Daily Papers

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

A primary goal of class-incremental learning is to strike a balance between stability and plasticity, where models should be both stable enough to retain knowledge learned from previously seen classes, and plastic enough to learn concepts from new classes. While previous works demonstrate strong performance on class-incremental benchmarks, it is not clear whether their success comes from the models being stable, plastic, or a mixture of both. This paper aims to shed light on how effectively recent class-incremental learning algorithms address the stability-plasticity trade-off. We establish analytical tools that measure the stability and plasticity of feature representations, and employ such tools to investigate models trained with various algorithms on large-scale class-incremental benchmarks. Surprisingly, we find that the majority of class-incremental learning algorithms heavily favor stability over plasticity, to the extent that the feature extractor of a model trained on the initial set of classes is no less effective than that of the final incremental model. Our observations not only inspire two simple algorithms that highlight the importance of feature representation analysis, but also suggest that class-incremental learning approaches, in general, should strive for better feature representation learning.

Catastrophic forgetting has been a major challenge in continual learning, where the model needs to learn new tasks with limited or no access to data from previously seen tasks. To tackle this challenge, methods based on knowledge distillation in feature space have been proposed and shown to reduce forgetting. However, most feature distillation methods directly constrain the new features to match the old ones, overlooking the need for plasticity. To achieve a better stability-plasticity trade-off, we propose Backward Feature Projection (BFP), a method for continual learning that allows the new features to change up to a learnable linear transformation of the old features. BFP preserves the linear separability of the old classes while allowing the emergence of new feature directions to accommodate new classes. BFP can be integrated with existing experience replay methods and boost performance by a significant margin. We also demonstrate that BFP helps learn a better representation space, in which linear separability is well preserved during continual learning and linear probing achieves high classification accuracy. The code can be found at https://github.com/rvl-lab-utoronto/BFP

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative methods address continual learning, and how they are adapted to particular challenges in realistic applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Continual learning aims to emulate the human ability to continually accumulate knowledge over sequential tasks. The main challenge is to maintain performance on previously learned tasks after learning new tasks, i.e., to avoid catastrophic forgetting. We propose a Channel-wise Lightweight Reprogramming (CLR) approach that helps convolutional neural networks (CNNs) overcome catastrophic forgetting during continual learning. We show that a CNN model trained on an old task (or self-supervised proxy task) could be ``reprogrammed" to solve a new task by using our proposed lightweight (very cheap) reprogramming parameter. With the help of CLR, we have a better stability-plasticity trade-off to solve continual learning problems: To maintain stability and retain previous task ability, we use a common task-agnostic immutable part as the shared ``anchor" parameter set. We then add task-specific lightweight reprogramming parameters to reinterpret the outputs of the immutable parts, to enable plasticity and integrate new knowledge. To learn sequential tasks, we only train the lightweight reprogramming parameters to learn each new task. Reprogramming parameters are task-specific and exclusive to each task, which makes our method immune to catastrophic forgetting. To minimize the parameter requirement of reprogramming to learn new tasks, we make reprogramming lightweight by only adjusting essential kernels and learning channel-wise linear mappings from anchor parameters to task-specific domain knowledge. We show that, for general CNNs, the CLR parameter increase is less than 0.6\% for any new task. Our method outperforms 13 state-of-the-art continual learning baselines on a new challenging sequence of 53 image classification datasets. Code and data are available at https://github.com/gyhandy/Channel-wise-Lightweight-Reprogramming

Continual Learning (CL) seeks to enable neural networks to incrementally acquire new knowledge (plasticity) while retaining existing knowledge (stability). While pre-trained models (PTMs) have become pivotal in CL, prevailing approaches freeze the PTM backbone to preserve stability, limiting their plasticity, particularly when encountering significant domain gaps in incremental tasks. Conversely, sequentially finetuning the entire PTM risks catastrophic forgetting of generalizable knowledge, exposing a critical stability-plasticity trade-off. To address this challenge, we propose Adapting PTMs before the core CL process (ACL), a novel framework that refines the PTM backbone through a plug-and-play adaptation phase before learning each new task with existing CL approaches (e.g., prompt tuning). ACL enhances plasticity by aligning embeddings with their original class prototypes while distancing them from others, theoretically and empirically shown to balance stability and plasticity. Extensive experiments demonstrate that ACL significantly improves CL performance across benchmarks and integrated methods, offering a versatile solution for PTM-based CL.

We address the problem of class incremental learning, which is a core step towards achieving adaptive vision intelligence. In particular, we consider the task setting of incremental learning with limited memory and aim to achieve better stability-plasticity trade-off. To this end, we propose a novel two-stage learning approach that utilizes a dynamically expandable representation for more effective incremental concept modeling. Specifically, at each incremental step, we freeze the previously learned representation and augment it with additional feature dimensions from a new learnable feature extractor. This enables us to integrate new visual concepts with retaining learned knowledge. We dynamically expand the representation according to the complexity of novel concepts by introducing a channel-level mask-based pruning strategy. Moreover, we introduce an auxiliary loss to encourage the model to learn diverse and discriminate features for novel concepts. We conduct extensive experiments on the three class incremental learning benchmarks and our method consistently outperforms other methods with a large margin.

Continual learning is a promising machine learning paradigm to learn new tasks while retaining previously learned knowledge over streaming training data. Till now, rehearsal-based methods, keeping a small part of data from old tasks as a memory buffer, have shown good performance in mitigating catastrophic forgetting for previously learned knowledge. However, most of these methods typically treat each new task equally, which may not adequately consider the relationship or similarity between old and new tasks. Furthermore, these methods commonly neglect sample importance in the continual training process and result in sub-optimal performance on certain tasks. To address this challenging problem, we propose Relational Experience Replay (RER), a bi-level learning framework, to adaptively tune task-wise relationships and sample importance within each task to achieve a better `stability' and `plasticity' trade-off. As such, the proposed method is capable of accumulating new knowledge while consolidating previously learned old knowledge during continual learning. Extensive experiments conducted on three publicly available datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) show that the proposed method can consistently improve the performance of all baselines and surpass current state-of-the-art methods.

How to train a generalizable meta-policy by continually learning a sequence of tasks? It is a natural human skill yet challenging to achieve by current reinforcement learning: the agent is expected to quickly adapt to new tasks (plasticity) meanwhile retaining the common knowledge from previous tasks (stability). We address it by "Continual Task Allocation via Sparse Prompting (CoTASP)", which learns over-complete dictionaries to produce sparse masks as prompts extracting a sub-network for each task from a meta-policy network. CoTASP trains a policy for each task by optimizing the prompts and the sub-network weights alternatively. The dictionary is then updated to align the optimized prompts with tasks' embedding, thereby capturing tasks' semantic correlations. Hence, relevant tasks share more neurons in the meta-policy network due to similar prompts while cross-task interference causing forgetting is effectively restrained. Given a meta-policy and dictionaries trained on previous tasks, new task adaptation reduces to highly efficient sparse prompting and sub-network finetuning. In experiments, CoTASP achieves a promising plasticity-stability trade-off without storing or replaying any past tasks' experiences. It outperforms existing continual and multi-task RL methods on all seen tasks, forgetting reduction, and generalization to unseen tasks.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

Various algorithms for continual learning (CL) have been designed with the goal of effectively alleviating the trade-off between stability and plasticity during the CL process. To achieve this goal, tuning appropriate hyperparameters for each algorithm is essential. As an evaluation protocol, it has been common practice to train a CL algorithm using diverse hyperparameter values on a CL scenario constructed with a benchmark dataset. Subsequently, the best performance attained with the optimal hyperparameter value serves as the criterion for evaluating the CL algorithm. In this paper, we contend that this evaluation protocol is not only impractical but also incapable of effectively assessing the CL capability of a CL algorithm. Returning to the fundamental principles of model evaluation in machine learning, we propose an evaluation protocol that involves Hyperparameter Tuning and Evaluation phases. Those phases consist of different datasets but share the same CL scenario. In the Hyperparameter Tuning phase, each algorithm is iteratively trained with different hyperparameter values to find the optimal hyperparameter values. Subsequently, in the Evaluation phase, the optimal hyperparameter values is directly applied for training each algorithm, and their performance in the Evaluation phase serves as the criterion for evaluating them. Through experiments on CIFAR-100 and ImageNet-100 based on the proposed protocol in class-incremental learning, we not only observed that the existing evaluation method fail to properly assess the CL capability of each algorithm but also observe that some recently proposed state-of-the-art algorithms, which reported superior performance, actually exhibit inferior performance compared to the previous algorithm.

