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Applications · Physics

Takeshi Koshizuka, Issei Sato

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a discrete weak form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

Social Aspects · Fairness, Equity, Justice and Safety

Kevin Zhang, Yonghan Jung, Divyat Mahajan, Karthikeyan Shanmugam, Shalmali Joshi

Identifying and measuring biases associated with sensitive attributes is a crucial consideration in healthcare to prevent treatment disparities. One prominent issue is inaccurate pulse oximeter readings, which tend to overestimate oxygen saturation for dark-skinned patients and misrepresent supplemental oxygen needs. Most existing research has revealed *statistical disparities* linking device measurement errors to patient outcomes in intensive care units (ICUs) without causal formalization. This study *causally* investigates how racial discrepancies in oximetry measurements affect invasive ventilation in ICU settings. We employ a causal inference-based approach using *path-specific effects* to isolate the impact of bias by race on clinical decision-making. To estimate these effects, we leverage a doubly robust estimator, propose its self-normalized variant for improved sample efficiency, and provide novel finite-sample guarantees. Our methodology is validated on semi-synthetic data and applied to two large real-world health datasets: MIMIC-IV and eICU. Contrary to prior work, our analysis reveals minimal impact of racial discrepancies on invasive ventilation rates. However, path-specific effects mediated by oxygen saturation disparity are more pronounced on ventilation duration, and the severity differs by dataset. Our work provides a novel pipeline for investigating potential disparities in clinical decision-making and, more importantly, highlights the necessity of causal methods to robustly assess fairness in healthcare.

Optimization · Large Scale, Parallel and Distributed

Ahmed Khaled, Satyen Kale, Arthur Douillard, Chi Jin, Rob Fergus, Manzil Zaheer

Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in such settings but methods like Local Stochastic Gradient Descent (Local SGD) show great promise to reduce the global communication need. Local SGD consists of three parts: a local optimization processes, an aggregation mechanism, and an outer optimizer that uses the aggregated updates from the nodes to produce a new model. While there exists an extensive literature on understanding the impact of hyperparameters in the local optimization process, the choice of outer optimizer and its hyperparameters is less clear. We study the role of the outer learning in Local SGD, and prove new convergence guarantees for the algorithm. In particular, we show that tuning the outer learning rate allows us to (a) trade off between optimization error and stochastic gradient noise variance, and (b) make up for ill-tuning of the inner learning rate. Our theory suggests that the outer learning rate should sometimes be set to values greater than $1$. We extend our results to apply to when we use momentum in the outer optimizer, and also introduce a novel data-dependent analysis of Local SGD that yields further insights on outer learning rate tuning. We conduct comprehensive experiments with standard language models and various outer optimizers to validate our theory.

Computer Vision · Image and Video Generation

Juan Rodriguez, Haotian Zhang, Abhay Puri, Rishav Pramanik, Aarash Feizi, Pascal Wichmann, Arnab Mondal, Mohammad R. Samsami, Rabiul Awal, Perouz Taslakian 等

Scalable Vector Graphics (SVG) offer a powerful format for representing visual designs as interpretable code. Recent advances in vision-language models (VLMs) have enabled high-quality SVG generation by framing the problem as a code generation task and leveraging large-scale pretraining. VLMs are particularly suitable for this task as they capture both global semantics and fine-grained visual patterns, while transferring knowledge across vision, natural language, and code domains. However, existing VLM approaches often struggle to produce faithful and efficient SVGs because they never observe the rendered images during training. Although differentiable rendering for autoregressive SVG code generation remains unavailable, rendered outputs can still be compared to original inputs, enabling evaluative feedback suitable for reinforcement learning (RL). We introduce Reinforcement Learning from Rendering Feedback, an RL method that enhances SVG generation in autoregressive VLMs by leveraging feedback from rendered SVG outputs. Given an input image, the model generates SVG roll-outs that are rendered and compared to the original image to compute a reward. This visual fidelity feedback guides the model toward producing more accurate, efficient, and semantically coherent SVGs. \method significantly outperforms supervised fine-tuning, addressing common failure modes and enabling precise, high-quality SVG generation with strong structural understanding and generalization.

