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Deep Learning · Theory

Niket Patel, Guido Montufar

We define the *local complexity* of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn low-dimensional feature representations have a lower local complexity. This allows us to connect recent empirical observations on feature learning at the level of the weight matrices with concrete properties of the learned functions. In particular, we show that the local complexity serves as an upper bound on the total variation of the function over the input data distribution and thus that feature learning can be related to adversarial robustness. Lastly, we consider how optimization drives ReLU networks towards solutions with lower local complexity. Overall, this work contributes a theoretical framework towards relating geometric properties of ReLU networks to different aspects of learning such as feature learning and representation cost.

Wenbin Wang, Yongcheng Jing, Liang Ding, Yingjie Wang, Li Shen, Yong Luo, Bo Du, Dacheng Tao

High-resolution (HR) image perception remains a key challenge in multimodal large language models (MLLMs). To drive progress beyond the limits of heuristic methods, this paper advances HR perception capabilities of MLLMs by harnessing cutting-edge long-context techniques such as retrieval-augmented generation (RAG). Towards this end, this paper presents the first study exploring the use of RAG to address HR perception challenges. Specifically, we propose Retrieval-Augmented Perception (RAP), a training-free framework that retrieves and fuses relevant image crops while preserving spatial context using the proposed Spatial-Awareness Layout. To accommodate different tasks, the proposed Retrieved-Exploration Search (RE-Search) dynamically selects the optimal number of crops based on model confidence and retrieval scores. Experimental results on HR benchmarks demonstrate the significant effectiveness of RAP, with LLaVA-v1.5-13B achieving a 43\% improvement on $V^*$ Bench and 19\% on HR-Bench. Code is available at https://github.com/DreamMr/RAP.

Deep Learning · Large Language Models

Yang Zhou, Hongyi Liu, Zhuoming Chen, Yuandong Tian, Beidi Chen

Recently, long-context large language models (LLMs) have shown strong performance in information retrieval and long-document QA. However, to tackle the most challenging intellectual problems, LLMs must reason effectively in long and complex contexts (e.g., frontier mathematical research). Studying how LLMs handle increasing reasoning complexity and context length is essential, yet existing benchmarks lack a solid basis for quantitative evaluation. Inspired by the abstraction of GSM-8K problems as computational graphs—and the ability to introduce noise by adding unnecessary nodes and edges—we develop a grade-school math problem generator capable of producing arithmetic problems with infinite difficulty and context length under fine-grained control. Using our newly synthesized GSM-$\infty$ benchmark, we comprehensively evaluate existing LLMs. We find a consistent sigmoid decline in reasoning performance as complexity increases, along with a systematic inference scaling trend: exponentially increasing inference computation yields only linear performance gains. These findings underscore the fundamental limitations of current long-context LLMs and the key challenges in scaling reasoning capabilities. Our GSM-$\infty$ benchmark provides a scalable and controllable testbed for systematically studying and advancing LLM reasoning in long and complex contexts.

Applications · Chemistry, Physics, and Earth Sciences

Seung Lee, Hojoon Kim, Yutack Park, Dawoon Jeong, Seungwu Han, Yeonhong Park, Jae W. Lee

Machine Learning Interatomic Potentials (MLIPs) enable efficient molecular dynamics (MD) simulations with high accuracy. While equivariant MLIPs achieve state-of-the-art accuracy, they face significant computational bottlenecks centered around their Tensor-Product layer, which account for up to 75\% of training time and cause substantial memory overhead. We present FlashTP, a highly optimized tensor-product library that addresses these inefficiencies through kernel fusion, sparse computation, and path-aggregated execution. FlashTP achieves up to 41.6$\times$ and 60.8$\times$ kernel speedups over _e3nn_ and NVIDIA cuEquivariance, respectively. For SevenNet-l3i5, it delivers 4.2$\times$ and 3.5$\times$ speedup while reducing peak memory usage by 6.3$\times$ and 6.2$\times$ for inference and training, respectively. The code is available at https://github.com/SNU-ARC/flashTP.