Training stability remains a critical bottleneck for Group Relative Policy Optimization (GRPO), often manifesting as a trade-off between reasoning plasticity and general capability retention. We identify a root cause as the geometric conflict between plasticity and stability gradients, which leads to destructive interference. Crucially, we argue that deterministic projection methods are suboptimal for GRPO as they overlook the intrinsic stochasticity of group-based gradient estimates. To address this, we propose Probabilistic Conflict Resolution (PCR), a Bayesian framework that models gradients as random variables. PCR dynamically arbitrates conflicts via an uncertainty-aware ``soft projection'' mechanism, optimizing the signal-to-noise ratio. Extensive experiments demonstrate that PCR significantly smooths the training trajectory and achieves superior performance in various reasoning tasks.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

We introduce a novel and general loss function, called Symmetric Contrastive (Sy-CON) loss, for effective continual self-supervised learning (CSSL). We first argue that the conventional loss form of continual learning which consists of single task-specific loss (for plasticity) and a regularizer (for stability) may not be ideal for contrastive loss based CSSL that focus on representation learning. Our reasoning is that, in contrastive learning based methods, the task-specific loss would suffer from decreasing diversity of negative samples and the regularizer may hinder learning new distinctive representations. To that end, we propose Sy-CON that consists of two losses (one for plasticity and the other for stability) with symmetric dependence on current and past models' negative sample embeddings. We argue our model can naturally find good trade-off between the plasticity and stability without any explicit hyperparameter tuning. We validate the effectiveness of our approach through extensive experiments, demonstrating that MoCo-based implementation of Sy-CON loss achieves superior performance compared to other state-of-the-art CSSL methods.

The intrinsic difficulty in adapting deep learning models to non-stationary environments limits the applicability of neural networks to real-world tasks. This issue is critical in practical supervised learning settings, such as the ones in which a pre-trained model computes projections toward a latent space where different task predictors are sequentially learned over time. As a matter of fact, incrementally fine-tuning the whole model to better adapt to new tasks usually results in catastrophic forgetting, with decreasing performance over the past experiences and losing valuable knowledge from the pre-training stage. In this paper, we propose a novel strategy to make the fine-tuning procedure more effective, by avoiding to update the pre-trained part of the network and learning not only the usual classification head, but also a set of newly-introduced learnable parameters that are responsible for transforming the input data. This process allows the network to effectively leverage the pre-training knowledge and find a good trade-off between plasticity and stability with modest computational efforts, thus especially suitable for on-the-edge settings. Our experiments on four image classification problems in a continual learning setting confirm the quality of the proposed approach when compared to several fine-tuning procedures and to popular continual learning methods.

Existing research has shown that large language models (LLMs) exhibit remarkable performance in language understanding and generation. However, when LLMs are continuously fine-tuned on complex and diverse domain-specific downstream tasks, the inference performance on historical tasks decreases dramatically, which is known as a catastrophic forgetting problem. A trade-off needs to be kept between learning plasticity and memory stability. Plenty of existing works have explored strategies like memory replay, regularization and parameter isolation, but little is known about the geometric connection of various adjacent minima in the continual LLMs fine-tuning scenarios. In this work, we investigate the geometric connections of different minima through the lens of mode connectivity, which means different minima can be connected by a low-loss valley. Through extensive experiments, we uncover the mode connectivity phenomenon in the LLMs continual learning scenario and find that it can strike a balance between plasticity and stability. Building upon these findings, we propose a simple yet effective method called Interpolation-based LoRA (I-LoRA), which constructs a dual-memory experience replay framework based on LoRA parameter interpolations. Extensive experiments and analysis on eight domain-specific CL benchmarks demonstrate that I-LoRA consistently show significant improvement over the previous state-of-the-art approaches with up to 11% performance gains, providing a strong baseline and insights for future research on the large language model continual learning problem. Our code is available at https://github.com/which47/LLMCL.

Offline-to-online reinforcement learning (RL) has emerged as a practical paradigm that leverages offline datasets for pretraining and online interactions for fine-tuning. However, its empirical behavior is highly inconsistent: design choices of online-fine tuning that work well in one setting can fail completely in another. We propose a stability--plasticity principle that can explain this inconsistency: we should preserve the knowledge of pretrained policy or offline dataset during online fine-tuning, whichever is better, while maintaining sufficient plasticity. This perspective identifies three regimes of online fine-tuning, each requiring distinct stability properties. We validate this framework through a large-scale empirical study, finding that the results strongly align with its predictions in 45 of 63 cases. This work provides a principled framework for guiding design choices in offline-to-online RL based on the relative performance of the offline dataset and the pretrained policy.

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose plasticity over the course of training even in relatively simple learning problems, but the mechanisms driving this phenomenon are still poorly understood. This paper conducts a systematic empirical analysis into plasticity loss, with the goal of understanding the phenomenon mechanistically in order to guide the future development of targeted solutions. We find that loss of plasticity is deeply connected to changes in the curvature of the loss landscape, but that it typically occurs in the absence of saturated units or divergent gradient norms. Based on this insight, we identify a number of parameterization and optimization design choices which enable networks to better preserve plasticity over the course of training. We validate the utility of these findings in larger-scale learning problems by applying the best-performing intervention, layer normalization, to a deep RL agent trained on the Arcade Learning Environment.

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

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

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

Multi-task reinforcement learning (MTRL) aims to endow a single agent with the ability to perform well on multiple tasks. Recent works have focused on developing novel sophisticated architectures to improve performance, often resulting in larger models; it is unclear, however, whether the performance gains are a consequence of the architecture design itself or the extra parameters. We argue that gains are mostly due to scale by demonstrating that naively scaling up a simple MTRL baseline to match parameter counts outperforms the more sophisticated architectures, and these gains benefit most from scaling the critic over the actor. Additionally, we explore the training stability advantages that come with task diversity, demonstrating that increasing the number of tasks can help mitigate plasticity loss. Our findings suggest that MTRL's simultaneous training across multiple tasks provides a natural framework for beneficial parameter scaling in reinforcement learning, challenging the need for complex architectural innovations.

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with inhibitory-excitatory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through neurons exhibiting rule-flipped plasticity. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

Deep neural networks coupled with fast simulation and improved computation have led to recent successes in the field of reinforcement learning (RL). However, most current RL-based approaches fail to generalize since: (a) the gap between simulation and real world is so large that policy-learning approaches fail to transfer; (b) even if policy learning is done in real world, the data scarcity leads to failed generalization from training to test scenarios (e.g., due to different friction or object masses). Inspired from H-infinity control methods, we note that both modeling errors and differences in training and test scenarios can be viewed as extra forces/disturbances in the system. This paper proposes the idea of robust adversarial reinforcement learning (RARL), where we train an agent to operate in the presence of a destabilizing adversary that applies disturbance forces to the system. The jointly trained adversary is reinforced -- that is, it learns an optimal destabilization policy. We formulate the policy learning as a zero-sum, minimax objective function. Extensive experiments in multiple environments (InvertedPendulum, HalfCheetah, Swimmer, Hopper and Walker2d) conclusively demonstrate that our method (a) improves training stability; (b) is robust to differences in training/test conditions; and c) outperform the baseline even in the absence of the adversary.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning rates affect the loss Hessian observed during training, we also analyze the effects of model initialization, architectural choices, and common training heuristics such as gradient clipping and learning rate warmup. Our results demonstrate that successful model and hyperparameter choices allow the early optimization trajectory to either avoid -- or navigate out of -- regions of high curvature and into flatter regions that tolerate a higher learning rate. Our results suggest a unifying perspective on how disparate mitigation strategies for training instability ultimately address the same underlying failure mode of neural network optimization, namely poor conditioning. Inspired by the conditioning perspective, we show that learning rate warmup can improve training stability just as much as batch normalization, layer normalization, MetaInit, GradInit, and Fixup initialization.