Probabilistic Methods · Bayesian Models and Methods

Zongbo Han, Jialong Yang, Guangyu Wang, Junfan Li, Qianli Xu, Mike Zheng Shou, Changqing Zhang

Vision-language foundation models (VLMs), such as CLIP, exhibit remarkable performance across a wide range of tasks. However, deploying these models can be unreliable when significant distribution gaps exist between training and test data, while fine-tuning for diverse scenarios is often costly. Cache-based test-time adapters offer an efficient alternative by storing representative test samples to guide subsequent classifications. Yet, these methods typically employ naive cache management with limited capacity, leading to severe catastrophic forgetting when samples are inevitably dropped during updates. In this paper, we propose DOTA (DistributiOnal Test-time Adaptation), a simple yet effective method addressing this limitation. Crucially, instead of merely memorizing individual test samples, DOTA continuously estimates the underlying distribution of the test data stream. Test-time posterior probabilities are then computed using these dynamically estimated distributions via Bayes' theorem for adaptation. This distribution-centric approach enables the model to continually learn and adapt to the deployment environment. Extensive experiments validate that DOTA significantly mitigates forgetting and achieves state-of-the-art performance compared to existing methods.

Optimization · Neural Network Optimization

Xiao Han, ZIMO ZHAO, Wanyu Wang, Maolin Wang, Zitao Liu, Yi Chang, Xiangyu Zhao

Recent advancements in Large Language Models (LLMs) have emphasized the critical role of fine-tuning (FT) techniques in adapting LLMs to specific tasks, especially when retraining from scratch is computationally infeasible. Fine-tuning enables LLMs to leverage task- or domain-specific data, producing models that more effectively meet the requirements of targeted applications. However, con- ventional FT approaches often suffer from catastrophic forgetting and suboptimal data efficiency, limiting their real-world applicability. To address these challenges, this paper proposes DEAL, a novel framework that integrates Low-Rank Adapta- tion (LoRA) with a continuous fine-tuning strategy. By incorporating knowledge retention and adaptive parameter update modules, the framework mitigates the limitations of existing FT methods while maintaining efficiency. Experiments on 15 diverse datasets show that DEAL consistently outperforms baseline methods, yielding substantial gains in task accuracy and resource efficiency. These find- ings demonstrate the potential of our approach to advance continual adaptation in LLMs by enhancing task performance while improving resource efficiency. The source code is publicly available at https://github.com/Applied-Machine-Learning-Lab/DEAL.

Applications · Robotics

Yifei Su, Ning Liu, Dong Chen, Zhen Zhao, Kun Wu, Meng Li, Zhiyuan Xu, Zhengping Che, Jian Tang

Generative modeling-based visuomotor policies have been widely adopted in robotic manipulation, attributed to their ability to model multimodal action distributions. However, the high inference cost of multi-step sampling limits its applicability in real-time robotic systems. Existing approaches accelerate sampling in generative modeling-based visuomotor policies by adapting techniques originally developed to speed up image generation. However, a major distinction exists: image generation typically produces independent samples without temporal dependencies, while robotic manipulation requires generating action trajectories with continuity and temporal coherence. To this end, we propose FreqPolicy, a novel approach that first imposes frequency consistency constraints on flow-based visuomotor policies. Our work enables the action model to capture temporal structure effectively while supporting efficient, high-quality one-step action generation. Concretely, we introduce a frequency consistency constraint objective that enforces alignment of frequency-domain action features across different timesteps along the flow, thereby promoting convergence of one-step action generation toward the target distribution. In addition, we design an adaptive consistency loss to capture structural temporal variations inherent in robotic manipulation tasks. We assess FreqPolicy on $53$ tasks across $3$ simulation benchmarks, proving its superiority over existing one-step action generators. We further integrate FreqPolicy into the vision-language-action (VLA) model and achieve acceleration without performance degradation on $40$ tasks of Libero. Besides, we show efficiency and effectiveness in real-world robotic scenarios with an inference frequency of $93.5$ Hz.