Social Aspects · Privacy

Justin Chen, Vincent Cohen-Addad, Alessandro Epasto, Morteza Zadimoghaddam

In the differentially private partition selection problem (a.k.a. set union, key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items. We propose an algorithm for this problem, MaxAdaptiveDegree (MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed in prior works.

Theory · Learning Theory

Robert Busa-Fekete, Travis Dick, Claudio Gentile, Haim Kaplan, Tomer Koren, Uri Stemmer

We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the goal is still to achieve small regret at the level of individual examples. We give results on the sample complexity of LLP under square loss, showing that our sample complexity is essentially optimal. From an algorithmic viewpoint, we rely on carefully designed variants of Empirical Risk Minimization, and Stochastic Gradient Descent algorithms, combined with ad hoc variance reduction techniques. On one hand, our theoretical results improve in important ways on the existing literature on LLP, specifically in the way the sample complexity depends on the bag size. On the other hand, we validate our algorithmic solutions on several datasets, demonstrating improved empirical performance (better accuracy for less samples) against recent baselines.

Deep Learning · Large Language Models

Hammad Rizwan, Domenic Rosati, Ga Wu, Hassan Sajjad

Model editing aims to modify the outputs of large language models after they are trained. Previous approaches have often involved direct alterations to model weights, which can result in model degradation. Recent techniques avoid making modifications to the model's weights by using an adapter that applies edits to the model when triggered by semantic similarity in the representation space. We demonstrate that current adapter methods are *critically vulnerable* to strong lexical biases, leading to issues such as applying edits to irrelevant prompts with overlapping words. This paper presents a principled approach to learning a disentangled representation space that facilitates precise localization of edits by maintaining distance between irrelevant prompts while preserving proximity among paraphrases. In our empirical study, we show that our method (Projector Editor Networks for Model Editing - PENME) achieves state-of-the-art model editing results while being more computationally efficient during inference than previous methods and adaptable across different architectures.

Reinforcement Learning

Chenyou Fan, Chenjia Bai, Zhao Shan, Haoran He, Yang Zhang, Zhen Wang

Diffusion models have demonstrated their capabilities in modeling trajectories of multi-tasks. However, existing multi-task planners or policies typically rely on task-specific demonstrations via multi-task imitation, or require task-specific reward labels to facilitate policy optimization via Reinforcement Learning (RL). They are costly due to the substantial human efforts required to collect expert data or design reward functions. To address these challenges, we aim to develop a versatile diffusion planner capable of leveraging large-scale inferior data that contains task-agnostic sub-optimal trajectories, with the ability to fast adapt to specific tasks. In this paper, we propose SODP, a two-stage framework that leverages Sub-Optimal data to learn a Diffusion Planner, which is generalizable for various downstream tasks. Specifically, in the pre-training stage, we train a foundation diffusion planner that extracts general planning capabilities by modeling the versatile distribution of multi-task trajectories, which can be sub-optimal and has wide data coverage. Then for downstream tasks, we adopt RL-based fine-tuning with task-specific rewards to quickly refine the diffusion planner, which aims to generate action sequences with higher task-specific returns. Experimental results from multi-task domains including Meta-World and Adroit demonstrate that SODP outperforms state-of-the-art methods with only a small amount of data for reward-guided fine-tuning.