We address a benchmark task in agile robotics: catching objects thrown at high-speed. This is a challenging task that involves tracking, intercepting, and cradling a thrown object with access only to visual observations of the object and the proprioceptive state of the robot, all within a fraction of a second. We present the relative merits of two fundamentally different solution strategies: (i) Model Predictive Control using accelerated constrained trajectory optimization, and (ii) Reinforcement Learning using zeroth-order optimization. We provide insights into various performance trade-offs including sample efficiency, sim-to-real transfer, robustness to distribution shifts, and whole-body multimodality via extensive on-hardware experiments. We conclude with proposals on fusing "classical" and "learning-based" techniques for agile robot control. Videos of our experiments may be found at https://sites.google.com/view/agile-catching

Artificial neural networks often suffer from catastrophic forgetting, where learning new concepts leads to a complete loss of previously acquired knowledge. We observe that this issue is particularly magnified in vision transformers (ViTs), where post-pre-training and fine-tuning on new tasks can significantly degrade the model's original general abilities. For instance, a DINO ViT-Base/16 pre-trained on ImageNet-1k loses over 70% accuracy on ImageNet-1k after just 10 iterations of fine-tuning on CIFAR-100. Overcoming this stability-plasticity dilemma is crucial for enabling ViTs to continuously learn and adapt to new domains while preserving their initial knowledge. In this work, we study two new parameter-efficient fine-tuning strategies: (1)~Block Expansion, and (2) Low-rank adaptation (LoRA). Our experiments reveal that using either Block Expansion or LoRA on self-supervised pre-trained ViTs surpass fully fine-tuned ViTs in new domains while offering significantly greater parameter efficiency. Notably, we find that Block Expansion experiences only a minimal performance drop in the pre-training domain, thereby effectively mitigating catastrophic forgetting in pre-trained ViTs.

Stable locomotion in precipitous environments is an essential capability of quadruped robots, demanding the ability to resist various external disturbances. However, recent learning-based policies only use basic domain randomization to improve the robustness of learned policies, which cannot guarantee that the robot has adequate disturbance resistance capabilities. In this paper, we propose to model the learning process as an adversarial interaction between the actor and a newly introduced disturber and ensure their optimization with H_{infty} constraint. In contrast to the actor that maximizes the discounted overall reward, the disturber is responsible for generating effective external forces and is optimized by maximizing the error between the task reward and its oracle, i.e., "cost" in each iteration. To keep joint optimization between the actor and the disturber stable, our H_{infty} constraint mandates the bound of ratio between the cost to the intensity of the external forces. Through reciprocal interaction throughout the training phase, the actor can acquire the capability to navigate increasingly complex physical disturbances. We verify the robustness of our approach on quadrupedal locomotion tasks with Unitree Aliengo robot, and also a more challenging task with Unitree A1 robot, where the quadruped is expected to perform locomotion merely on its hind legs as if it is a bipedal robot. The simulated quantitative results show improvement against baselines, demonstrating the effectiveness of the method and each design choice. On the other hand, real-robot experiments qualitatively exhibit how robust the policy is when interfering with various disturbances on various terrains, including stairs, high platforms, slopes, and slippery terrains. All code, checkpoints, and real-world deployment guidance will be made public.

Benchmarking the tradeoff between neural network accuracy and training time is computationally expensive. Here we show how a multiplicative cyclic learning rate schedule can be used to construct a tradeoff curve in a single training run. We generate cyclic tradeoff curves for combinations of training methods such as Blurpool, Channels Last, Label Smoothing and MixUp, and highlight how these cyclic tradeoff curves can be used to evaluate the effects of algorithmic choices on network training efficiency.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

Methods for controlling large language models (LLMs), including local weight fine-tuning, LoRA-based adaptation, and activation-based interventions, are often studied in isolation, obscuring their connections and making comparison difficult. In this work, we present a unified view that frames these interventions as dynamic weight updates induced by a control signal, placing them within a single conceptual framework. Building on this view, we propose a unified preference-utility analysis that separates control effects into preference, defined as the tendency toward a target concept, and utility, defined as coherent and task-valid generation, and measures both on a shared log-odds scale using polarity-paired contrastive examples. Across methods, we observe a consistent trade-off between preference and utility: stronger control increases preference while predictably reducing utility. We further explain this behavior through an activation manifold perspective, in which control shifts representations along target-concept directions to enhance preference, while utility declines primarily when interventions push representations off the model's valid-generation manifold. Finally, we introduce a new steering approach SPLIT guided by this analysis that improves preference while better preserving utility. Code is available at https://github.com/zjunlp/EasyEdit/blob/main/examples/SPLIT.md.

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so far. However, we show that even with a perfect approximation to the joint loss, these approaches still suffer from temporary but substantial forgetting when starting to train on a new task. Motivated by this 'stability gap', we propose that continual learning strategies should focus not only on the optimization objective, but also on the way this objective is optimized. While there is some continual learning work that alters the optimization trajectory (e.g., using gradient projection techniques), this line of research is positioned as alternative to improving the optimization objective, while we argue it should be complementary. To evaluate the merits of our proposition, we plan to combine replay-approximated joint objectives with gradient projection-based optimization routines to test whether the addition of the latter provides benefits in terms of (1) alleviating the stability gap, (2) increasing the learning efficiency and (3) improving the final learning outcome.

Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role remains poorly understood for deep learning. In this work, we highlight that the role of weight decay in modern deep learning is different from its regularization effect studied in classical learning theory. For deep networks on vision tasks trained with multipass SGD, we show how weight decay modifies the optimization dynamics enhancing the ever-present implicit regularization of SGD via the loss stabilization mechanism. In contrast, for large language models trained with nearly one-epoch training, we describe how weight decay balances the bias-variance tradeoff in stochastic optimization leading to lower training loss and improved training stability. Overall, we present a unifying perspective from ResNets on vision tasks to LLMs: weight decay is never useful as an explicit regularizer but instead changes the training dynamics in a desirable way. The code is available at https://github.com/tml-epfl/why-weight-decay

Plasticity, the ability of a neural network to evolve with new data, is crucial for high-performance and sample-efficient visual reinforcement learning (VRL). Although methods like resetting and regularization can potentially mitigate plasticity loss, the influences of various components within the VRL framework on the agent's plasticity are still poorly understood. In this work, we conduct a systematic empirical exploration focusing on three primary underexplored facets and derive the following insightful conclusions: (1) data augmentation is essential in maintaining plasticity; (2) the critic's plasticity loss serves as the principal bottleneck impeding efficient training; and (3) without timely intervention to recover critic's plasticity in the early stages, its loss becomes catastrophic. These insights suggest a novel strategy to address the high replay ratio (RR) dilemma, where exacerbated plasticity loss hinders the potential improvements of sample efficiency brought by increased reuse frequency. Rather than setting a static RR for the entire training process, we propose Adaptive RR, which dynamically adjusts the RR based on the critic's plasticity level. Extensive evaluations indicate that Adaptive RR not only avoids catastrophic plasticity loss in the early stages but also benefits from more frequent reuse in later phases, resulting in superior sample efficiency.

The increasing computational demands of foundation models have spurred research into low-precision training, with 4-bit floating-point (FP4) formats emerging as a frontier for maximizing hardware throughput. While numerous techniques have been proposed to stabilize FP4 training, they often present isolated solutions with varying, and not always clear, computational overheads. This paper aims to provide a unified view of the design space of FP4 training. We introduce a comprehensive, quantisation gradient-based framework for microscaling quantization that allows for a theoretical analysis of the computational costs associated with different stabilization methods on both the forward and backward passes. Using a simulator built on this framework, we conduct an extensive empirical study across a wide range of machine learning tasks, including regression, image classification, diffusion models, and language models. By systematically evaluating thousands of combinations of techniques, such as novel gradient approximations, rounding strategies, and scaling methods, we identify which configurations offer the most favourable performance-to-overhead trade-off. We find that the techniques enabling the best trade-off involve carefully combining Hadamard transformations, tensor scaling and stochastic rounding. We further find that using UE5M3 as a scaling factor potentially offers a good compromise between range and precision with manageable computational overhead.

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data.