General Machine Learning · Representation Learning

Yasser Khalil, Mehdi Setayesh, Hongliang Li

Machine unlearning (MU) aims to remove the influence of specific ''forget'' data from a trained model while preserving its knowledge of the remaining ''retain'' data. Existing MU methods based on label manipulation or model weight perturbations often achieve limited unlearning effectiveness. To address this, we introduce CoUn, a novel MU framework inspired by the observation that a model retrained from scratch using only retain data classifies forget data based on their semantic similarity to the retain data. CoUn emulates this behavior by adjusting learned data representations through contrastive learning (CL) and supervised learning, applied exclusively to retain data. Specifically, CoUn (1) leverages semantic similarity between data samples to indirectly adjust forget representations using CL, and (2) maintains retain representations within their respective clusters through supervised learning. Extensive experiments across various datasets and model architectures show that CoUn consistently outperforms state-of-the-art MU baselines in unlearning effectiveness. Additionally, integrating our CL module into existing baselines empowers their unlearning effectiveness.

Reinforcement Learning · Deep RL

wenlong deng, Yi Ren, Muchen Li, Danica J. Sutherland, Xiaoxiao Li, Christos Thrampoulidis

Reinforcement learning (RL) has become popular in enhancing the reasoning capabilities of large language models (LLMs), with Group Relative Policy Optimization (GRPO) emerging as a widely used algorithm in recent systems. Despite GRPO's widespread adoption, we identify a previously unrecognized phenomenon we term Lazy Likelihood Displacement (LLD), wherein the likelihood of correct responses marginally increases or even decreases during training. This behavior mirrors a recently discovered misalignment issue in Direct Preference Optimization (DPO), attributed to the influence of negative gradients. We provide a theoretical analysis of GRPO’s learning dynamic, identifying the source of LLD as the naive penalization of all tokens in incorrect responses with the same strength. To address this, we develop a method called NTHR, which downweights penalties on tokens contributing to the LLD. Unlike prior DPO-based approaches, NTHR takes advantage of GRPO’s group-based structure, using correct responses as anchors to identify influential tokens. Experiments on math reasoning benchmarks demonstrate that NTHR effectively mitigates LLD, yielding consistent performance gains across models ranging from 0.5B to 3B parameters.

Theory · Learning Theory

Tianwei Wang, Xinhui Ma, Wei Pang

Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the classic Hopfield neural network (HNN). Starting from a continuous-time dynamical model of HNNs, we extend the formulation to the quaternionic domain and establish the existence and uniqueness of fixed points with asymptotic stability. For the learning rules, we introduce a periodic projection strategy that modifies standard gradient descent by periodically projecting each $4\times 4$ block of the weight matrix onto the closest quaternionic structure in the least-squares sense. This approach preserves both convergence and quaternionic consistency throughout training. Benefiting from this rigorous mathematical foundation, the experimental model implementation achieves high accuracy, fast convergence, and strong reliability across randomly generated target sets. Moreover, the evolution trajectories of the QSHNN exhibit well-bounded curvature, i.e., sufficient smoothness, which is crucial for applications such as control systems or path planning modules in robotic arms, where joint postures are parameterized by quaternion neurons. Beyond these application scenarios, the proposed model offers a practical implementation framework and a general mathematical methodology for designing neural networks under hypercomplex or non-commutative algebraic structures.

