit in very different contexts. This paper demonstrates that advanced Multimodal Large Language Models (MLLMs) exhibit similar tendencies. While these models are designed to respond queries under safety mechanism, they sometimes reject harmless queries in the presence of certain visual stimuli, disregarding the benign nature of their contexts. As the initial step in investigating this behavior, we identify three types of stimuli that trigger the oversensitivity of existing MLLMs: Exaggerated Risk, Negated Harm, and Counterintuitive Interpretation. To systematically evaluate MLLMs' oversensitivity to these stimuli, we propose the Multimodal OverSenSitivity Benchmark (MOSSBench). This toolkit consists of 300 manually collected benign multimodal queries, cross-verified by third-party reviewers (AMT). Empirical studies using MOSSBench on 20 MLLMs reveal several insights: (1). Oversensitivity is prevalent among SOTA MLLMs, with refusal rates reaching up to 76% for harmless queries. (2). Safer models are more oversensitive: increasing safety may inadvertently raise caution and conservatism in the model's responses. (3). Different types of stimuli tend to cause errors at specific stages -- perception, intent reasoning, and safety judgement -- in the response process of MLLMs. These findings highlight the need for refined safety mechanisms that balance caution with contextually appropriate responses, improving the reliability of MLLMs in real-world applications. We make our project available at https://turningpoint-ai.github.io/MOSSBench/.

Large language models (LLMs) can produce erroneous responses that sound fluent and convincing, raising the risk that users will rely on these responses as if they were correct. Mitigating such overreliance is a key challenge. Through a think-aloud study in which participants use an LLM-infused application to answer objective questions, we identify several features of LLM responses that shape users' reliance: explanations (supporting details for answers), inconsistencies in explanations, and sources. Through a large-scale, pre-registered, controlled experiment (N=308), we isolate and study the effects of these features on users' reliance, accuracy, and other measures. We find that the presence of explanations increases reliance on both correct and incorrect responses. However, we observe less reliance on incorrect responses when sources are provided or when explanations exhibit inconsistencies. We discuss the implications of these findings for fostering appropriate reliance on LLMs.

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. On several challenging math benchmarks, ePF significantly outperforms strong baselines and achieves up to a 50 % relative improvement in task reward. Together, these methods improve PF's resilience by balancing the exploration of diverse solution spaces with the exploitation of high-reward regions, ultimately leading to higher-quality solutions.

The prevailing paradigm in large language model (LLM) development is to pretrain a base model, then perform further training to improve performance and model behavior. However, hyperparameter optimization and scaling laws have been studied primarily from the perspective of the base model's validation loss, ignoring downstream adaptability. In this work, we study pretraining from the perspective of model plasticity, that is, the ability of the base model to successfully adapt to downstream tasks through fine-tuning. We focus on the role of weight decay, a key regularization parameter during pretraining. Through systematic experiments, we show that models trained with larger weight decay values are more plastic, meaning they show larger performance gains when fine-tuned on downstream tasks. This phenomenon can lead to counterintuitive trade-offs where base models that perform worse after pretraining can perform better after fine-tuning. Further investigation of weight decay's mechanistic effects on model behavior reveals that it encourages linearly separable representations, regularizes attention matrices, and reduces overfitting on the training data. In conclusion, this work demonstrates the importance of using evaluation metrics beyond cross-entropy loss for hyperparameter optimization and casts light on the multifaceted role of that a single optimization hyperparameter plays in shaping model behavior.

Vision-language models are increasingly deployed in high-stakes settings, yet their susceptibility to sycophantic manipulation remains poorly understood, particularly in relation to how these models represent visual information internally. Whether models whose visual representations more closely mirror human neural processing are also more resistant to adversarial pressure is an open question with implications for both neuroscience and AI safety. We investigate this question by evaluating 12 open-weight vision-language models spanning 6 architecture families and a 40times parameter range (256M--10B) along two axes: brain alignment, measured by predicting fMRI responses from the Natural Scenes Dataset across 8 human subjects and 6 visual cortex regions of interest, and sycophancy, measured through 76,800 two-turn gaslighting prompts spanning 5 categories and 10 difficulty levels. Region-of-interest analysis reveals that alignment specifically in early visual cortex (V1--V3) is a reliable negative predictor of sycophancy (r = -0.441, BCa 95\% CI [-0.740, -0.031]), with all 12 leave-one-out correlations negative and the strongest effect for existence denial attacks (r = -0.597, p = 0.040). This anatomically specific relationship is absent in higher-order category-selective regions, suggesting that faithful low-level visual encoding provides a measurable anchor against adversarial linguistic override in vision-language models. We release our code on https://github.com/aryashah2k/Gaslight-Gatekeep-Sycophantic-Manipulation{GitHub} and dataset on https://huggingface.co/datasets/aryashah00/Gaslight-Gatekeep-V1-V3{Hugging Face}

