NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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5,812篇论文

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  • Spotlight
    73912.7%
  • Poster
    4,98085.7%

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NeurIPS should lead scientific consensus on AI policy

Rishi Bommasani

展开摘要

Designing wise AI policy is a grand challenge for society. To design such policy, policymakers should place a premium on rigorous evidence and scientific consensus. While several mechanisms exist for evidence generation, and nascent mechanisms tackle evidence synthesis, we identify a complete void on consensus formation. In this position paper, we argue NeurIPS should actively catalyze scientific consensus on AI policy. Beyond identifying the current deficit in consensus formation mechanisms, we argue that NeurIPS is the best option due its strengths and the paucity of compelling alternatives. To make progress, we recommend initial pilots for NeurIPS by distilling lessons from the IPCC's leadership to build scientific consensus on climate policy. We dispel predictable counters that AI researchers disagree too much to achieve consensus and that policy engagement is not the business of NeurIPS. NeurIPS leads AI on many fronts, and it should champion scientific consensus to create policy that better realizes the benefits of AI.

Oral
DexFlyWheel: A Scalable and Self-improving Data Generation Framework for Dexterous Manipulation

Kefei Zhu, Fengshuo Bai, YuanHao Xiang, Yishuai Cai, Xinglin Chen, Ruochong Li, Xingtao Wang, Hao Dong, Yaodong Yang, Xiaopeng Fan, Yuanpei Chen

展开摘要

Dexterous manipulation is critical for advancing robot capabilities in real-world applications, yet diverse and high-quality datasets remain scarce. Existing data collection methods either rely on human teleoperation or require significant human engineering, or generate data with limited diversity, which restricts their scalability and generalization. In this paper, we introduce DexFlyWheel, a scalable data generation framework that employs a self-improving cycle to continuously enrich data diversity. Starting from efficient seed demonstrations warmup, DexFlyWheel expands the dataset through iterative cycles. Each cycle follows a closed-loop pipeline that integrates Imitation Learning (IL), residual Reinforcement Learning (RL), rollout trajectory collection, and data augmentation. Specifically, IL extracts human-like behaviors from demonstrations, and residual RL enhances policy generalization. The learned policy is then used to generate trajectories in simulation, which are further augmented across diverse environments and spatial configurations before being fed back into the next cycle. Over successive iterations, a self-improving data flywheel effect emerges, producing datasets that cover diverse scenarios and thereby scaling policy performance. Experimental results demonstrate that DexFlyWheel generates over 2,000 diverse demonstrations across four challenging tasks. Policies trained on our dataset achieve an average success rate of 81.9\% on the challenge test sets and successfully transfer to the real world through digital twin, achieving a 78.3\% success rate on dual-arm lift tasks.

Spotlight
Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization

Yamato Arai, Yuma Ichikawa

展开摘要

Layer-wise PTQ is a promising technique for compressing large language models (LLMs), due to its simplicity and effectiveness without requiring retraining. However, recent progress in this area is saturating, underscoring the need to revisit its core limitations and explore further improvements. We address this challenge by identifying a key limitation of existing layer-wise PTQ methods: the growth of quantization errors across layers significantly degrades performance, particularly in low-bit regimes. To address this fundamental issue, we propose Quantization Error Propagation (QEP), a general, lightweight, and scalable framework that enhances layer-wise PTQ by explicitly propagating quantization errors and compensating for accumulated errors. QEP also offers a tunable propagation mechanism that prevents overfitting and controls computational overhead, enabling the framework to adapt to various architectures and resource budgets. Extensive experiments on several LLMs demonstrate that QEP-enhanced layer-wise PTQ achieves substantially higher accuracy than existing methods. Notably, the gains are most pronounced in the extremely low-bit quantization regime.