Matbench Discovery simulates the deployment of machine learning (ML) energy models in a high-throughput search for stable inorganic crystals. We address the disconnect between (i) thermodynamic stability and formation energy and (ii) in-domain vs out-of-distribution performance. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with further insights into trade-offs between various performance metrics. To answer the question which ML methodology performs best at materials discovery, our initial release explores a variety of models including random forests, graph neural networks (GNN), one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials (UIP). Ranked best-to-worst by their test set F1 score on thermodynamic stability prediction, we find CHGNet > M3GNet > MACE > ALIGNN > MEGNet > CGCNN > CGCNN+P > Wrenformer > BOWSR > Voronoi tessellation fingerprints with random forest. The top 3 models are UIPs, the winning methodology for ML-guided materials discovery, achieving F1 scores of ~0.6 for crystal stability classification and discovery acceleration factors (DAF) of up to 5x on the first 10k most stable predictions compared to dummy selection from our test set. We also highlight a sharp disconnect between commonly used global regression metrics and more task-relevant classification metrics. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV/atom above the convex hull where most materials are. Our results highlight the need to focus on classification metrics that actually correlate with improved stability hit rate.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

Deep neural policies have recently been installed in a diverse range of settings, from biotechnology to automated financial systems. However, the utilization of deep neural networks to approximate the value function leads to concerns on the decision boundary stability, in particular, with regard to the sensitivity of policy decision making to indiscernible, non-robust features due to highly non-convex and complex deep neural manifolds. These concerns constitute an obstruction to understanding the reasoning made by deep neural policies, and their foundational limitations. Hence, it is crucial to develop techniques that aim to understand the sensitivities in the learnt representations of neural network policies. To achieve this we introduce a theoretically founded method that provides a systematic analysis of the unstable directions in the deep neural policy decision boundary across both time and space. Through experiments in the Arcade Learning Environment (ALE), we demonstrate the effectiveness of our technique for identifying correlated directions of instability, and for measuring how sample shifts remold the set of sensitive directions in the neural policy landscape. Most importantly, we demonstrate that state-of-the-art robust training techniques yield learning of disjoint unstable directions, with dramatically larger oscillations over time, when compared to standard training. We believe our results reveal the fundamental properties of the decision process made by reinforcement learning policies, and can help in constructing reliable and robust deep neural policies.

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.

Knowledge distillation transfers knowledge from a large model to a small one via task and distillation losses. In this paper, we observe a trade-off between task and distillation losses, i.e., introducing distillation loss limits the convergence of task loss. We believe that the trade-off results from the insufficient optimization of distillation loss. The reason is: The teacher has a lower task loss than the student, and a lower distillation loss drives the student more similar to the teacher, then a better-converged task loss could be obtained. To break the trade-off, we propose the Distillation-Oriented Trainer (DOT). DOT separately considers gradients of task and distillation losses, then applies a larger momentum to distillation loss to accelerate its optimization. We empirically prove that DOT breaks the trade-off, i.e., both losses are sufficiently optimized. Extensive experiments validate the superiority of DOT. Notably, DOT achieves a +2.59% accuracy improvement on ImageNet-1k for the ResNet50-MobileNetV1 pair. Conclusively, DOT greatly benefits the student's optimization properties in terms of loss convergence and model generalization. Code will be made publicly available.

We consider the problem of training a deep neural network on a given classification task, e.g., ImageNet-1K (IN1K), so that it excels at both the training task as well as at other (future) transfer tasks. These two seemingly contradictory properties impose a trade-off between improving the model's generalization and maintaining its performance on the original task. Models trained with self-supervised learning tend to generalize better than their supervised counterparts for transfer learning; yet, they still lag behind supervised models on IN1K. In this paper, we propose a supervised learning setup that leverages the best of both worlds. We extensively analyze supervised training using multi-scale crops for data augmentation and an expendable projector head, and reveal that the design of the projector allows us to control the trade-off between performance on the training task and transferability. We further replace the last layer of class weights with class prototypes computed on the fly using a memory bank and derive two models: t-ReX that achieves a new state of the art for transfer learning and outperforms top methods such as DINO and PAWS on IN1K, and t-ReX* that matches the highly optimized RSB-A1 model on IN1K while performing better on transfer tasks. Code and pretrained models: https://europe.naverlabs.com/t-rex

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal LR can be accurately extrapolated from low-cost experiments. In this paper, we formalize this investigation into two distinct research paradigms: Fitting and Transfer. Within the Fitting Paradigm, we innovatively introduce a Scaling Law for search factor, effectively reducing the search complexity from O(n^3) to O(n*C_D*C_η) via predictive modeling. Within the Transfer Paradigm, we extend the principles of μTransfer to the Mixture of Experts (MoE) architecture, broadening its applicability to encompass model depth, weight decay, and token horizons. By pushing the boundaries of existing hyperparameter research in terms of scale, we conduct a comprehensive comparison between these two paradigms. Our empirical results challenge the scalability of the widely adopted μ Transfer in large-scale pre-training scenarios. Furthermore, we provide a rigorous analysis through the dual lenses of training stability and feature learning to elucidate the underlying reasons why module-wise parameter tuning underperforms in large-scale settings. This work offers systematic practical guidelines and a fresh theoretical perspective for optimizing industrial-level pre-training.

Most existing works focus on improving robustness against adversarial attacks bounded by a single l_p norm using adversarial training (AT). However, these AT models' multiple-norm robustness (union accuracy) is still low, which is crucial since in the real-world an adversary is not necessarily bounded by a single norm. The tradeoffs among robustness against multiple l_p perturbations and accuracy/robustness make obtaining good union and clean accuracy challenging. We design a logit pairing loss to improve the union accuracy by analyzing the tradeoffs from the lens of distribution shifts. We connect natural training (NT) with AT via gradient projection, to incorporate useful information from NT into AT, where we empirically and theoretically show it moderates the accuracy/robustness tradeoff. We propose a novel training framework RAMP, to boost the robustness against multiple l_p perturbations. RAMP can be easily adapted for robust fine-tuning and full AT. For robust fine-tuning, RAMP obtains a union accuracy up to 53.3% on CIFAR-10, and 29.1% on ImageNet. For training from scratch, RAMP achieves a union accuracy of 44.6% and good clean accuracy of 81.2% on ResNet-18 against AutoAttack on CIFAR-10. Beyond multi-norm robustness RAMP-trained models achieve superior universal robustness, effectively generalizing against a range of unseen adversaries and natural corruptions.

Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse agents choose policies that minimize risk, occasionally sacrificing expected value. These preferences can be framed through utility theory. We focus on the specific case of the exponential utility function, where we can derive the Bellman equations and employ various reinforcement learning algorithms with few modifications. However, these methods suffer from numerical instability due to the need for exponent computation throughout the process. To address this, we introduce a numerically stable and mathematically sound loss function based on the Itakura-Saito divergence for learning state-value and action-value functions. We evaluate our proposed loss function against established alternatives, both theoretically and empirically. In the experimental section, we explore multiple financial scenarios, some with known analytical solutions, and show that our loss function outperforms the alternatives.

Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot learning, and adversarially robust learning. However, little work has theoretically investigated the effect of generative data augmentation. To fill this gap, we establish a general stability bound in this not independently and identically distributed (non-i.i.d.) setting, where the learned distribution is dependent on the original train set and generally not the same as the true distribution. Our theoretical result includes the divergence between the learned distribution and the true distribution. It shows that generative data augmentation can enjoy a faster learning rate when the order of divergence term is o(maxleft( log(m)beta_m, 1 / m)right), where m is the train set size and beta_m is the corresponding stability constant. We further specify the learning setup to the Gaussian mixture model and generative adversarial nets. We prove that in both cases, though generative data augmentation does not enjoy a faster learning rate, it can improve the learning guarantees at a constant level when the train set is small, which is significant when the awful overfitting occurs. Simulation results on the Gaussian mixture model and empirical results on generative adversarial nets support our theoretical conclusions. Our code is available at https://github.com/ML-GSAI/Understanding-GDA.