The leakage of benchmark data into the training data has emerged as a significant challenge for evaluating the capabilities of large language models (LLMs). In this work, we challenge the common assumption that small-scale contamination renders benchmark evaluations invalid. First, we experimentally quantify the magnitude of benchmark overfitting based on scaling along three dimensions: The number of model parameters (up to 1.6B), the number of times an example is seen (up to 144), and the number of training tokens (up to 40B). If model and data follow the Chinchilla scaling laws, minor contamination indeed leads to overfitting. At the same time, even 144 times of contamination can be forgotten if the training data is scaled beyond five times Chinchilla, a regime characteristic of many modern LLMs. Continual pre-training of OLMo-7B corroborates these results. Next, we study the impact of the weight decay parameter on example forgetting, showing that empirical forgetting occurs faster than the cumulative weight decay. This allows us to gauge the degree of example forgetting in large-scale training runs, indicating that many LLMs, including Lllama 3 405B, have forgotten the data seen at the beginning of training.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

Attention sinks and massive activations are recurring and closely related phenomena in Transformer models. Existing studies have largely focused on the forward pass, making it unclear whether their connection is direct or mediated by a training-time mechanism. We study this question from the perspective of backpropagation. Empirically and theoretically, we show that under causal mask, attention sinks can induce pronounced gradient concentration, which we term gradient sinks. Furthermore, in pre-norm architectures with RMSNorm, massive activations can be understood as an adaptive response to this localized gradient pressure during training. To test this hypothesis, we introduce V-scale, a modification that adjusts value-path backpropagated gradients. In pretrained V-scale models, attention sinks are preserved whereas massive activations are suppressed. These results support the interpretation that gradient sink is a key training-time mediator linking attention sinks and massive activations.

We find that the response length of reasoning LLMs, whether trained by reinforcement learning or supervised learning, drastically increases for ill-posed questions with missing premises (MiP), ending up with redundant and ineffective thinking. This newly introduced scenario exacerbates the general overthinking issue to a large extent, which we name as the MiP-Overthinking. Such failures are against the ``test-time scaling law'' but have been widely observed on multiple datasets we curated with MiP, indicating the harm of cheap overthinking and a lack of critical thinking. Surprisingly, LLMs not specifically trained for reasoning exhibit much better performance on the MiP scenario, producing much shorter responses that quickly identify ill-posed queries. This implies a critical flaw of the current training recipe for reasoning LLMs, which does not encourage efficient thinking adequately, leading to the abuse of thinking patterns. To further investigate the reasons behind such failures, we conduct fine-grained analyses of the reasoning length, overthinking patterns, and location of critical thinking on different types of LLMs. Moreover, our extended ablation study reveals that the overthinking is contagious through the distillation of reasoning models' responses. These results improve the understanding of overthinking and shed novel insights into mitigating the problem.

Foundation models are transitioning from offline predictors to deployed systems expected to operate over long time horizons. In real deployments, objectives are not fixed: domains drift, user preferences evolve, and new tasks appear after the model has shipped. This elevates continual learning and instant personalization from optional features to core architectural requirements. Yet most adaptation pipelines still follow a static weight paradigm: after training (or after any adaptation step), inference executes a single parameter vector regardless of user intent, domain, or instance-specific constraints. This treats the trained or adapted model as a single point in parameter space. In heterogeneous and continually evolving regimes, distinct objectives can induce separated feasible regions over parameters, forcing any single shared update into compromise, interference, or overspecialization. As a result, continual learning and personalization are often implemented as repeated overwriting of shared weights, risking degradation of previously learned behaviors. We propose HY-WU (Weight Unleashing), a memory-first adaptation framework that shifts adaptation pressure away from overwriting a single shared parameter point. HY-WU implements functional (operator-level) memory as a neural module: a generator that synthesizes weight updates on-the-fly from the instance condition, yielding instance-specific operators without test-time optimization.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

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.

The ability of language models in RAG systems to selectively refuse to answer based on flawed context is critical for safety, yet remains a significant failure point. Our large-scale study reveals that even frontier models struggle in this setting, with refusal accuracy dropping below 50% on multi-document tasks, while exhibiting either dangerous overconfidence or overcaution. Static benchmarks fail to reliably evaluate this capability, as models exploit dataset-specific artifacts and memorize test instances. We introduce RefusalBench, a generative methodology that programmatically creates diagnostic test cases through controlled linguistic perturbation. Our framework employs 176 distinct perturbation strategies across six categories of informational uncertainty and three intensity levels. Evaluation of over 30 models uncovers systematic failure patterns: refusal comprises separable detection and categorization skills, and neither scale nor extended reasoning improves performance. We find that selective refusal is a trainable, alignment-sensitive capability, offering a clear path for improvement. We release two benchmarks -- RefusalBench-NQ (single document) and RefusalBench-GaRAGe (multi-document) -- and our complete generation framework to enable continued, dynamic evaluation of this critical capability.