General Machine Learning · Causality

Mingjia Li, Hong Qian, Tian-Zuo Wang, ShujunLi, Min Zhang, Aimin Zhou

Causal discovery aims to identify causal relationships from observational data. Recently, optimization-based causal discovery methods have attracted extensive attention in the literature due to their efficiency in handling high-dimensional problems. However, we observe that optimization-based methods often perform well on certain problems but struggle with others. This paper identifies a specific characteristic of causal structural equations that determines the difficulty of identification in causal discovery and, in turn, the performance of optimization-based methods. We conduct an in-depth study of the additive noise model (ANM) and propose to further divide identifiable problems into strongly and weakly identifiable types based on the difficulty of identification. We also provide a sufficient condition to distinguish the two categories. Inspired by these findings, this paper further proposes GENE, a generic method for addressing strongly and weakly identifiable problems in a unified way under the ANM assumption. GENE adopts an order-based search framework that incorporates conditional independence tests into order fitness evaluation, ensuring effectiveness on weakly identifiable problems. In addition, GENE restricts the dimensionality of the effect variables to ensure \emph{scale invariance}, a property crucial for practical applications. Experiments demonstrate that GENE is uniquely effective in addressing weakly identifiable problems while also remaining competitive with state-of-the-art causal discovery algorithms for strongly identifiable problems.

Guibin Zhang, Luyang Niu, Junfeng Fang, Kun Wang, LEI BAI, Xiang Wang

Large Language Model (LLM)-empowered multi-agent systems extend the cognitive boundaries of individual agents through disciplined collaboration and interaction, while constructing these systems often requires labor-intensive manual designs. Despite the availability of methods to automate the design of agentic workflows, they typically seek to identify a static, complex, one-size-fits-all system, which, however, fails to dynamically allocate inference resources based on the difficulty and domain of each query. To address this challenge, we shift away from the pursuit of a monolithic agentic system, instead optimizing the \textbf{agentic supernet}, a probabilistic and continuous distribution of agentic architectures. We introduce \textbf{MaAS}, an automated framework that samples query-dependent agentic systems from the supernet, delivering high-quality solutions and tailored resource allocation (\textit{e.g.}, LLM calls, tool calls, token cost). Comprehensive evaluation across six benchmarks demonstrates that MaAS \textbf{(I)} requires only $6\\sim45\\%$ of the inference costs of existing handcrafted or automated multi-agent systems, \textbf{(II)} surpasses them by $0.54\\%\sim11.82\\%$, and \textbf{(III)} enjoys superior cross-dataset and cross-LLM-backbone transferability.

Deep Learning · Large Language Models

Yuchen Lin, Ronan Le Bras, Kyle Richardson, Ashish Sabharwal, Radha Poovendran, Peter Clark, Yejin Choi

We investigate the logical reasoning capabilities of Large Language Models (LLMs) and their scalability across complex deductive tasks. Using ZebraLogic, a newly developed benchmark dataset of logic grid puzzles derived from constraint satisfaction problems (CSPs), we systematically evaluate LLM performance. ZebraLogic spans a broad range of search space complexities and incorporates diverse logical constraints, providing a controlled environment to assess reasoning abilities. Our results reveal a significant decline in accuracy as problem complexity increases—a phenomenon we term the “curse of complexity.” Notably, this limitation persists even with scaling model size and inference-time computation, suggesting fundamental constraints in current LLM reasoning capabilities. Additionally, we explore strategies such as Best-of-N sampling, backtracking mechanisms, and self-verification prompts to enhance logical reasoning performance. Our findings provide critical insights into the scaling behavior of LLMs, highlight their limitations, and outline potential directions for advancing their reasoning capabilities.

Social Aspects · Accountability, Transparency, and Interpretability

Tuomas Oikarinen, Ge Yan, Lily Weng

Understanding the function of individual units in a neural network is an important building block for mechanistic interpretability. This is often done by generating a simple text explanation of the behavior of individual neurons or units. For these explanations to be useful, we must understand how reliable and truthful they are. In this work we unify many existing explanation evaluation methods under one mathematical framework. This allows us to compare and contrast existing evaluation metrics, understand the evaluation pipeline with increased clarity and apply existing statistical concepts on the evaluation. In addition, we propose two simple sanity checks on the evaluation metrics and show that many commonly used metrics fail these tests and do not change their score after massive changes to the concept labels. Based on our experimental and theoretical results, we propose guidelines that future evaluations should follow and identify a set of reliable evaluationmetrics.