Probabilistic Methods · Gaussian Processes

Siavash Ameli, Chris van der Heide, Liam Hodgkinson, Michael Mahoney

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in scale, the corresponding covariance and kernel matrices become increasingly large, often reaching magnitudes that make their direct formation impractical or impossible. Existing techniques typically rely on matrix-vector products, which can provide efficient approximations, if the matrix spectrum behaves well. However, in settings like distributed learning, or when the matrix is defined only indirectly, access to the full data set can be restricted to only very small sub-matrices of the original matrix. In these cases, the matrix of nominal interest is not even available as an implicit operator, meaning that even matrix-vector products may not be available. In such settings, the matrix is "impalpable", in the sense that we have access to only masked snapshots of it. We draw on principles from free probability theory to introduce a novel method of "free decompression" to estimate the spectrum of such matrices. Our method can be used to extrapolate from the empirical spectral densities of small submatrices to infer the eigenspectrum of extremely large (impalpable) matrices (that we cannot form or even evaluate with full matrix-vector products). We demonstrate the effectiveness of this approach through a series of examples, comparing its performance against known limiting distributions from random matrix theory in synthetic settings, as well as applying it to submatrices of real-world datasets, matching them with their full empirical eigenspectra.

Reinforcement Learning · Everything Else

Jiawen Yu, Hairuo Liu, Qiaojun Yu, Jieji Ren, Ce Hao, Haitong Ding, Guangyu Huang, Guofan Huang, Yan Song, Panpan Cai 等

Vision-Language-Action (VLA) models have advanced general-purpose robotic manipulation by leveraging pretrained visual and linguistic representations. However, they struggle with contact-rich tasks that require fine-grained control involving force, especially under visual occlusion or dynamic uncertainty. To address these limitations, we propose \textbf{ForceVLA}, a novel end-to-end manipulation framework that treats external force sensing as a first-class modality within VLA systems. ForceVLA introduces \textbf{FVLMoE}, a force-aware Mixture-of-Experts fusion module that dynamically integrates pretrained visual-language embeddings with real-time 6-axis force feedback during action decoding. This enables context-aware routing across modality-specific experts, enhancing the robot's ability to adapt to subtle contact dynamics. We also introduce \textbf{ForceVLA-Data}, a new dataset comprising synchronized vision, proprioception, and force-torque signals across five contact-rich manipulation tasks. ForceVLA improves average task success by 23.2\% over strong $\pi_0$-based baselines, achieving up to 80\% success in tasks such as plug insertion. Our approach highlights the importance of multimodal integration for dexterous manipulation and sets a new benchmark for physically intelligent robotic control. Code and data will be released at https://sites.google.com/view/forcevla2025/.

Social Aspects · Trustworthy Machine Learning

Yonggang Zhang, Jun Nie, Xinmei Tian, Mingming Gong, Kun Zhang, Bo Han

The increasing realism of generated images has raised significant concerns about their potential misuse, necessitating robust detection methods. Current approaches mainly rely on training binary classifiers, which depend heavily on the quantity and quality of available generated images. In this work, we propose a novel framework that exploits geometric differences between the data manifolds of natural and generated images. To exploit this difference, we employ a pair of functions engineered to yield consistent outputs for natural images but divergent outputs for generated ones, leveraging the property that their gradients reside in mutually orthogonal subspaces. This design enables a simple yet effective detection method: an image is identified as generated if a transformation along its data manifold induces a significant change in the loss value of a self-supervised model pre-trained on natural images. Further more, to address diminishing manifold disparities in advanced generative models, we leverage normalizing flows to amplify detectable differences by extruding generated images away from the natural image manifold. Extensive experiments demonstrate the efficacy of this method.

Applications · Language, Speech and Dialog

Hongjin Qian, Zheng Liu

Augmenting large language models (LLMs) with external retrieval has become a standard method to address their inherent knowledge cutoff limitations. However, traditional retrieval-augmented generation methods employ static, pre-inference retrieval strategies, making them inadequate for complex tasks involving ambiguous, multi-step, or evolving information needs. Recent advances in test-time scaling techniques have demonstrated significant potential in enabling LLMs to dynamically interact with external tools, motivating the shift toward adaptive inference-time retrieval. Inspired by Information Foraging Theory (IFT), we propose InForage, a reinforcement learning framework that formalizes retrieval-augmented reasoning as a dynamic information-seeking process. Unlike existing approaches, InForage explicitly rewards intermediate retrieval quality, encouraging LLMs to iteratively gather and integrate information through adaptive search behaviors. To facilitate training, we construct a human-guided dataset capturing iterative search and reasoning trajectories for complex, real-world web tasks. Extensive evaluations across general question answering, multi-hop reasoning tasks, and a newly developed real-time web QA dataset demonstrate InForage's superior performance over baseline methods. These results highlight InForage's effectiveness in building robust, adaptive, and efficient reasoning agents. We provide all codes and datasets in the supplementary materials.