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time τ_gen at which models begin to generate high-quality samples, and a later time τ_mem beyond which memorization emerges. Crucially, we find that τ_mem increases linearly with the training set size n, while τ_gen remains constant. This creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when n becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Fine-tuning is becoming widely used for leveraging the power of pre-trained foundation models in new downstream tasks. While there are many successes of fine-tuning on various tasks, recent studies have observed challenges in the generalization of fine-tuned models to unseen distributions (i.e., out-of-distribution; OOD). To improve OOD generalization, some previous studies identify the limitations of fine-tuning data and regulate fine-tuning to preserve the general representation learned from pre-training data. However, potential limitations in the pre-training data and models are often ignored. In this paper, we contend that overly relying on the pre-trained representation may hinder fine-tuning from learning essential representations for downstream tasks and thus hurt its OOD generalization. It can be especially catastrophic when new tasks are from different (sub)domains compared to pre-training data. To address the issues in both pre-training and fine-tuning data, we propose a novel generalizable fine-tuning method LEVI (Layer-wise Ensemble of different VIews), where the pre-trained model is adaptively ensembled layer-wise with a small task-specific model, while preserving its efficiencies. By combining two complementing models, LEVI effectively suppresses problematic features in both the fine-tuning data and pre-trained model and preserves useful features for new tasks. Broad experiments with large language and vision models show that LEVI greatly improves fine-tuning generalization via emphasizing different views from fine-tuning data and pre-trained features.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem y = beta^{*top} x +xi with sparse beta^*, neither minimum ell_1 or ell_2 norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of ell_1 and ell_2 interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

Continual learning (CL), which aims to learn a sequence of tasks, has attracted significant recent attention. However, most work has focused on the experimental performance of CL, and theoretical studies of CL are still limited. In particular, there is a lack of understanding on what factors are important and how they affect "catastrophic forgetting" and generalization performance. To fill this gap, our theoretical analysis, under overparameterized linear models, provides the first-known explicit form of the expected forgetting and generalization error. Further analysis of such a key result yields a number of theoretical explanations about how overparameterization, task similarity, and task ordering affect both forgetting and generalization error of CL. More interestingly, by conducting experiments on real datasets using deep neural networks (DNNs), we show that some of these insights even go beyond the linear models and can be carried over to practical setups. In particular, we use concrete examples to show that our results not only explain some interesting empirical observations in recent studies, but also motivate better practical algorithm designs of CL.

This paper introduces a new biologically-inspired training method named Continual Learning through Adjustment Suppression and Sparsity Promotion (CLASSP). CLASSP is based on two main principles observed in neuroscience, particularly in the context of synaptic transmission and Long-Term Potentiation (LTP). The first principle is a decay rate over the weight adjustment, which is implemented as a generalization of the AdaGrad optimization algorithm. This means that weights that have received many updates should have lower learning rates as they likely encode important information about previously seen data. However, this principle results in a diffuse distribution of updates throughout the model, as it promotes updates for weights that haven't been previously updated, while a sparse update distribution is preferred to leave weights unassigned for future tasks. Therefore, the second principle introduces a threshold on the loss gradient. This promotes sparse learning by updating a weight only if the loss gradient with respect to that weight is above a certain threshold, i.e. only updating weights with a significant impact on the current loss. Both principles reflect phenomena observed in LTP, where a threshold effect and a gradual saturation of potentiation have been observed. CLASSP is implemented in a Python/PyTorch class, making it applicable to any model. When compared with Elastic Weight Consolidation (EWC) using Computer Vision and sentiment analysis datasets, CLASSP demonstrates superior performance in terms of accuracy and memory footprint.

Pre-trained vision-language models, such as CLIP, show impressive zero-shot recognition ability and can be easily transferred to specific downstream tasks via prompt tuning, even with limited training data. However, existing prompt tuning methods face two main challenges: (1) In few-shot scenarios, data scarcity often leads to overfitting, making the model sensitive to changes in the input domain. (2) To mitigate overfitting, these methods typically rely on complex task-specific model architectures and sensitive hyperparameter tuning, severely restricting their general applicability. To address these issues, we propose a simpler and more general framework called GLAD (Generalizable LoRA tuning with RegulArized GraDient). We show that merely applying LoRA achieves performance in downstream tasks comparable to current state-of-the-art prompt-based methods. While LoRA is effective and easy to use, it remains susceptible to overfitting in few-shot learning scenarios. To mitigate this risk, we introduce a gradient-based regularization technique. This technique effectively steers the optimization trajectory, encouraging the model to find a more stable parameter region that is robust to variations in data distribution. Through extensive experiments conducted on 15 benchmark datasets, we demonstrate that GLAD outperforms previous tuning approaches in terms of base-to-novel class generalization, image domain generalization, and cross-dataset generalization. The code will be publicly available.