Modern deep-learning systems are specialized to problem settings in which training occurs once and then never again, as opposed to continual-learning settings in which training occurs continually. If deep-learning systems are applied in a continual learning setting, then it is well known that they may fail to remember earlier examples. More fundamental, but less well known, is that they may also lose their ability to learn on new examples, a phenomenon called loss of plasticity. We provide direct demonstrations of loss of plasticity using the MNIST and ImageNet datasets repurposed for continual learning as sequences of tasks. In ImageNet, binary classification performance dropped from 89\% accuracy on an early task down to 77\%, about the level of a linear network, on the 2000th task. Loss of plasticity occurred with a wide range of deep network architectures, optimizers, activation functions, batch normalization, dropout, but was substantially eased by L^2-regularization, particularly when combined with weight perturbation. Further, we introduce a new algorithm -- continual backpropagation -- which slightly modifies conventional backpropagation to reinitialize a small fraction of less-used units after each example and appears to maintain plasticity indefinitely.

The "alignment tax" of post-training is typically framed as a drop in task accuracy. We show it also involves a severe loss of calibration, making models overconfident, less reliable, and model outputs less diverse. We show that this trade-off can be navigated effectively via a simple post-hoc intervention: interpolating between a model's weights before and after alignment. Crucially, this is not a strict trade-off. We find that the process consistently reveals Pareto-optimal interpolations - models that improve accuracy beyond both parents while substantially recovering the calibration lost during alignment. Our work demonstrates that simple model merging provides a computationally efficient method for mitigating the full scope of the alignment tax, yielding models that are more capable and more reliable.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) L^2 distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) L^2 and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

Generative flow networks (GFlowNets) are a family of algorithms for training a sequential sampler of discrete objects under an unnormalized target density and have been successfully used for various probabilistic modeling tasks. Existing training objectives for GFlowNets are either local to states or transitions, or propagate a reward signal over an entire sampling trajectory. We argue that these alternatives represent opposite ends of a gradient bias-variance tradeoff and propose a way to exploit this tradeoff to mitigate its harmful effects. Inspired by the TD(lambda) algorithm in reinforcement learning, we introduce subtrajectory balance or SubTB(lambda), a GFlowNet training objective that can learn from partial action subsequences of varying lengths. We show that SubTB(lambda) accelerates sampler convergence in previously studied and new environments and enables training GFlowNets in environments with longer action sequences and sparser reward landscapes than what was possible before. We also perform a comparative analysis of stochastic gradient dynamics, shedding light on the bias-variance tradeoff in GFlowNet training and the advantages of subtrajectory balance.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Most 3D object generators focus on aesthetic quality, often neglecting physical constraints necessary in applications. One such constraint is that the 3D object should be self-supporting, i.e., remains balanced under gravity. Prior approaches to generating stable 3D objects used differentiable physics simulators to optimize geometry at test-time, which is slow, unstable, and prone to local optima. Inspired by the literature on aligning generative models to external feedback, we propose Direct Simulation Optimization (DSO), a framework to use the feedback from a (non-differentiable) simulator to increase the likelihood that the 3D generator outputs stable 3D objects directly. We construct a dataset of 3D objects labeled with a stability score obtained from the physics simulator. We can then fine-tune the 3D generator using the stability score as the alignment metric, via direct preference optimization (DPO) or direct reward optimization (DRO), a novel objective, which we introduce, to align diffusion models without requiring pairwise preferences. Our experiments show that the fine-tuned feed-forward generator, using either DPO or DRO objective, is much faster and more likely to produce stable objects than test-time optimization. Notably, the DSO framework works even without any ground-truth 3D objects for training, allowing the 3D generator to self-improve by automatically collecting simulation feedback on its own outputs.

Alternatives to backpropagation have long been studied to better understand how biological brains may learn. Recently, they have also garnered interest as a way to train neural networks more efficiently. By relaxing constraints inherent to backpropagation (e.g., symmetric feedforward and feedback weights, sequential updates), these methods enable promising prospects, such as local learning. However, the tradeoffs between different methods in terms of final task performance, convergence speed, and ultimately compute and data requirements are rarely outlined. In this work, we use scaling laws to study the ability of Direct Feedback Alignment~(DFA) to train causal decoder-only Transformers efficiently. Scaling laws provide an overview of the tradeoffs implied by a modeling decision, up to extrapolating how it might transfer to increasingly large models. We find that DFA fails to offer more efficient scaling than backpropagation: there is never a regime for which the degradation in loss incurred by using DFA is worth the potential reduction in compute budget. Our finding comes at variance with previous beliefs in the alternative training methods community, and highlights the need for holistic empirical approaches to better understand modeling decisions.

Model-based reinforcement learning promises to learn an optimal policy from fewer interactions with the environment compared to model-free reinforcement learning by learning an intermediate model of the environment in order to predict future interactions. When predicting a sequence of interactions, the rollout length, which limits the prediction horizon, is a critical hyperparameter as accuracy of the predictions diminishes in the regions that are further away from real experience. As a result, with a longer rollout length, an overall worse policy is learned in the long run. Thus, the hyperparameter provides a trade-off between quality and efficiency. In this work, we frame the problem of tuning the rollout length as a meta-level sequential decision-making problem that optimizes the final policy learned by model-based reinforcement learning given a fixed budget of environment interactions by adapting the hyperparameter dynamically based on feedback from the learning process, such as accuracy of the model and the remaining budget of interactions. We use model-free deep reinforcement learning to solve the meta-level decision problem and demonstrate that our approach outperforms common heuristic baselines on two well-known reinforcement learning environments.

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are sample-centric: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a distribution-centric perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

Learning rate scheduling is essential in transformer training, where the final annealing plays a crucial role in getting the best performance. However, the mechanisms behind this cooldown phase, with its characteristic drop in loss, remain poorly understood. To address this, we provide a comprehensive analysis focusing solely on the cooldown phase in the Warmup-Stable-Decay (WSD) learning rate scheduler. Our analysis reveals that different cooldown shapes reveal a fundamental bias-variance trade-off in the resulting models, with shapes that balance exploration and exploitation consistently outperforming alternatives. Similarly, we find substantial performance variations x2013 comparable to those from cooldown shape selection x2013 when tuning AdamW hyperparameters. Notably, we observe consistent improvements with higher values of beta_2 during cooldown. From a loss landscape perspective, we provide visualizations of the landscape during cooldown, supporting the river valley loss perspective empirically. These findings offer practical recommendations for configuring the WSD scheduler in transformer training, emphasizing the importance of optimizing the cooldown phase alongside traditional hyperparameter tuning.

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

Proactive interventions by LLM critic models are often assumed to improve reliability, yet their effects at deployment time are poorly understood. We show that a binary LLM critic with strong offline accuracy (AUROC 0.94) can nevertheless cause severe performance degradation, inducing a 26 percentage point (pp) collapse on one model while affecting another by near zero pp. This variability demonstrates that LLM critic accuracy alone is insufficient to determine whether intervention is safe. We identify a disruption-recovery tradeoff: interventions may recover failing trajectories but also disrupt trajectories that would have succeeded. Based on this insight, we propose a pre-deployment test that uses a small pilot of 50 tasks to estimate whether intervention is likely to help or harm, without requiring full deployment. Across benchmarks, the test correctly anticipates outcomes: intervention degrades performance on high-success tasks (0 to -26 pp), while yielding a modest improvement on the high-failure ALFWorld benchmark (+2.8 pp, p=0.014). The primary value of our framework is therefore identifying when not to intervene, preventing severe regressions before deployment.

Direct Preference Optimization (DPO) and its variants have become increasingly popular for aligning language models with human preferences. These methods aim to teach models to better distinguish between chosen (or preferred) and rejected (or dispreferred) responses. However, prior research has identified that the probability of chosen responses often decreases during training, and this phenomenon is known as likelihood displacement. To tackle this challenge, in this work we introduce \method to controllably shift the distribution of the chosen probability. Then, we show that \method exhibits a fundamental trade-off between improving the chosen probability and sacrificing the reward margin, as supported by both theoretical analysis and experimental validation. Furthermore, we demonstrate the superiority of \method over DPO on downstream tasks such as MT-Bench and a designed win rate experiment. We believe this study shows that the likelihood displacement issue of DPO can be effectively mitigated with a simple, theoretically grounded solution. Our code is available at https://github.com/Meaquadddd/DPO-Shift.