Computer Vision · Classification and Understanding

Fei Ye, Yongcheng Zhong, Qihe Liu, Adrian G. Bors, Jingling sun, Rongyao Hu, shijie zhou

Plasticity and stability denote the ability to assimilate new tasks while preserving previously acquired knowledge, representing two important concepts in continual learning. Recent research addresses stability by leveraging pre-trained models to provide informative representations, yet the efficacy of these methods is highly reliant on the choice of the pre-trained backbone, which may not yield optimal plasticity. This paper addresses this limitation by introducing a streamlined and potent framework that orchestrates multiple different pre-trained backbones to derive semantically rich multi-source representations. We propose an innovative Multi-Scale Interaction and Dynamic Fusion (MSIDF) technique to process and selectively capture the most relevant parts of multi-source features through a series of learnable attention modules, thereby helping to learn better decision boundaries to boost performance. Furthermore, we introduce a novel Multi-Level Representation Optimization (MLRO) strategy to adaptively refine the representation networks, offering adaptive representations that enhance plasticity. To mitigate over-regularization issues, we propose a novel Adaptive Regularization Optimization (ARO) method to manage and optimize a switch vector that selectively governs the updating process of each representation layer, which promotes the new task learning. The proposed MLRO and ARO approaches are collectively optimized within a unified optimization framework to achieve an optimal trade-off between plasticity and stability. Our extensive experimental evaluations reveal that the proposed framework attains state-of-the-art performance. The source code of our algorithm is available at https://github.com/CL-Coder236/LMSRR.

Theory · Everything Else

Etienne Gauthier, Francis Bach, Michael Jordan

We introduce *Backward Conformal Prediction*, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and allows the conformal set size to vary, our approach defines a rule that constrains how prediction set sizes behave based on the observed data, and adapts the coverage level accordingly. Our method builds on two key foundations: (i) recent results by Gauthier et al. [2025] on post-hoc validity using e-values, which ensure marginal coverage of the form $\mathbb{P}(Y_{\rm test} \in \hat C_n^{\tilde{\alpha}}(X_{\rm test})) \ge 1 - \mathbb{E}[\tilde{\alpha}]$ up to a first-order Taylor approximation for any data-dependent miscoverage $\tilde{\alpha}$, and (ii) a novel leave-one-out estimator $\hat{\alpha}^{\rm LOO}$ of the marginal miscoverage $\mathbb{E}[\tilde{\alpha}]$ based on the calibration set, ensuring that the theoretical guarantees remain computable in practice. This approach is particularly useful in applications where large prediction sets are impractical such as medical diagnosis. We provide theoretical results and empirical evidence supporting the validity of our method, demonstrating that it maintains computable coverage guarantees while ensuring interpretable, well-controlled prediction set sizes.

Deep Learning · Generative Models and Autoencoders

Hadi Hosseini, Samarth Khanna, Ronak Singh

The rise of Large Language Models (LLMs) has driven progress in reasoning tasks, from program synthesis to scientific hypothesis generation, yet their ability to handle ranked preferences and structured algorithms in combinatorial domains remains underexplored. We study matching markets, a core framework behind applications like resource allocation and ride-sharing, which require reconciling individual ranked preferences to ensure stable outcomes. We evaluate seven state‐of‐the‐art models on a hierarchy of preference‐based reasoning tasks---ranging from stable‐matching generation to instability detection, instability resolution, and fine-grained preference queries---to systematically expose their logical and algorithmic limitations in handling ranked inputs. Surprisingly, even top-performing models with advanced reasoning struggle to resolve instability in large markets, often failing to identify blocking pairs or execute algorithms iteratively. We further show that parameter-efficient fine-tuning (LoRA) significantly improves performance in small markets, but fails to bring about a similar improvement on large instances, suggesting the need for more sophisticated strategies to improve LLMs' reasoning with larger-context inputs.