We build new test sets for the CIFAR-10 and ImageNet datasets. Both benchmarks have been the focus of intense research for almost a decade, raising the danger of overfitting to excessively re-used test sets. By closely following the original dataset creation processes, we test to what extent current classification models generalize to new data. We evaluate a broad range of models and find accuracy drops of 3% - 15% on CIFAR-10 and 11% - 14% on ImageNet. However, accuracy gains on the original test sets translate to larger gains on the new test sets. Our results suggest that the accuracy drops are not caused by adaptivity, but by the models' inability to generalize to slightly "harder" images than those found in the original test sets.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory.

Large language models (LLMs) often appear to excel on public benchmarks, but these high scores may mask an overreliance on dataset-specific surface cues rather than true language understanding. We introduce the Chameleon Benchmark Overfit Detector (C-BOD), a meta-evaluation framework that systematically distorts benchmark prompts via a parametric transformation and detects overfitting of LLMs. By rephrasing inputs while preserving their semantic content and labels, C-BOD exposes whether a model's performance is driven by memorized patterns. Evaluated on the MMLU benchmark using 26 leading LLMs, our method reveals an average performance degradation of 2.15% under modest perturbations, with 20 out of 26 models exhibiting statistically significant differences. Notably, models with higher baseline accuracy exhibit larger performance differences under perturbation, and larger LLMs tend to be more sensitive to rephrasings indicating that both cases may overrely on fixed prompt patterns. In contrast, the Llama family and models with lower baseline accuracy show insignificant degradation, suggesting reduced dependency on superficial cues. Moreover, C-BOD's dataset- and model-agnostic design allows easy integration into training pipelines to promote more robust language understanding. Our findings challenge the community to look beyond leaderboard scores and prioritize resilience and generalization in LLM evaluation.

Standard evaluation protocols reveal a counterintuitive phenomenon: on 7.7% of benchmark problems spanning five datasets, larger language models underperform smaller ones by 28.4 percentage points despite 10-100x more parameters. Through systematic evaluation of 31 models (0.5B-405B parameters) across 1,485 problems, we identify the mechanism as spontaneous scale-dependent verbosity that introduces errors through overelaboration. Causal intervention experiments demonstrate this reflects correctable prompt design rather than fundamental capability limitations. Constraining large models to produce brief responses improves accuracy by 26 percentage points and reduces performance gaps by up to two-thirds. Most critically, brevity constraints completely reverse performance hierarchies on mathematical reasoning and scientific knowledge benchmarks, with large models achieving 7.7-15.9 percentage point advantages over small models -- direct inversions of the original gaps. These reversals prove large models possess superior latent capabilities that universal prompting masks. We validate findings through three independent contamination tests and demonstrate inverse scaling operates continuously across the full parameter spectrum, with dataset-specific optimal scales ranging from 0.5B to 3.0B parameters. Our results establish that maximizing large model performance requires scale-aware prompt engineering rather than universal evaluation protocols, with immediate implications for deployment: prompt adaptation simultaneously improves accuracy and reduces computational costs.

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.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental to the robustness of DNNs. This paper presents a theoretical explanation of robust overfitting for DNNs. Specifically, we non-trivially extend the neural tangent kernel (NTK) theory to AT and prove that an adversarially trained wide DNN can be well approximated by a linearized DNN. Moreover, for squared loss, closed-form AT dynamics for the linearized DNN can be derived, which reveals a new AT degeneration phenomenon: a long-term AT will result in a wide DNN degenerates to that obtained without AT and thus cause robust overfitting. Based on our theoretical results, we further design a method namely Adv-NTK, the first AT algorithm for infinite-width DNNs. Experiments on real-world datasets show that Adv-NTK can help infinite-width DNNs enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. The code is available at https://github.com/fshp971/adv-ntk.

Pre-trained weights have become a cornerstone of modern deep learning, enabling efficient knowledge transfer and improving downstream task performance, especially in data-scarce scenarios. However, a fundamental question remains: how can we obtain better pre-trained weights that encapsulate more knowledge beyond the given dataset? In this work, we introduce KNowledge-Overflowed Weights (KNOW) prediction, a novel strategy that leverages structured forgetting and its inversion to synthesize knowledge-enriched weights. Our key insight is that sequential fine-tuning on progressively downsized datasets induces a structured forgetting process, which can be modeled and reversed to recover knowledge as if trained on a larger dataset. We construct a dataset of weight transitions governed by this controlled forgetting and employ meta-learning to model weight prediction effectively. Specifically, our KNowledge-Overflowed Weights Nowcaster (KNOWN) acts as a hyper-model that learns the general evolution of weights and predicts enhanced weights with improved generalization. Extensive experiments across diverse datasets and architectures demonstrate that KNOW prediction consistently outperforms Naive fine-tuning and simple weight prediction, leading to superior downstream performance. Our work provides a new perspective on reinterpreting forgetting dynamics to push the limits of knowledge transfer. The code and pre-trained model are available at https://github.com/jjh6297/KNOW