Like generic multi-task learning, continual learning has the nature of multi-objective optimization, and therefore faces a trade-off between the performance of different tasks. That is, to optimize for the current task distribution, it may need to compromise performance on some previous tasks. This means that there exist multiple models that are Pareto-optimal at different times, each addressing a distinct task performance trade-off. Researchers have discussed how to train particular models to address specific trade-off preferences. However, existing algorithms require training overheads proportional to the number of preferences -- a large burden when there are multiple, possibly infinitely many, preferences. As a response, we propose Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base in the form of a convex hull of model parameter distributions and (2) obtains particular models to address task trade-off preferences with zero-shot. That is, IBCL does not require any additional training overhead to generate preference-addressing models from its knowledge base. We show that models obtained by IBCL have guarantees in identifying the Pareto optimal parameters. Moreover, experiments on standard image classification and NLP tasks support this guarantee. Statistically, IBCL improves average per-task accuracy by at most 23% and peak per-task accuracy by at most 15% with respect to the baseline methods, with steadily near-zero or positive backward transfer. Most importantly, IBCL significantly reduces the training overhead from training 1 model per preference to at most 3 models for all preferences.

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

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.

Natural intelligences (NIs) thrive in a dynamic world - they learn quickly, sometimes with only a few samples. In contrast, artificial intelligences (AIs) typically learn with a prohibitive number of training samples and computational power. What design principle difference between NI and AI could contribute to such a discrepancy? Here, we investigate the role of weight polarity: development processes initialize NIs with advantageous polarity configurations; as NIs grow and learn, synapse magnitudes update, yet polarities are largely kept unchanged. We demonstrate with simulation and image classification tasks that if weight polarities are adequately set a priori, then networks learn with less time and data. We also explicitly illustrate situations in which a priori setting the weight polarities is disadvantageous for networks. Our work illustrates the value of weight polarities from the perspective of statistical and computational efficiency during learning.

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

Emergent properties have been widely adopted as a term to describe behavior not present in smaller models but observed in larger models. Recent work suggests that the trade-off incurred by quantization is also an emergent property, with sharp drops in performance in models over 6B parameters. In this work, we ask "are quantization cliffs in performance solely a factor of scale?" Against a backdrop of increased research focus on why certain emergent properties surface at scale, this work provides a useful counter-example. We posit that it is possible to optimize for a quantization friendly training recipe that suppresses large activation magnitude outliers. Here, we find that outlier dimensions are not an inherent product of scale, but rather sensitive to the optimization conditions present during pre-training. This both opens up directions for more efficient quantization, and poses the question of whether other emergent properties are inherent or can be altered and conditioned by optimization and architecture design choices. We successfully quantize models ranging in size from 410M to 52B with minimal degradation in performance.

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

We present a novel approach to determine the constitutive properties of metals under large plastic strains and strain rates that otherwise are difficult to access using conventional materials testing methods. The approach exploits large-strain plastic flow past a sharp wedge, coupled with high-speed photography and image velocimetry to capture the underlying plastic flow dynamics. The inverse problem of estimating material parameters from the flow field is solved using an iterative optimization procedure that minimizes the gap between internal and external plastic work. A major advantage of the method is that it neither makes any assumptions about the flow nor requires computational simulations. To counter the problem of non-unique parameter estimates, we propose a parameterization scheme that takes advantage of the functional form of the constitutive model and reformulates the problem into a more tractable form to identify plasticity parameters uniquely. We present studies to illustrate the principle of the method with two materials with widely different plastic flow characteristics: copper (strain hardening) and a lead-free solder alloy (rate sensitive and deformation history dependent). The results demonstrate the efficacy of the method in reliably determining the material parameters under high strain/strain rate conditions of relevance to a range of practical engineering problems.

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. We provide a mathematical proof showing the convergence of the ConFIG method, and it is evaluated across a range of challenging PINN scenarios. ConFIG consistently shows superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at https://tum-pbs.github.io/ConFIG

The ability to learn new concepts continually is necessary in this ever-changing world. However, deep neural networks suffer from catastrophic forgetting when learning new categories. Many works have been proposed to alleviate this phenomenon, whereas most of them either fall into the stability-plasticity dilemma or take too much computation or storage overhead. Inspired by the gradient boosting algorithm to gradually fit the residuals between the target model and the previous ensemble model, we propose a novel two-stage learning paradigm FOSTER, empowering the model to learn new categories adaptively. Specifically, we first dynamically expand new modules to fit the residuals between the target and the output of the original model. Next, we remove redundant parameters and feature dimensions through an effective distillation strategy to maintain the single backbone model. We validate our method FOSTER on CIFAR-100 and ImageNet-100/1000 under different settings. Experimental results show that our method achieves state-of-the-art performance. Code is available at: https://github.com/G-U-N/ECCV22-FOSTER.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and memory overhead for the optimizer itself. In this work, we identify and quantify the design features governing the memory, compute, and performance trade-offs for many learned and hand-designed optimizers. We further leverage our analysis to construct a learned optimizer that is both faster and more memory efficient than previous work. Our model and training code are open source.

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

Despite the popularity of Shapley Values in explaining neural text classification models, computing them is prohibitive for large pretrained models due to a large number of model evaluations. In practice, Shapley Values are often estimated with a small number of stochastic model evaluations. However, we show that the estimated Shapley Values are sensitive to random seed choices -- the top-ranked features often have little overlap across different seeds, especially on examples with longer input texts. This can only be mitigated by aggregating thousands of model evaluations, which on the other hand, induces substantial computational overheads. To mitigate the trade-off between stability and efficiency, we develop an amortized model that directly predicts each input feature's Shapley Value without additional model evaluations. It is trained on a set of examples whose Shapley Values are estimated from a large number of model evaluations to ensure stability. Experimental results on two text classification datasets demonstrate that our amortized model estimates Shapley Values accurately with up to 60 times speedup compared to traditional methods. Furthermore, the estimated values are stable as the inference is deterministic. We release our code at https://github.com/yangalan123/Amortized-Interpretability.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

Falling is an inherent risk of humanoid mobility. Maintaining stability is thus a primary safety focus in robot control and learning, yet no existing approach fully averts loss of balance. When instability does occur, prior work addresses only isolated aspects of falling: avoiding falls, choreographing a controlled descent, or standing up afterward. Consequently, humanoid robots lack integrated strategies for impact mitigation and prompt recovery when real falls defy these scripts. We aim to go beyond keeping balance to make the entire fall-and-recovery process safe and autonomous: prevent falls when possible, reduce impact when unavoidable, and stand up when fallen. By fusing sparse human demonstrations with reinforcement learning and an adaptive diffusion-based memory of safe reactions, we learn adaptive whole-body behaviors that unify fall prevention, impact mitigation, and rapid recovery in one policy. Experiments in simulation and on a Unitree G1 demonstrate robust sim-to-real transfer, lower impact forces, and consistently fast recovery across diverse disturbances, pointing towards safer, more resilient humanoids in real environments. Videos are available at https://firm2025.github.io/.

We examine two properties of AI systems: capability (what a system can do) and steerability (how reliably one can shift behavior toward intended outcomes). A central question is whether capability growth reduces steerability and risks control collapse. We also distinguish between authorized steerability (builders reliably reaching intended behaviors) and unauthorized steerability (attackers eliciting disallowed behaviors). This distinction highlights a fundamental safety--security dilemma of AI models: safety requires high steerability to enforce control (e.g., stop/refuse), while security requires low steerability for malicious actors to elicit harmful behaviors. This tension presents a significant challenge for open-weight models, which currently exhibit high steerability via common techniques like fine-tuning or adversarial attacks. Using Qwen3 and InstrumentalEval, we find that a short anti-instrumental prompt suffix sharply reduces the measured convergence rate (e.g., shutdown avoidance, self-replication). For Qwen3-30B Instruct, the convergence rate drops from 81.69% under a pro-instrumental suffix to 2.82% under an anti-instrumental suffix. Under anti-instrumental prompting, larger aligned models show lower convergence rates than smaller ones (Instruct: 2.82% vs. 4.23%; Thinking: 4.23% vs. 9.86%). Code is available at github.com/j-hoscilowicz/instrumental_steering.