Weijia Shi, Akshita Bhagia, Kevin Farhat, Niklas Muennighoff, Jacob Morrison, Evan Walsh, Dustin Schwenk, Shayne Longpre, Jake Poznanski, Allyson Ettinger 等

We introduce FlexOLMo, a new class of language models (LMs) that supports (1) distributed training without data sharing, where different model parameters are independently trained on private datasets, and (2) data-flexible inference, where these parameters along with their associated data can be easily included or excluded from model inferences with no further training. FlexOLMo employs a mixture-of-experts (MoE) architecture where each expert is trained independently on private datasets and later integrated through a new nonparametric routing without any joint training across datasets. FlexOLMo is trained on FLEXMIX, a corpus we curate comprising seven restricted sets, either real or realistic approximations, alongside publicly available datasets. We evaluate models with up to 37 billion parameters (20 billion active) on 31 diverse downstream tasks. We show that a general expert trained on public data can be effectively combined with independently trained experts from other data owners significantly benefiting from these restricted sets (an average 41% relative improvement) while allowing flexible opt-out at inference time (e.g., for users without appropriate licenses or permissions). Our approach also outperforms prior model merging methods by 10.1% on average and surpasses the standard MoE trained without data restrictions using the same training FLOPs. Altogether, FlexOLMo enables training on restricted data while keeping data local and supports fine-grained control of data access at inference.

Applications · Physics

Siyi Chen, Yixuan Jia, Qing Qu, He Sun, Jeffrey Fessler

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman Filter, Particle Filter) presuppose full knowledge of the true dynamics, which is not always satisfied in practice, while purely data-driven solvers learn a deterministic mapping between observations and states and therefore miss the intrinsic stochasticity of real processes. Recently, score-based diffusion models have shown promise for DA by learning a global diffusion prior to represent stochastic dynamics. However, their one-shot generation lacks stepwise physical consistency and struggles with complex stochastic processes. To address these issues, we propose FlowDAS, a generative DA framework that employs stochastic interpolants to learn state transition dynamics through step-by-step stochastic updates. By incorporating observations into each transition, FlowDAS can produce stable, measurement-consistent forecasts. Experiments on Lorenz-63, Navier–Stokes super-resolution/sparse-observation scenarios, and large-scale weather forecasting—where dynamics are partly or wholly unknown—show that FlowDAS surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility. Our implementation is available at https://github.com/umjiayx/FlowDAS.

Deep Learning · Generative Models and Autoencoders

Chao-Chung Wu, Zhi Rui Tam, Chieh-Yen Lin, Yun-Nung (Vivian) Chen, Shao-Hua Sun, Hung-yi Lee

Maintaining consistent model performance across domains is a fundamental challenge in machine learning. While recent work has explored using LLM-generated data for fine-tuning, its impact on cross-domain generalization remains poorly understood. This paper presents a systematic analysis revealing that fine-tuning with LLM-generated data not only improves target task performance but also reduces non-target task degradation compared to fine-tuning with ground truth data. Through analyzing the data sequence in tasks of various domains, we demonstrate that this enhancement of non-target task robustness stems from the reduction of high perplexity tokens found in LLM-generated sequences. Following our findings, we showed that masking high perplexity tokens in ground truth training data achieves similar non-target task performance preservation, comparable to using LLM-generated data. Extensive experiments across different model families and scales, including Gemma 2 IT 2B, Llama 3 8B Instruct, and three additional models, agree with our findings. To the best of our knowledge, this is the first work to provide an empirical explanation based on token perplexity reduction to mitigate catastrophic forgetting in LLMs after fine-tuning, offering valuable insights for developing more robust fine-tuning strategies.