We consider multi-agent reinforcement learning (MARL) for cooperative communication and coordination tasks. MARL agents can be brittle because they can overfit their training partners' policies. This overfitting can produce agents that adopt policies that act under the expectation that other agents will act in a certain way rather than react to their actions. Our objective is to bias the learning process towards finding reactive strategies towards other agents' behaviors. Our method, transfer empowerment, measures the potential influence between agents' actions. Results from three simulated cooperation scenarios support our hypothesis that transfer empowerment improves MARL performance. We discuss how transfer empowerment could be a useful principle to guide multi-agent coordination by ensuring reactiveness to one's partner.

As post-training processes utilize increasingly large datasets and base models continue to grow in size, the computational demands and implementation challenges of existing algorithms are escalating significantly. In this paper, we propose modeling the changes at the logits level during post-training using a separate neural network (i.e., the value network). After training this network on a small base model using demonstrations, this network can be seamlessly integrated with other pre-trained models during inference, enables them to achieve similar capability enhancements. We systematically investigate the best practices for this paradigm in terms of pre-training weights and connection schemes. We demonstrate that the resulting value network has broad transferability across pre-trained models of different parameter sizes within the same family, models undergoing continuous pre-training within the same family, and models with different vocabularies across families. In certain cases, it can achieve performance comparable to full-parameter fine-tuning. Furthermore, we explore methods to enhance the transferability of the value model and prevent overfitting to the base model used during training.

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.

Recent thinking models solve complex reasoning tasks by scaling test-time compute, but this scaling must be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient, generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under- and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention over a long reasoning trajectory to identify important steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate reasoning budget commensurate with example difficulty. Our approach improves accuracy, reduces reasoning steps, and enables adaptive thinking compared to base models and other RL baselines. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC also shows strong generalization: although our models are trained on math datasets, they show accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis further verifies that TRAAC provides fine-grained adjustments to thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they often suffer from overthinking, expending redundant computational steps on simple problems, or underthinking, failing to explore sufficient reasoning paths despite inherent capabilities. These issues lead to inefficiencies and potential inaccuracies, limiting practical deployment in resource-constrained settings. Existing methods to mitigate overthinking, such as suppressing reflective keywords or adjusting reasoning length, may inadvertently induce underthinking, compromising accuracy. Therefore, we propose ReBalance, a training-free framework that achieves efficient reasoning with balanced thinking. ReBalance leverages confidence as a continuous indicator of reasoning dynamics, identifying overthinking through high confidence variance and underthinking via consistent overconfidence. By aggregating hidden states from a small-scale dataset into reasoning mode prototypes, we compute a steering vector to guide LRMs' reasoning trajectories. A dynamic control function modulates this vector's strength and direction based on real-time confidence, pruning redundancy during overthinking, and promoting exploration during underthinking. Extensive experiments conducted on four models ranging from 0.5B to 32B, and across nine benchmarks in math reasoning, general question answering, and coding tasks demonstrate that ReBalance effectively reduces output redundancy while improving accuracy, offering a general, training-free, and plug-and-play strategy for efficient and robust LRM deployment. Code is available at https://github.com/yu-lin-li/ReBalance .

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50% post-unlearning to nearly 100% with fine-tuning on just the retain set -- i.e., zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, L_2-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

Adversarial training improves the robustness of neural networks against adversarial attacks, albeit at the expense of the trade-off between standard and robust generalization. To unveil the underlying factors driving this phenomenon, we examine the layer-wise learning capabilities of neural networks during the transition from a standard to an adversarial setting. Our empirical findings demonstrate that selectively updating specific layers while preserving others can substantially enhance the network's learning capacity. We therefore propose CURE, a novel training framework that leverages a gradient prominence criterion to perform selective conservation, updating, and revision of weights. Importantly, CURE is designed to be dataset- and architecture-agnostic, ensuring its applicability across various scenarios. It effectively tackles both memorization and overfitting issues, thus enhancing the trade-off between robustness and generalization and additionally, this training approach also aids in mitigating "robust overfitting". Furthermore, our study provides valuable insights into the mechanisms of selective adversarial training and offers a promising avenue for future research.

