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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  • Poster
    4,98085.7%

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An Evidence-Based Post-Hoc Adjustment Framework for Anomaly Detection Under Data Contamination

Sukanya Patra, Souhaib Ben Taieb

展开摘要

Unsupervised anomaly detection (AD) methods typically assume clean training data, yet real-world datasets often contain undetected or mislabeled anomalies, leading to significant performance degradation. Existing solutions require access to the training pipelines, data or prior knowledge of the proportions of anomalies in the data, limiting their real-world applicability. To address this challenge, we propose EPHAD, a simple yet effective test-time adaptation framework that updates the outputs of AD models trained on contaminated datasets using evidence gathered at test time. Our approach integrates the prior knowledge captured by the AD model trained on contaminated datasets with evidence derived from multimodal foundation models like Contrastive Language-Image Pre-training (CLIP), classical AD methods like the Latent Outlier Factor or domain-specific knowledge. We illustrate the intuition behind EPHAD using a synthetic toy example and validate its effectiveness through comprehensive experiments across eight visual AD datasets, twenty-six tabular AD datasets, and a real-world industrial AD dataset. Additionally, we conduct an ablation study to analyse hyperparameter influence and robustness to varying contamination levels, demonstrating the versatility and robustness of EPHAD across diverse AD models and evidence pairs. To ensure reproducibility, our code is publicly available at https://github.com/sukanyapatra1997/EPHAD.

Spotlight
REOBench: Benchmarking Robustness of Earth Observation Foundation Models

Xiang Li, Yong Tao, Siyuan Zhang, Siwei Liu, Zhitong Xiong, Chunbo Luo, Lu Liu, Mykola Pechenizkiy, Xiao Xiang Zhu, Tianjin Huang

展开摘要

Earth observation foundation models have shown strong generalization across multiple Earth observation tasks, but their robustness under real-world perturbations remains underexplored. To bridge this gap, we introduce REOBench, the first comprehensive benchmark for evaluating the robustness of Earth observation foundation models across six tasks and twelve types of image corruptions, including both appearance-based and geometric perturbations. To ensure realistic and fine-grained evaluation, our benchmark focuses on high-resolution optical remote sensing images, which are widely used in critical applications such as urban planning and disaster response. We conduct a systematic evaluation of a broad range of models trained using masked image modeling, contrastive learning, and vision-language pre-training paradigms. Our results reveal that (1) existing Earth observation foundation models experience significant performance degradation when exposed to input corruptions. (2) The severity of degradation varies across tasks, model architectures, backbone sizes, and types of corruption, with performance drop varying from less than 1% to over 25%. (3) Vision-language models show enhanced robustness, particularly in multimodal tasks. REOBench underscores the vulnerability of current Earth observation foundation models to real-world corruptions and provides actionable insights for developing more robust and reliable models.

Poster
PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling

Minju Jo, Woojin Cho, Uvini Balasuriya Mudiyanselage, Seungjun Lee, Noseong Park, Kookjin Lee

展开摘要

Scientific machine learning often involves representing complex solution fields that exhibit high-frequency features such as sharp transitions, fine-scale oscillations, and localized structures. While implicit neural representations (INRs) have shown promise for continuous function modeling, capturing such high-frequency behavior remains a challenge—especially when modeling multiple solution fields with a shared network. Prior work addressing spectral bias in INRs has primarily focused on single-instance settings, limiting scalability and generalization. In this work, we propose Global Fourier Modulation (GFM), a novel modulation technique that injects high-frequency information at each layer of the INR through Fourier-based reparameterization. This enables compact and accurate representation of multiple solution fields using low-dimensional latent vectors. Building upon GFM, we introduce PDEfuncta, a meta-learning framework designed to learn multi-modal solution fields and support generalization to new tasks. Through empirical studies on diverse scientific problems, we demonstrate that our method not only improves representational quality but also shows potential for forward and inverse inference tasks without the need for retraining.

Poster
SeerAttention: Self-distilled Attention Gating for Efficient Long-context Prefilling

Yizhao Gao, Zhichen Zeng, DaYou Du, Shijie Cao, Peiyuan Zhou, Jiaxing Qi, Junjie Lai, Hayden Kwok-Hay So, Ting Cao, Fan Yang, Mao Yang