Deep Learning · Large Language Models

Jerry Huang, Peng Lu, QIUHAO Zeng

Recent advances in natural language processing (NLP) have opened up greater opportunities to enable fine-tuned large language models (LLMs) to behave as more powerful interactive agents through improved instruction-following ability. However, understanding how this impacts confidence calibration for reliable model output has not been researched in full. In this work, we examine various open-sourced LLMs, identifying significant calibration degradation after instruction tuning in each. Seeking a practical solution, we look towards label smoothing, which has been shown as an effective method to regularize for overconfident predictions but has yet to be widely adopted in the supervised fine-tuning (SFT) of LLMs. We first provide insight as to why label smoothing is sufficient to maintain calibration throughout the SFT process. However, settings remain where the effectiveness of smoothing is severely diminished, in particular the case of large vocabulary LLMs (LV-LLMs). We posit the cause to stem from the ability to become over-confident, which has a direct relationship with the hidden size and vocabulary size, and justify this theoretically and experimentally. Finally, we address an outstanding issue regarding the memory footprint of the cross-entropy loss computation in the label smoothed loss setting, designing a customized kernel to dramatically reduce memory consumption without sacrificing speed or performance in comparison to existing solutions for non-smoothed losses.

Deep Learning · Algorithms

Shyam Nuggehalli, Jifan Zhang, Lalit Jain, Robert Nowak

Class imbalance severely impacts machine learning performance on minority classes in real-world applications. While various solutions exist, active learning offers a fundamental fix by strategically collecting balanced, informative labeled examples from abundant unlabeled data. We introduce DIRECT, an algorithm that identifies class separation boundaries and selects the most uncertain nearby examples for annotation. By reducing the problem to one-dimensional active learning, DIRECT leverages established theory to handle batch labeling and label noise -- another common challenge in data annotation that particularly affects active learning methods.Our work presents the first comprehensive study of active learning under both class imbalance and label noise. Extensive experiments on imbalanced datasets show DIRECT reduces annotation costs by over 60\% compared to state-of-the-art active learning methods and over 80\% versus random sampling, while maintaining robustness to label noise.

Deep Learning · Generative Models and Autoencoders

Lukas Lao Beyer, Tianhong Li, Xinlei Chen, Sertac Karaman, Kaiming He

Commonly used image tokenizers produce a 2D grid of spatially arranged tokens. In contrast, so-called *1D* image tokenizers represent images as highly compressed one-dimensional sequences of as few as 32 discrete tokens. We find that the high degree of compression achieved by a 1D tokenizer with vector quantization enables image editing and generative capabilities through heuristic manipulation of tokens, demonstrating that even very crude manipulations -- such as copying and replacing tokens between latent representations of images -- enable fine-grained image editing by transferring appearance and semantic attributes. Motivated by the expressivity of the 1D tokenizer's latent space, we construct an image generation pipeline leveraging gradient-based test-time optimization of tokens with plug-and-play loss functions such as reconstruction or CLIP similarity. Our approach is demonstrated for inpainting and text-guided image editing use cases, and can generate diverse and realistic samples without requiring training of any generative model.

Reinforcement Learning

Chia-Han Yeh, Tse-Sheng Nan, Risto Vuorio, Wei Hung, Hung-Yen Wu, Shao-Hua Sun, Ping-Chun Hsieh

Policy learning under action constraints plays a central role in ensuring safe behaviors in various robot control and resource allocation applications.In this paper, we study a new problem setting termed Action-Constrained Imitation Learning (ACIL), where an action-constrained imitator aims to learn from a demonstrative expert with larger action space.The fundamental challenge of ACIL lies in the unavoidable mismatch of occupancy measure between the expert and the imitator caused by the action constraints. We tackle this mismatch through trajectory alignment and propose DTWIL, which replaces the original expert demonstrations with a surrogate dataset that follows similar state trajectories while adhering to the action constraints. Specifically, we recast trajectory alignment as a planning problem and solve it via Model Predictive Control, which aligns the surrogate trajectories with the expert trajectories based on the Dynamic Time Warping (DTW) distance. Through extensive experiments, we demonstrate that learning from the dataset generated by DTWIL significantly enhances performance across multiple robot control tasks and outperforms various benchmark imitation learning algorithms in terms of sample efficiency.