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models (LLMs). However, prevailing RLVR methods exhibit a systematic bias toward exploitation over exploration, as evidenced by improved pass@1 but reduced pass@K (K>1) performance. To understand this issue, we analyze training dynamics of RLVR methods by tracking the token-level probability distributions over vocabulary candidates. Our analysis reveals a consistent probability concentration effect where the top-1 candidate increasingly accumulates probability mass and suppresses that of other candidates. More importantly, stronger over-concentration correlates with worse pass@K performance. Inspired by this finding, we propose Simple Pass@K Optimization (SimKO), a method designed to mitigate the over-concentration issue, thereby encouraging exploration. SimKO operates in an asymmetrical manner. For verified-correct responses, it boosts the probabilities of the top-K candidates. For verified-incorrect responses, it applies stronger penalties to the top-1 candidate. We observe that this asymmetric design is particularly effective at mitigating over-concentration when applied at tokens with high entropy. Across various math and logical-reasoning benchmarks, SimKO consistently yields higher pass@K for a wide range of K, providing a simple way to improve RLVR's exploration.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 13%, with several families of models (e.g., Phi and Mistral) showing evidence of systematic overfitting across almost all model sizes. At the same time, many models, especially those on the frontier, (e.g., Gemini/GPT/Claude) show minimal signs of overfitting. Further analysis suggests a positive relationship (Spearman's r^2=0.32) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that many models may have partially memorized GSM8k.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as physics-informed simulators in which accurate forecasts in real time with a minimal lag are required. The present neural network designs include millions of parameters, which makes it difficult to install such complex models on devices that have limited memory. Compression techniques might be able to resolve these issues by decreasing the size of CNN models that are created by reducing the number of parameters that contribute to the complexity of the models. We propose a compressed tensor format of convolutional layer, a priori, before the training of the neural network. 3-way kernels or 2-way kernels in convolutional layers are replaced by one-way fiters. The overfitting phenomena will be reduced also. The time needed to make predictions or time required for training using the original Convolutional Neural Networks model would be cut significantly if there were fewer parameters to deal with. In this paper we present a method of a priori compressing convolutional neural networks for finite element (FE) predictions of physical data. Afterwards we validate our a priori compressed models on physical data from a FE model solving a 2D wave equation. We show that the proposed convolutinal compression technique achieves equivalent performance as classical convolutional layers with fewer trainable parameters and lower memory footprint.

Overparameterized neural networks can be highly accurate on average on an i.i.d. test set yet consistently fail on atypical groups of the data (e.g., by learning spurious correlations that hold on average but not in such groups). Distributionally robust optimization (DRO) allows us to learn models that instead minimize the worst-case training loss over a set of pre-defined groups. However, we find that naively applying group DRO to overparameterized neural networks fails: these models can perfectly fit the training data, and any model with vanishing average training loss also already has vanishing worst-case training loss. Instead, the poor worst-case performance arises from poor generalization on some groups. By coupling group DRO models with increased regularization---a stronger-than-typical L2 penalty or early stopping---we achieve substantially higher worst-group accuracies, with 10-40 percentage point improvements on a natural language inference task and two image tasks, while maintaining high average accuracies. Our results suggest that regularization is important for worst-group generalization in the overparameterized regime, even if it is not needed for average generalization. Finally, we introduce a stochastic optimization algorithm, with convergence guarantees, to efficiently train group DRO models.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

Membership inference attacks (MIAs) aim to determine whether a specific sample was used to train a predictive model. Knowing this may indeed lead to a privacy breach. Most MIAs, however, make use of the model's prediction scores - the probability of each output given some input - following the intuition that the trained model tends to behave differently on its training data. We argue that this is a fallacy for many modern deep network architectures. Consequently, MIAs will miserably fail since overconfidence leads to high false-positive rates not only on known domains but also on out-of-distribution data and implicitly acts as a defense against MIAs. Specifically, using generative adversarial networks, we are able to produce a potentially infinite number of samples falsely classified as part of the training data. In other words, the threat of MIAs is overestimated, and less information is leaked than previously assumed. Moreover, there is actually a trade-off between the overconfidence of models and their susceptibility to MIAs: the more classifiers know when they do not know, making low confidence predictions, the more they reveal the training data.

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.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Single-step adversarial training (SSAT) has demonstrated the potential to achieve both efficiency and robustness. However, SSAT suffers from catastrophic overfitting (CO), a phenomenon that leads to a severely distorted classifier, making it vulnerable to multi-step adversarial attacks. In this work, we observe that some adversarial examples generated on the SSAT-trained network exhibit anomalous behaviour, that is, although these training samples are generated by the inner maximization process, their associated loss decreases instead, which we named abnormal adversarial examples (AAEs). Upon further analysis, we discover a close relationship between AAEs and classifier distortion, as both the number and outputs of AAEs undergo a significant variation with the onset of CO. Given this observation, we re-examine the SSAT process and uncover that before the occurrence of CO, the classifier already displayed a slight distortion, indicated by the presence of few AAEs. Furthermore, the classifier directly optimizing these AAEs will accelerate its distortion, and correspondingly, the variation of AAEs will sharply increase as a result. In such a vicious circle, the classifier rapidly becomes highly distorted and manifests as CO within a few iterations. These observations motivate us to eliminate CO by hindering the generation of AAEs. Specifically, we design a novel method, termed Abnormal Adversarial Examples Regularization (AAER), which explicitly regularizes the variation of AAEs to hinder the classifier from becoming distorted. Extensive experiments demonstrate that our method can effectively eliminate CO and further boost adversarial robustness with negligible additional computational overhead.