Poster
WorldModelBench: Judging Video Generation Models As World Models

Dacheng Li, Yunhao Fang, Yukang Chen, Shuo Yang, Shiyi Cao, Justin Wong, Michael Luo, Xiaolong Wang, Hongxu Yin, Joseph E. Gonzalez, Ion Stoica, Song Han, Yao Lu

展开摘要

Video generation models have rapidly progressed, positioning themselves as video world models capable of supporting decision-making applications like robotics and autonomous driving. However, current benchmarks fail to rigorously evaluate these claims, focusing only on general video quality, ignoring important factors to world models such as physics adherence. To bridge this gap, we propose WorldModelBench, a benchmark designed to evaluate the world modeling capabilities of video generation models in application-driven domains. WorldModelBench offers two key advantages: (1) Against to nuanced world modeling violations: By incorporating instruction-following and physics-adherence dimensions, WorldModelBench detects subtle violations, such as irregular changes in object size that breach the mass conservation law—issues overlooked by prior benchmarks. (2) Aligned with large-scale human preferences: We crowd-source 67K human labels to accurately measure 14 frontier models. Using our high-quality human labels, we further fine-tune an accurate judger to automate the evaluation procedure, achieving 9.9% lower error in predicting world modeling violations than GPT-4o with 2B parameters. In addition, we demonstrate that training to align human annotations by maximizing the rewards from the judger noticeably improve the world modeling capability. The dataset is hosted in HuggingFace at https://huggingface.co/datasets/Efficient-Large-Model/worldmodelbench. The code to run evaluation is available at https://github.com/WorldModelBench-Team/WorldModelBench.

Poster
Video-R1: Reinforcing Video Reasoning in MLLMs

Kaituo Feng, Kaixiong Gong, Bohao Li, Zonghao Guo, Yibing Wang, Tianshuo Peng, Junfei Wu, Xiaoying Zhang, Benyou Wang, Xiangyu Yue

展开摘要

Inspired by DeepSeek-R1's success in eliciting reasoning abilities through rule-based reinforcement learning (RL), we introduce Video-R1 as the first attempt to systematically explore the R1 paradigm for incentivizing video reasoning within multimodal large language models (MLLMs). However, directly applying RL training with the GRPO algorithm to video reasoning presents two primary challenges: (i) a lack of temporal modeling for video reasoning, and (ii) the scarcity of high-quality video-reasoning data. To address these issues, we first propose the T-GRPO algorithm, which encourages models to utilize temporal information in videos for reasoning. Additionally, instead of relying solely on video data, we incorporate high-quality image-reasoning data into the training process. We have constructed two datasets: Video-R1-CoT-165k for SFT cold start and Video-R1-260k for RL training, both comprising image and video data. Experimental results demonstrate that Video-R1 achieves significant improvements on video reasoning benchmarks such as VideoMMMU and VSI-Bench, as well as on general video benchmarks including MVBench and TempCompass, etc. Notably, Video-R1-7B attains a 37.1\% accuracy on video spatial reasoning benchmark VSI-bench, surpassing the commercial proprietary model GPT-4o. All code, models, and data will be released.

Poster
LookWhere? Efficient Visual Recognition by Learning Where to Look and What to See from Self-Supervision

Anthony Fuller, Yousef Yassin, Junfeng Wen, Tarek Ibrahim, Daniel Kyrollos, James R Green, Evan Shelhamer

展开摘要

Vision transformers are ever larger, more accurate, and more expensive to compute. At high resolution, the expense is even more extreme as the number of tokens grows quadratically in the image size. We turn to adaptive computation to cope with this cost by learning to predict where to compute. Our LookWhere method divides the computation between a low-resolution selector and a high-resolution extractor without ever processing the full high-resolution input. We jointly pretrain the selector and extractor without task supervision by distillation from a self-supervised teacher, in effect learning where and what to compute at the same time. Unlike prior token reduction methods, which pay to save by pruning already-computed tokens, and prior token selection methods, which require complex and expensive per-task optimization, LookWhere economically and accurately selects and extracts transferrable representations of images. We show that LookWhere excels at sparse recognition on high-resolution inputs (Traffic Signs), maintaining accuracy while reducing FLOPs by 17x and time by 4x, and standard recognition tasks that are global (ImageNet classification) and local (ADE20K segmentation), improving accuracy while reducing time by 1.36x.