DARTS is a popular algorithm for neural architecture search (NAS). Despite its great advantage in search efficiency, DARTS often suffers weak stability, which reflects in the large variation among individual trials as well as the sensitivity to the hyper-parameters of the search process. This paper owes such instability to an optimization gap between the super-network and its sub-networks, namely, improving the validation accuracy of the super-network does not necessarily lead to a higher expectation on the performance of the sampled sub-networks. Then, we point out that the gap is due to the inaccurate estimation of the architectural gradients, based on which we propose an amended estimation method. Mathematically, our method guarantees a bounded error from the true gradients while the original estimation does not. Our approach bridges the gap from two aspects, namely, amending the estimation on the architectural gradients, and unifying the hyper-parameter settings in the search and re-training stages. Experiments on CIFAR10 and ImageNet demonstrate that our approach largely improves search stability and, more importantly, enables DARTS-based approaches to explore much larger search spaces that have not been investigated before.

Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization (boldsymbolμP) provides a theoretical safeguard for width-invariant Θ(1) activation control, whereas emerging optimizers like Muon are only ``half-aligned'' with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the Spectral Sphere Optimizer (SSO), which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully boldsymbolμP-aligned optimization process. To enable large-scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

Generative adversial network (GAN) is a type of generative model that maps a high-dimensional noise to samples in target distribution. However, the dimension of noise required in GAN is not well understood. Previous approaches view GAN as a mapping from a continuous distribution to another continous distribution. In this paper, we propose to view GAN as a discrete sampler instead. From this perspective, we build a connection between the minimum noise required and the bits to losslessly compress the images. Furthermore, to understand the behaviour of GAN when noise dimension is limited, we propose divergence-entropy trade-off. This trade-off depicts the best divergence we can achieve when noise is limited. And as rate distortion trade-off, it can be numerically solved when source distribution is known. Finally, we verifies our theory with experiments on image generation.

Adaptive chatbots that mimic a user's linguistic style can build rapport and engagement, yet unconstrained mimicry risks an agent that feels unstable or sycophantic. We present a computational evaluation framework that makes the core design tension explicit: balancing moment-to-moment linguistic synchrony against long-term persona stability. Using an 8-dimensional style vector and a closed-loop "base+delta" prompting architecture, we simulate and compare explicit adaptation policies - Uncapped, Cap, Exponential Moving Average (EMA), Dead-Band, and Hybrids - on a human-log dataset. Our analysis maps a clear Pareto frontier: bounded policies achieve substantial gains in stability at a modest cost to synchrony. For example, a Hybrid (EMA+Cap) raises stability from 0.542 to 0.878 (+62%) while reducing synchrony by only 17%. We confirm this trade-off through large-scale replications on three public corpora (DailyDialog, Persona-Chat, EmpatheticDialogues) and LLM-in-the-loop validation across two model families. Furthermore, we quantify "prompt legibility," showing that frontier policies reduce instruction churn and cut jarring register flips (major tone changes) from 0.254 to 0.092, yielding systems that are easier to reason about and maintain. Taken together, our framework provides a general evaluation harness for style adaptation; a systematic ablation that identifies Pareto-efficient policies; robust validation across diverse datasets and models; and novel legibility metrics linking policy choices to system maintainability.

A large body of research in continual learning is devoted to overcoming the catastrophic forgetting of neural networks by designing new algorithms that are robust to the distribution shifts. However, the majority of these works are strictly focused on the "algorithmic" part of continual learning for a "fixed neural network architecture", and the implications of using different architectures are mostly neglected. Even the few existing continual learning methods that modify the model assume a fixed architecture and aim to develop an algorithm that efficiently uses the model throughout the learning experience. However, in this work, we show that the choice of architecture can significantly impact the continual learning performance, and different architectures lead to different trade-offs between the ability to remember previous tasks and learning new ones. Moreover, we study the impact of various architectural decisions, and our findings entail best practices and recommendations that can improve the continual learning performance.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility--learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification. Numerical experiments across several axes validate the theory by comparing destructive utility policies against our proposed two-gate policies that preserve learnability.

We apply preference learning to the task of language model-guided design of novel structural alloys. In contrast to prior work that focuses on generating stable inorganic crystals, our approach targets the synthesizeability of a specific structural class: BCC/B2 superalloys, an underexplored family of materials with potential applications in extreme environments. Using three open-weight models (LLaMA-3.1, Gemma-2, and OLMo-2), we demonstrate that language models can be optimized for multiple design objectives using a single, unified reward signal through Direct Preference Optimization (DPO). Unlike prior approaches that rely on heuristic or human-in-the-loop feedback (costly), our reward signal is derived from thermodynamic phase calculations, offering a scientifically grounded criterion for model tuning. To our knowledge, this is the first demonstration of preference-tuning a language model using physics-grounded feedback for structural alloy design. The resulting framework is general and extensible, providing a path forward for intelligent design-space exploration across a range of physical science domains.

While effective post-training integrates Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), the optimal mechanism for utilizing expert trajectories remains unresolved. We propose the Plasticity-Ceiling Framework to theoretically ground this landscape, decomposing performance into foundational SFT performance and the subsequent RL plasticity. Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability deficits of synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the SFT Stable or Mild Overfitting Sub-phase maximizes the final ceiling by securing foundational SFT performance without compromising RL plasticity; (2) Refuting ``Less is More'' in the context of SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) Identifying that the Minimum SFT Validation Loss serves as a robust indicator for selecting the expert trajectories that maximize the final performance ceiling. Our findings provide actionable guidelines for maximizing the value extracted from expert trajectories.

Large language model (LLM) reinforcement learning has increasingly relied on group-based policy optimization frameworks, such as GRPO and GSPO, to achieve stable fine-tuning at scale. However, a fundamental trade-off persists between optimization granularity and training stability. While GSPO improves robustness via sequence-level optimization, its monolithic treatment of sequences introduces severe inefficiencies: its conservative clipping mechanism indiscriminately discards valid training samples-a phenomenon we term gradient underutilization-and its uniform credit assignment fails to capture the heterogeneous contributions of critical reasoning steps. In this work, we propose Entropy Importance Sampling Policy Optimization (ESPO), a novel framework that reconciles fine-grained control with training stability. ESPO decomposes sequences into groups based on predictive entropy, enabling (1) Entropy-driven Importance Sampling to capture intra-sequence heterogeneity, and (2) Entropy-adaptive Clipping to dynamically allocate trust regions based on model uncertainty. Extensive experiments on mathematical reasoning benchmarks demonstrate that ESPO not only accelerates convergence but also achieves state-of-the-art performance, notably improving accuracy on the challenging HMMT benchmark from 4.4% to 13.13%.

Model merging has shown great promise at combining expert models, but the benefit of merging is unclear when merging ``generalist'' models trained on many tasks. We explore merging in the context of large (sim100B) models, by recycling checkpoints that exhibit tradeoffs among different tasks. Such checkpoints are often created in the process of developing a frontier model, and many suboptimal ones are usually discarded. Given a pool of model checkpoints obtained from different training runs (e.g., different stages, objectives, hyperparameters, and data mixtures), which naturally show tradeoffs across different language capabilities (e.g., instruction following vs. code generation), we investigate whether merging can recycle such suboptimal models into a Pareto-optimal one. Our optimization algorithm tunes the weight of each checkpoint in a linear combination, resulting in a Pareto-optimal models that outperforms both individual models and merge-based baselines. Further analysis shows that good merges tend to include almost all checkpoints with with non-zero weights, indicating that even seemingly bad initial checkpoints can contribute to good final merges.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Exemplar-free class-incremental learning is very challenging due to the negative effect of catastrophic forgetting. A balance between stability and plasticity of the incremental process is needed in order to obtain good accuracy for past as well as new classes. Existing exemplar-free class-incremental methods focus either on successive fine tuning of the model, thus favoring plasticity, or on using a feature extractor fixed after the initial incremental state, thus favoring stability. We introduce a method which combines a fixed feature extractor and a pseudo-features generator to improve the stability-plasticity balance. The generator uses a simple yet effective geometric translation of new class features to create representations of past classes, made of pseudo-features. The translation of features only requires the storage of the centroid representations of past classes to produce their pseudo-features. Actual features of new classes and pseudo-features of past classes are fed into a linear classifier which is trained incrementally to discriminate between all classes. The incremental process is much faster with the proposed method compared to mainstream ones which update the entire deep model. Experiments are performed with three challenging datasets, and different incremental settings. A comparison with ten existing methods shows that our method outperforms the others in most cases.