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

Collecting high-quality training examples for language model fine-tuning is expensive, with practical budgets limiting the amount of data that can be procured. We investigate whether example difficulty affects GRPO training effectiveness by comparing selection strategies (easy, medium, hard, random) across multiple models and reasoning tasks. Training on the hardest 10\% of examples (those where the base model fails most often) yields dramatic performance gains up to 47\%, while easy examples produce minimal improvements of 3-15\%. This occurs because GRPO requires outcome variance to generate learning signals; hard examples maintain mixed success/failure outcomes throughout training while easy examples quickly converge to consistent success, eliminating learning opportunities. Moreover, models trained on hard examples show superior out-of-distribution generalization, with only hard-trained models achieving meaningful gains on the AIME2025 benchmark. Our findings provide clear guidance: when budget-constrained, prioritize collecting and annotating examples where your base model struggles, as these drive nearly all learning value in GRPO fine-tuning

Large language models can resist task-misaligned activation steering during inference, sometimes recovering mid-generation to produce improved responses even when steering remains active. We term this Endogenous Steering Resistance (ESR). Using sparse autoencoder (SAE) latents to steer model activations, we find that Llama-3.3-70B shows substantial ESR, while smaller models from the Llama-3 and Gemma-2 families exhibit the phenomenon less frequently. We identify 26 SAE latents that activate differentially during off-topic content and are causally linked to ESR in Llama-3.3-70B. Zero-ablating these latents reduces the multi-attempt rate by 25%, providing causal evidence for dedicated internal consistency-checking circuits. We demonstrate that ESR can be deliberately enhanced through both prompting and training: meta-prompts instructing the model to self-monitor increase the multi-attempt rate by 4x for Llama-3.3-70B, and fine-tuning on self-correction examples successfully induces ESR-like behavior in smaller models. These findings have dual implications: ESR could protect against adversarial manipulation but might also interfere with beneficial safety interventions that rely on activation steering. Understanding and controlling these resistance mechanisms is important for developing transparent and controllable AI systems. Code is available at github.com/agencyenterprise/endogenous-steering-resistance.

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present in the context. We study harmful imitation through the lens of a model's internal representations, and identify two related phenomena: "overthinking" and "false induction heads". The first phenomenon, overthinking, appears when we decode predictions from intermediate layers, given correct vs. incorrect few-shot demonstrations. At early layers, both demonstrations induce similar model behavior, but the behavior diverges sharply at some "critical layer", after which the accuracy given incorrect demonstrations progressively decreases. The second phenomenon, false induction heads, are a possible mechanistic cause of overthinking: these are heads in late layers that attend to and copy false information from previous demonstrations, and whose ablation reduces overthinking. Beyond scientific understanding, our results suggest that studying intermediate model computations could be a promising avenue for understanding and guarding against harmful model behaviors.

Can AI agents predict whether they will succeed at a task? We study agentic uncertainty by eliciting success probability estimates before, during, and after task execution. All results exhibit agentic overconfidence: some agents that succeed only 22% of the time predict 77% success. Counterintuitively, pre-execution assessment with strictly less information tends to yield better discrimination than standard post-execution review, though differences are not always significant. Adversarial prompting reframing assessment as bug-finding achieves the best calibration.

Large Reasoning Models (LRMs) represent a breakthrough in AI problem-solving capabilities, but their effectiveness in interactive environments can be limited. This paper introduces and analyzes overthinking in LRMs. A phenomenon where models favor extended internal reasoning chains over environmental interaction. Through experiments on software engineering tasks using SWE Bench Verified, we observe three recurring patterns: Analysis Paralysis, Rogue Actions, and Premature Disengagement. We propose a framework to study these behaviors, which correlates with human expert assessments, and analyze 4018 trajectories. We observe that higher overthinking scores correlate with decreased performance, with reasoning models exhibiting stronger tendencies toward overthinking compared to non-reasoning models. Our analysis reveals that simple efforts to mitigate overthinking in agentic environments, such as selecting the solution with the lower overthinking score, can improve model performance by almost 30% while reducing computational costs by 43%. These results suggest that mitigating overthinking has strong practical implications. We suggest that by leveraging native function-calling capabilities and selective reinforcement learning overthinking tendencies could be mitigated. We also open-source our evaluation framework and dataset to facilitate research in this direction at https://github.com/AlexCuadron/Overthinking.