Poster
DreamPRM: Domain-reweighted Process Reward Model for Multimodal Reasoning

Qi Cao, Ruiyi Wang, Ruiyi Zhang, Sai Ashish Somayajula, Pengtao Xie

展开摘要

Reasoning has substantially improved the performance of large language models (LLMs) on complicated tasks. Central to the current reasoning studies, Process Reward Models (PRMs) offer a fine-grained evaluation of intermediate reasoning steps and guide the reasoning process. However, extending PRMs to multimodal large language models (MLLMs) introduces challenges. Since multimodal reasoning covers a wider range of tasks compared to text-only scenarios, the resulting distribution shift from the training to testing sets is more severe, leading to greater generalization difficulty. Training a reliable multimodal PRM, therefore, demands large and diverse datasets to ensure sufficient coverage. However, current multimodal reasoning datasets suffer from a marked quality imbalance, which degrades PRM performance and highlights the need for an effective data selection strategy. To address the issues, we introduce DreamPRM, a domain-reweighted training framework for multimodal PRMs which employs bi-level optimization. In the lower-level optimization, DreamPRM performs fine-tuning on multiple datasets with domain weights, allowing the PRM to prioritize high-quality reasoning signals and alleviating the impact of dataset quality imbalance. In the upper-level optimization, the PRM is evaluated on a separate meta-learning dataset; this feedback updates the domain weights through an aggregation loss function, thereby improving the generalization capability of trained PRM. Extensive experiments on multiple multimodal reasoning benchmarks covering both mathematical and general reasoning show that test-time scaling with DreamPRM consistently improves the performance of state-of-the-art MLLMs. Further comparisons reveal that DreamPRM's domain-reweighting strategy surpasses other data selection methods and yields higher accuracy gains than existing test-time scaling approaches. Notably, DreamPRM achieves a top-1 accuracy of 85.2% on the MathVista leaderboard using the o4-mini model, demonstrating strong generalization capability in complex multimodal reasoning tasks.

Poster
Validating LLM-as-a-Judge Systems under Rating Indeterminacy

Luke Guerdan, Solon Barocas, Ken Holstein, Hanna Wallach, Steven Wu, Alexandra Chouldechova

展开摘要

The LLM-as-a-judge paradigm, in which a judge LLM system replaces human raters in rating the outputs of other generative AI (GenAI) systems, plays a critical role in scaling and standardizing GenAI evaluations. To validate such judge systems, evaluators assess human--judge agreement by first collecting multiple human ratings for each item in a validation corpus, then aggregating the ratings into a single, per-item gold label rating. For many items, however, rating criteria may admit multiple valid interpretations, so a human or LLM rater may deem multiple ratings "reasonable" or "correct." We call this condition rating indeterminacy. Problematically, many rating tasks that contain rating indeterminacy rely on forced-choice elicitation, whereby raters are instructed to select only one rating for each item. In this paper, we introduce a framework for validating LLM-as-a-judge systems under rating indeterminacy. We draw theoretical connections between different measures of judge system performance under different human--judge agreement metrics, and different rating elicitation and aggregation schemes. We demonstrate that differences in how humans and LLMs resolve rating indeterminacy when responding to forced-choice rating instructions can heavily bias LLM-as-a-judge validation. Through extensive experiments involving 11 real-world rating tasks and 9 commercial LLMs, we show that standard validation approaches that rely upon forced-choice ratings select judge systems that are highly suboptimal, performing as much as 31% worse than judge systems selected by our approach that uses multi-label "response set" ratings to account for rating indeterminacy. We conclude with concrete recommendations for more principled approaches to LLM-as-a-judge validation.