Social Aspects · Accountability, Transparency, and Interpretability

Nils Palumbo, Ravi Mangal, Zifan Wang, Saranya Vijayakumar, Corina Pasareanu, Somesh Jha

Mechanistic interpretability aims to reverse engineer the computation performed by a neural network in terms of its internal components. Although there is a growing body of research on mechanistic interpretation of neural networks, the notion of a *mechanistic interpretation* itself is often ad-hoc. Inspired by the notion of abstract interpretation from the program analysis literature that aims to develop approximate semantics for programs, we give a set of axioms that formally characterize a mechanistic interpretation as a description that approximately captures the semantics of the neural network under analysis in a compositional manner. We demonstrate the applicability of these axioms for validating mechanistic interpretations on an existing, well-known interpretability study as well as on a new case study involving a Transformer-based model trained to solve the well-known 2-SAT problem.

General Machine Learning · Kernel methods

Zhitong Xu, Da Long, Yiming Xu, Guang Yang, Shandian Zhe, Houman Owhadi

We introduce a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing challenges with a large number of collocation points, our approach eliminates these operators from the kernel. We model the solution using a standard kernel interpolation form and differentiate the interpolant to compute the derivatives. Our framework obviates the need for complex Gram matrix construction between solutions and their derivatives, allowing for a straightforward implementation and scalable computation. As an instance, we allocate the collocation points on a grid and adopt a product kernel, which yields a Kronecker product structure in the interpolation. This structure enables us to avoid computing the full Gram matrix, reducing costs and scaling efficiently to a large number of collocation points. We provide a proof of the convergence and rate analysis of our method under appropriate regularity assumptions. In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.

General Machine Learning · Scalable Algorithms

Supratim Shit, Gurmehak chadha, Surendra kumar, Bapi Chatterjee

Coreset, as a summary of training data, offers an efficient approach for reducing data processing and storage complexity during training. In the emerging vertical federated learning (VFL) setting, where scattered clients store different data features, it directly reduces communication complexity. In this work, we introduce coresets construction for regularized logistic regression both in centralized and VFL settings. Additionally, we improve the coreset size for regularized linear regression in the VFL setting. We also eliminate the dependency of the coreset size on a property of the data due to the VFL setting. The improvement in the coreset sizes is due to our novel coreset construction algorithms that capture the reduced model complexity due to the added regularization and its subsequent analysis. In experiments, we provide extensive empirical evaluation that backs our theoretical claims. We also report the performance of our coresets by comparing the models trained on the complete data and on the coreset.

Social Aspects · Safety

Yang Zhang, Er Jin, Yanfei Dong, Yixuan Wu, Phil Torr, Ashkan Khakzar, Johannes Stegmaier, Kenji Kawaguchi

Recent advances in generative models have demonstrated remarkable capabilities in producing high-quality images, but their reliance on large-scale unlabeled data has raised significant safety and copyright concerns. Efforts to address these issues by erasing unwanted concepts have shown promise. However, many existing erasure methods involve excessive modifications that compromise the overall utility of the model.In this work, we address these issues by formulating a novel minimalist concept erasure objective based *only* on the distributional distance of final generation outputs. Building on our formulation, we derive a tractable loss for differentiable optimization that leverages backpropagation through all generation steps in an end-to-end manner. We also conduct extensive analysis to show theoretical connections with other models and methods. To improve the robustness of the erasure, we incorporate neuron masking as an alternative to model fine-tuning. Empirical evaluations on state-of-the-art flow-matching models demonstrate that our method robustly erases concepts without degrading overall model performance, paving the way for safer and more responsible generative models.