Test-time training (TTT) adapts language models through gradient-based updates at inference. But is adaptation the right strategy? We study compute-optimal test-time strategies for verifiable execution-grounded (VEG) tasks, domains like GPU kernel optimization where a deterministic evaluator provides dense, continuous reward signals. Using KernelBench as our testbed and a 120B-parameter model (GPT-OSS-120B with LoRA adaptation), we find that search outperforms minimal adaptation (1-5 gradient steps): Best-of-N sampling achieves 90% task success (18/20 tasks) at K=64 across the full KernelBench L1 eval set while TTT's best checkpoint reaches only 30.6% (3-seed mean), with TTT's "equivalent K" falling below 1, worse than single-sample inference. The failure mode is over-sharpening: gradient updates collapse diversity toward mediocre solutions rather than discovering optimal ones. Our main contribution is surprisal-guided selection: selecting the highest-surprisal (lowest-confidence) correct sample yields 80% success vs. 50% for most-confident selection, a 30% improvement. Extending to surprisal-guided-top3 matches oracle performance at 100%. This zero-cost strategy, validated through length-controlled analysis, recovers oracle performance. For dense-reward VEG tasks, compute should be allocated to sample diversity and intelligent selection rather than gradient adaptation. The surprisal-guided selection principle may generalize to other execution-grounded domains where optimal solutions occupy the distribution tail.

Determining whether inputs are out-of-distribution (OOD) is an essential building block for safely deploying machine learning models in the open world. However, previous methods relying on the softmax confidence score suffer from overconfident posterior distributions for OOD data. We propose a unified framework for OOD detection that uses an energy score. We show that energy scores better distinguish in- and out-of-distribution samples than the traditional approach using the softmax scores. Unlike softmax confidence scores, energy scores are theoretically aligned with the probability density of the inputs and are less susceptible to the overconfidence issue. Within this framework, energy can be flexibly used as a scoring function for any pre-trained neural classifier as well as a trainable cost function to shape the energy surface explicitly for OOD detection. On a CIFAR-10 pre-trained WideResNet, using the energy score reduces the average FPR (at TPR 95%) by 18.03% compared to the softmax confidence score. With energy-based training, our method outperforms the state-of-the-art on common benchmarks.

Deep learning is often criticized by two serious issues which rarely exist in natural nervous systems: overfitting and catastrophic forgetting. It can even memorize randomly labelled data, which has little knowledge behind the instance-label pairs. When a deep network continually learns over time by accommodating new tasks, it usually quickly overwrites the knowledge learned from previous tasks. Referred to as the {\it neural variability}, it is well-known in neuroscience that human brain reactions exhibit substantial variability even in response to the same stimulus. This mechanism balances accuracy and plasticity/flexibility in the motor learning of natural nervous systems. Thus it motivates us to design a similar mechanism named {\it artificial neural variability} (ANV), which helps artificial neural networks learn some advantages from ``natural'' neural networks. We rigorously prove that ANV plays as an implicit regularizer of the mutual information between the training data and the learned model. This result theoretically guarantees ANV a strictly improved generalizability, robustness to label noise, and robustness to catastrophic forgetting. We then devise a {\it neural variable risk minimization} (NVRM) framework and {\it neural variable optimizers} to achieve ANV for conventional network architectures in practice. The empirical studies demonstrate that NVRM can effectively relieve overfitting, label noise memorization, and catastrophic forgetting at negligible costs. Code: \url{https://github.com/zeke-xie/artificial-neural-variability-for-deep-learning.

Recent Large Reasoning Models (LRMs) have achieved remarkable progress on task-specific benchmarks, yet their evaluation methods remain constrained by isolated problem-solving paradigms. Existing benchmarks predominantly assess single-question reasoning through sequential testing, resulting critical limitations: (1) vulnerability to data contamination and less challenging (e.g., DeepSeek-R1 achieves 97.0% on MATH500), forcing costly and perpetual creation of new questions with large human efforts, (2) failure to evaluate models under multi-context pressure, a key requirement for real-world deployment. To bridge this gap, we present REST (Reasoning Evaluation through Simultaneous Testing), a stress-testing framework that concurrently exposes LRMs to multiple problems simultaneously. Beyond basic reasoning, REST specifically evaluates several under-tested capabilities: contextual priority allocation, cross-problem interference resistance, and dynamic cognitive load management. Our evaluation reveals several striking findings: Even state-of-the-art (SOTA) models like DeepSeek-R1 exhibit substantial performance degradation under stress testing. Crucially, REST demonstrates stronger discriminative power than existing benchmarks, revealing pronounced performance differences among models that exhibit similar, near-ceiling performance under single-question evaluations. Some key mechanistic insights emerge from our analysis: (1) the "overthinking trap" is a critical factor contributing to the performance degradation; (2) the models trained with "long2short" technique preserve more accuracy of their single-problem performance under REST, outperforming standard-trained counterparts. These results establish REST as a cost-efficient, future-proof evaluation paradigm that better reflects real-world reasoning demands while reducing reliance on continuous human annotation.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.