Poster
QoQ-Med: Building Multimodal Clinical Foundation Models with Domain-Aware GRPO Training

Wei Dai, Peilin Chen, Chanakya Ekbote, Paul Pu Liang

展开摘要

Clinical decision‑making routinely demands reasoning over heterogeneous data, yet existing multimodal language models (MLLMs) remain largely vision‑centric and fail to generalize across clinical specialties. To bridge this gap, we introduce QoQ-Med-7B/32B, the first open generalist clinical foundation model that jointly reasons across medical images, time‑series signals, and text reports. QoQ-Med is trained with Domain‑aware Relative Policy Optimization (DRPO), a novel reinforcement‑learning objective that hierarchically scales normalized rewards according to domain rarity and modality difficulty, mitigating performance imbalance caused by skewed clinical data distributions. Trained on 2.61 million instruction tuning pairs spanning 9 clinical domains, we show that DRPO training boosts diagnostic performance by 43% in macro‑F1 on average across all visual domains as compared to other critic-free training methods like GRPO. Furthermore, with QoQ-Med trained on intensive segmentation data, it is able to highlight salient regions related to the diagnosis, with an IoU 10x higher than open models while reaching the performance of OpenAI o4-mini. To foster reproducibility and downstream research, we release (i) the full model weights, (ii) the modular training pipeline, and (iii) all intermediate reasoning traces.

Oral
InfiFPO: Implicit Model Fusion via Preference Optimization in Large Language Models

Yanggan Gu, Yuanyi Wang, Zhaoyi Yan, Yiming Zhang, Qi Zhou, Fei Wu, Hongxia Yang

展开摘要

Model fusion combines multiple Large Language Models (LLMs) with different strengths into a more powerful, integrated model through lightweight training methods. Existing works on model fusion focus primarily on supervised fine-tuning (SFT), leaving preference alignment (PA) —a critical phase for enhancing LLM performance—largely unexplored. The current few fusion methods on PA phase, like WRPO, simplify the process by utilizing only response outputs from source models while discarding their probability information. To address this limitation, we propose InfiFPO, a preference optimization method for implicit model fusion. InfiFPO replaces the reference model in Direct Preference Optimization (DPO) with a fused source model that synthesizes multi-source probabilities at the sequence level, circumventing complex vocabulary alignment challenges in previous works and meanwhile maintaining the probability information. By introducing probability clipping and max-margin fusion strategies, InfiFPO enables the pivot model to align with human preferences while effectively distilling knowledge from source models. Comprehensive experiments on 11 widely-used benchmarks demonstrate that InfiFPO consistently outperforms existing model fusion and preference optimization methods. When using Phi-4 as the pivot model, InfiFPO improves its average performance from 79.95 to 83.33 on 11 benchmarks, significantly improving its capabilities in mathematics, coding, and reasoning tasks.

Spotlight
Sharper Convergence Rates for Nonconvex Optimisation via Reduction Mappings

Evan Markou, Thalaiyasingam Ajanthan, Stephen Gould

展开摘要

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be exploited through reduction mappings that reparametrise part of the parameter space to lie on the solution manifold. These reductions naturally arise from inner optimisation problems and effectively remove redundant directions, yielding a lower-dimensional objective. In this work, we introduce a general framework to understand how such reductions influence the optimisation landscape. We show that well-designed reduction mappings improve curvature properties of the objective, leading to better-conditioned problems and theoretically faster convergence for gradient-based methods. Our analysis unifies a range of scenarios where structural information at optimality is leveraged to accelerate convergence, offering a principled explanation for the empirical gains observed in such optimisation algorithms.

Spotlight
Offline Actor-Critic for Average Reward MDPs

William Powell, Jeongyeol Kwon, Qiaomin Xie, Hanbaek Lyu

展开摘要

We study offline policy optimization for infinite-horizon average-reward Markov decision processes (MDPs) with large or infinite state spaces. Specifically, we propose a pessimistic actor-critic algorithm that uses a computationally efficient linear function class for value function estimation. At the core of our method is a critic that computes a pessimistic estimate of the average reward under the current policy, as well as the corresponding policy gradient, by solving a fixed-point Bellman equation, rather than solving a successive sequence of regression problems as in finite horizon settings. This procedure reduces to solving a second-order cone program, which is computationally tractable. Our theoretical analysis is based on a weak partial data coverage assumption, which requires only that the offline data aligns well with the expected feature vector of a comparator policy. Under this condition, we show that our algorithm achieves the optimal sample complexity of O(\varepsilon^{-2}) for learning a near-optimal policy, up to model misspecification errors.