In Multi-Task Learning (MTL), tasks may compete and limit the performance achieved on each other, rather than guiding the optimization to a solution, superior to all its single-task trained counterparts. Since there is often not a unique solution optimal for all tasks, practitioners have to balance tradeoffs between tasks' performance, and resort to optimality in the Pareto sense. Most MTL methodologies either completely neglect this aspect, and instead of aiming at learning a Pareto Front, produce one solution predefined by their optimization schemes, or produce diverse but discrete solutions. Recent approaches parameterize the Pareto Front via neural networks, leading to complex mappings from tradeoff to objective space. In this paper, we conjecture that the Pareto Front admits a linear parameterization in parameter space, which leads us to propose Pareto Manifold Learning, an ensembling method in weight space. Our approach produces a continuous Pareto Front in a single training run, that allows to modulate the performance on each task during inference. Experiments on multi-task learning benchmarks, ranging from image classification to tabular datasets and scene understanding, show that Pareto Manifold Learning outperforms state-of-the-art single-point algorithms, while learning a better Pareto parameterization than multi-point baselines.

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of stability." In this paper, we develop theory that can describe the dynamics of optimization in this regime. Our key insight is that while the *exact* trajectory of an oscillatory optimizer may be challenging to analyze, the *time-averaged* (i.e. smoothed) trajectory is often much more tractable. To analyze an optimizer, we derive a differential equation called a "central flow" that characterizes this time-averaged trajectory. We empirically show that these central flows can predict long-term optimization trajectories for generic neural networks with a high degree of numerical accuracy. By interpreting these central flows, we are able to understand how gradient descent makes progress even as the loss sometimes goes up; how adaptive optimizers "adapt" to the local loss landscape; and how adaptive optimizers implicitly navigate towards regions where they can take larger steps. Our results suggest that central flows can be a valuable theoretical tool for reasoning about optimization in deep learning.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years, conventional neural networks often fail to address these two critical aspects simultaneously or even independently. Inspired by natural physical systems and established literature, input convex architectures are known to enhance computational efficiency in optimization tasks, whereas Lipschitz-constrained architectures improve robustness. However, combining these properties within a single model requires careful review, as inappropriate methods for enforcing one property can undermine the other. To overcome this, we introduce a novel network architecture, termed Input Convex Lipschitz Recurrent Neural Networks (ICLRNNs). This architecture seamlessly integrates the benefits of convexity and Lipschitz continuity, enabling fast and robust neural network-based modeling and optimization. The ICLRNN outperforms existing recurrent units in both computational efficiency and robustness. Additionally, it has been successfully applied to practical engineering scenarios, such as modeling and control of chemical process and the modeling and real-world solar irradiance prediction for solar PV system planning at LHT Holdings in Singapore. Source code is available at https://github.com/killingbear999/ICLRNN.

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

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.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Analysis of learned representations has a blind spot: it focuses on similarity, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce geometric stability, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present Shesha, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated (ρapprox 0.01) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2times more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability (ρ= 0.89-0.96); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying how reliably systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

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

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently diverse dynamics, while varying resolutions and dimensionalities challenge efficient training on modern hardware. Through empirical and theoretical analysis, we incorporate new approaches to mitigate these obstacles, including a harmonic-analysis-based stabilization method, load-balanced distributed 2D and 3D training strategies, and compute-adaptive tokenization. Using these tools, we develop Walrus, a transformer-based foundation model developed primarily for fluid-like continuum dynamics. Walrus is pretrained on nineteen diverse scenarios spanning astrophysics, geoscience, rheology, plasma physics, acoustics, and classical fluids. Experiments show that Walrus outperforms prior foundation models on both short and long term prediction horizons on downstream tasks and across the breadth of pretraining data, while ablation studies confirm the value of our contributions to forecast stability, training throughput, and transfer performance over conventional approaches. Code and weights are released for community use.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

Scaling data and compute is critical to the success of machine learning. However, scaling demands predictability: we want methods to not only perform well with more compute or data, but also have their performance be predictable from small-scale runs, without running the large-scale experiment. In this paper, we show that value-based off-policy RL methods are predictable despite community lore regarding their pathological behavior. First, we show that data and compute requirements to attain a given performance level lie on a Pareto frontier, controlled by the updates-to-data (UTD) ratio. By estimating this frontier, we can predict this data requirement when given more compute, and this compute requirement when given more data. Second, we determine the optimal allocation of a total resource budget across data and compute for a given performance and use it to determine hyperparameters that maximize performance for a given budget. Third, this scaling behavior is enabled by first estimating predictable relationships between hyperparameters, which is used to manage effects of overfitting and plasticity loss unique to RL. We validate our approach using three algorithms: SAC, BRO, and PQL on DeepMind Control, OpenAI gym, and IsaacGym, when extrapolating to higher levels of data, compute, budget, or performance.

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.

In robotics, catastrophic interference continues to restrain policy training across environments. Efforts to combat catastrophic interference to date focus on novel neural architectures or training methods, with a recent emphasis on policies with good initial settings that facilitate training in new environments. However, none of these methods to date have taken into account how the physical architecture of the robot can obstruct or facilitate catastrophic interference, just as the choice of neural architecture can. In previous work we have shown how aspects of a robot's physical structure (specifically, sensor placement) can facilitate policy learning by increasing the fraction of optimal policies for a given physical structure. Here we show for the first time that this proxy measure of catastrophic interference correlates with sample efficiency across several search methods, proving that favorable loss landscapes can be induced by the correct choice of physical structure. We show that such structures can be found via co-optimization -- optimization of a robot's structure and control policy simultaneously -- yielding catastrophic interference resistant robot structures and policies, and that this is more efficient than control policy optimization alone. Finally, we show that such structures exhibit sensor homeostasis across environments and introduce this as the mechanism by which certain robots overcome catastrophic interference.

Machine learning force fields (MLFFs) have revolutionized molecular simulations by providing quantum mechanical accuracy at the speed of molecular mechanical computations. However, a fundamental reliance of these models on fixed-cutoff architectures limits their applicability to macromolecular systems where long-range interactions dominate. We demonstrate that this locality constraint causes force prediction errors to scale monotonically with system size, revealing a critical architectural bottleneck. To overcome this, we establish the systematically designed MolLR25 ({Mol}ecules with {L}ong-{R}ange effect) benchmark up to 1200 atoms, generated using high-fidelity DFT, and introduce E2Former-LSR, an equivariant transformer that explicitly integrates long-range attention blocks. E2Former-LSR exhibits stable error scaling, achieves superior fidelity in capturing non-covalent decay, and maintains precision on complex protein conformations. Crucially, its efficient design provides up to 30% speedup compared to purely local models. This work validates the necessity of non-local architectures for generalizable MLFFs, enabling high-fidelity molecular dynamics for large-scale chemical and biological systems.

This study proposes a modularized deep learning-based loading protocol for optimal parameter estimation of Bouc-Wen (BW) class models. The protocol consists of two key components: optimal loading history construction and CNN-based rapid parameter estimation. Each component is decomposed into independent sub-modules tailored to distinct hysteretic behaviors-basic hysteresis, structural degradation, and pinching effect-making the protocol adaptable to diverse hysteresis models. Three independent CNN architectures are developed to capture the path-dependent nature of these hysteretic behaviors. By training these CNN architectures on diverse loading histories, minimal loading sequences, termed loading history modules, are identified and then combined to construct an optimal loading history. The three CNN models, trained on the respective loading history modules, serve as rapid parameter estimators. Numerical evaluation of the protocol, including nonlinear time history analysis of a 3-story steel moment frame and fragility curve construction for a 3-story reinforced concrete frame, demonstrates that the proposed protocol significantly reduces total analysis time while maintaining or improving estimation accuracy. The proposed protocol can be extended to other hysteresis models, suggesting a systematic approach for identifying general hysteresis models.