Poster
Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

Daniel Ovalle, Lorenz T. Biegler, Ignacio E Grossmann, Carl D Laird, Mateo Dulce Rubio

展开摘要

We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible with probability at least $1{-}\alpha$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.

Spotlight
Q3R: Quadratic Reweighted Rank Regularizer for Effective Low-Rank Training

Ipsita Ghosh, Ethan Nguyen, Christian Kümmerle

展开摘要

Parameter-efficient training, based on low-rank optimization, has become a highly successful tool for fine-tuning large deep-learning models. However, these methods fail at low-rank pre-training tasks where maintaining the low-rank structure and the objective remains a challenging task. We propose the Quadratic Reweighted Rank Regularizer dubbed Q3R, which leads to a novel low-rank inducing training strategy inspired by the iteratively reweighted least squares (IRLS) framework. Q3R is based on a quadratic regularizer term which majorizes a smoothed log determinant serving as rank surrogate objective. Unlike other low-rank training techniques, Q3R is able to train weight matrices with prescribed, low target ranks of models that achieve comparable predictive performance as dense models, with small computational overhead, while remaining fully compatible with existing architectures. In experiments, we are able to truncate 60% of the parameters of a ViT-Tiny parameters with marginal loss in CIFAR-10 performance and up to 80% with only 4% accuracy drop. The efficacy of Q3R is confirmed on Transformers across both image and language tasks, including for low-rank fine-tuning.

Poster
Large Language Bayes

Justin Domke

展开摘要

Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint distribution over formal models, latent variables, and data. A posterior over latent variables follows by conditioning on observed data and integrating over formal models. This presents a challenging inference problem. We suggest an inference recipe that amounts to generating many formal models from the large language model, performing approximate inference on each, and then doing a weighted aver- age. This is justified and analyzed as a combination of self-normalized importance sampling, MCMC, and importance-weighted variational inference. Experimentally, this produces sensible predictions from only data and an informal problem description, without the need to specify a formal model.

Poster
Efficient Safe Meta-Reinforcement Learning: Provable Near-Optimality and Anytime Safety

Siyuan Xu, Minghui Zhu

展开摘要

This paper studies the problem of safe meta-reinforcement learning (safe meta-RL), where an agent efficiently adapts to unseen tasks while satisfying safety constraints at all times during adaptation. We propose a framework consisting of two complementary modules: safe policy adaptation and safe meta-policy training. The first module introduces a novel one-step safe policy adaptation method that admits a closed-form solution, ensuring monotonic improvement, constraint satisfaction at every step, and high computational efficiency. The second module develops a Hessian-free meta-training algorithm that incorporates safety constraints on the meta-policy and leverages the analytical form of the adapted policy to enable scalable optimization. Together, these modules yield three key advantages over existing safe meta-RL methods: (i) superior optimality, (ii) anytime safety guarantee, and (iii) high computational efficiency. Beyond existing safe meta-RL analyses, we prove the anytime safety guarantee of policy adaptation and provide a lower bound of the expected total reward of the adapted policies compared with the optimal policies, which shows that the adapted policies are nearly optimal. Empirically, our algorithm achieves superior optimality, strict safety compliance, and substantial computational gains—up to 70\% faster training and 50\% faster testing—across diverse locomotion and navigation benchmarks.

Poster
Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models

Taha Entesari, Arman Hatami, Rinat Khaziev, Anil Ramakrishna, Mahyar Fazlyab

展开摘要

Large Language Models (LLMs) deployed in real-world settings increasingly face the need to unlearn sensitive, outdated, or proprietary information. Existing unlearning methods typically formulate forgetting and retention as a regularized trade-off, combining both objectives into a single scalarized loss. This often leads to unstable optimization and degraded performance on retained data, especially under aggressive forgetting. We propose a new formulation of LLM unlearning as a constrained optimization problem: forgetting is enforced via a novel logit-margin flattening loss that explicitly drives the output distribution toward uniformity on a designated forget set, while retention is preserved through a hard constraint on a separate retain set. Compared to entropy-based objectives, our loss is softmax-free, numerically stable, and maintains non-vanishing gradients, enabling more efficient and robust optimization. We solve the constrained problem using a scalable primal-dual algorithm that exposes the trade-off between forgetting and retention through the dynamics of the dual variable, all without any extra computational overhead. Evaluations on the TOFU and MUSE benchmarks across diverse LLM architectures demonstrate that our approach consistently matches or exceeds state-of-the-art baselines, effectively removing targeted information while preserving downstream utility.

Poster
New Parallel and Streaming Algorithms for Directed Densest Subgraph

Slobodan Mitrović, Theodore Pan, Mahdi Qaempanah, Mohammad Amin Raeisi

展开摘要

Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing massive data. We consider two such models: Massively Parallel Computation (MPC) and semi-streaming. We show how to find a $(2+\varepsilon)$-approximation in $\tilde{O}(\sqrt{\log n})$ MPC rounds with sublinear memory per machine. This improves the state-of-the-art results by Bahmani et al. (WAW 2014) and Mitrovic \& Pan (ICML 2024). Moreover, we show how to find an $O(\log n)$-approximation in a single pass in semi-streaming. This is in stark contrast to prior work, which implies $\tilde{\Omega}(n^{1/6})$-approximation for a single pass; a better approximation is known only for randomized streams (Mitrovi\'c \& Pan). This is the first deterministic single-pass semi-streaming algorithm for the densest subgraph problem, both for undirected and directed graphs. Our semi-streaming approach is also an insertion-only dynamic algorithm, attaining the first directed densest subgraph algorithm with $O(\log^2 n)$ worst-case update time while using sub-linear memory. We empirically evaluate our approaches in two ways. First, we illustrate that our single-pass semi-streaming algorithm performs much better than the theoretical guarantee. Specifically, its approximation on temporal datasets matches the $(2+\varepsilon)$-approximation of an $O(\log n)$-pass algorithm by Bahmani et al. (VLDB 2012). Second, we demonstrate that our MPC algorithm requires fewer rounds than prior work.

Poster
From Dormant to Deleted: Tamper-Resistant Unlearning Through Weight-Space Regularization

Shoaib Ahmed Siddiqui, Adrian Weller, David Krueger, Gintare Karolina Dziugaite, Michael Curtis Mozer, Eleni Triantafillou

展开摘要

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

Poster
Robust learning of halfspaces under log-concave marginals

Jane Lange, Arsen Vasilyan

展开摘要

We say that a classifier is $\text{\emph{adversarially robust}}$ to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified differently. The $\text{\emph{boundary volume}}$ is the probability that a point falls within distance $r$ of a point with a different label. This work studies the task of learning a hypothesis with small boundary volume, where the input is distributed as a subgaussian isotropic log-concave distribution over $\mathbb{R}^d$. Linear threshold functions are adversarially robust; they have boundary volume proportional to $r$. Such concept classes are efficiently learnable by polynomial regression, which produces a polynomial threshold function (PTF), but PTFs in general may have boundary volume $\Omega(1)$, even for $r \ll 1$. We give an algorithm that agnostically learns linear threshold functions and returns a classfier with boundary volume $O(r+\varepsilon)$ at radius of perturbation $r$. The time and sample complexity of $d^{\tilde{O}(1/\varepsilon^2)}$ matches the complexity of polynomial regression. Our algorithm augments the classic approach of polynomial regression with three additional steps:\ $\quad$ a) performing the $\ell_1$-error regression under $\ell_1$ noise sensitivity constraints,\ $\quad$ b) a structured partitioning and rounding step that returns a Boolean classifier with error $\mathrm{opt} + O(\varepsilon)$ and noise sensitivity $O(r+\varepsilon)$ simultaneously, and \ $\quad c)$ a local corrector that ``smooths'' a function with low noise sensitivity into a function that is adversarially robust.

Spotlight