展开摘要

Attention is the cornerstone of modern Large Language Models (LLMs). Yet its quadratic complexity hinders efficiency and scalability, especially for long-context processing. A promising approach is to leverage sparsity in attention. However, existing sparsity-based solutions predominantly rely on predefined patterns or heuristics at the attention head level, struggling to adapt dynamically to different contexts efficiently. We propose SeerAttention, a simple yet effective attention mechanism that directly learns the block-level attention sparsity from the LLM itself. Inspired by the gating mechanism in Mixture of Experts (MoE), SeerAttention augments the conventional attention with a **learnable gate** that **selectively activates important blocks** within the attention map. Specifically, the gate first pools the query (Q) and key (K) tensors along the sequence dimension and processes them through learnable linear layers. The resulting matrices are then multiplied together to produce the gating scores, which are used to predict block-level attention sparsity. Combined with our block-sparse FlashAttention kernel, SeerAttention can achieve significant speedup on GPUs. When applied to pre-trained LLMs, SeerAttention only requires training the gate parameters in a lightweight self-distillation manner, allowing rapid convergence. Our evaluation results demonstrate that SeerAttention achieves better model accuracy and lower latency for long-context pre-filling compared to prior methods. Code is available at: https://github.com/microsoft/SeerAttention.

Poster
VIKI‑R: Coordinating Embodied Multi-Agent Cooperation via Reinforcement Learning

Li Kang, Xiufeng Song, Heng Zhou, Yiran Qin, Jie Yang, Xiaohong Liu, Philip Torr, Lei Bai, Zhenfei Yin

展开摘要

Coordinating multiple embodied agents in dynamic environments remains a core challenge in artificial intelligence, requiring both perception-driven reasoning and scalable cooperation strategies. While recent works have leveraged large language models (LLMs) for multi-agent planning, a few have begun to explore vision-language models (VLMs) for visual reasoning. However, these VLM-based approaches remain limited in their support for diverse embodiment types. In this work, we introduce VIKI-Bench, the first hierarchical benchmark tailored for embodied multi-agent cooperation, featuring three structured levels: agent activation, task planning, and trajectory perception. VIKI-Bench includes diverse robot embodiments, multi-view visual observations, and structured supervision signals to evaluate reasoning grounded in visual inputs. To demonstrate the utility of VIKI-Bench, we propose VIKI-R, a two-stage framework that fine-tunes a pretrained vision-language model (VLM) using Chain-of-Thought annotated demonstrations, followed by reinforcement learning under multi-level reward signals. Our extensive experiments show that VIKI-R significantly outperforms baselines method across all task levels. Furthermore, we show that reinforcement learning enables the emergence of compositional cooperation patterns among heterogeneous agents. Together, VIKI-Bench and VIKI-R offer a unified testbed and method for advancing multi-agent, visual-driven cooperation in embodied AI systems.

Poster
Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Models

Huajie Tan, Yuheng Ji, Xiaoshuai Hao, Xiansheng Chen, Pengwei Wang, Zhongyuan Wang, Shanghang Zhang

展开摘要

Visual reasoning abilities play a crucial role in understanding complex multimodal data, advancing both domain-specific applications and artificial general intelligence (AGI). Existing methods enhance Vision-Language Models (VLMs) through Chain-of-Thought (CoT) supervised fine-tuning using meticulously annotated data. However, this approach may lead to overfitting and cognitive rigidity, limiting the model’s generalization ability under domain shifts and reducing real-world applicability. To overcome these limitations, we propose Reason-RFT, a two-stage reinforcement fine-tuning framework for visual reasoning. First, Supervised Fine-Tuning (SFT) with curated CoT data activates the reasoning potential of VLMs. This is followed by reinforcement learning based on Group Relative Policy Optimization (GRPO), which generates multiple reasoning-response pairs to enhance adaptability to domain shifts. To evaluate Reason-RFT, we reconstructed a comprehensive dataset covering visual counting, structural perception, and spatial transformation, serving as a benchmark for systematic assessment across three key dimensions. Experimental results highlight three advantages: (1) performance enhancement, with Reason-RFT achieving state-of-the-art results and outperforming both open-source and proprietary models; (2) generalization superiority, maintaining robust performance under domain shifts across various tasks; and (3) data efficiency, excelling in few-shot learning scenarios and surpassing full-dataset SFT baselines. Reason-RFT introduces a novel training paradigm for visual reasoning and marks a significant step forward in multimodal research.

Poster
URLs Help, Topics Guide: Understanding Metadata Utility in LLM Training

Dongyang Fan, Vinko Sabolčec, Martin Jaggi

展开摘要

Large Language Models (LLMs) are commonly pretrained on vast corpora of text without utilizing contextual metadata such as source, quality, or topic, leading to a context-free learning paradigm. While recent studies suggest that adding metadata like URL information as context (i.e., auxiliary inputs not used in the loss calculation) can improve training efficiency and downstream performance, they offer limited understanding of which types of metadata are truly effective and under what conditions. In this work, we conduct a systematic evaluation and find that not all metadata types contribute equally. Only URL context speeds up training, whereas quality scores and topic/format domain information offer no clear benefit. Furthermore, the improved downstream performances of URL conditioning emerge only when longer prompts are used at inference time. In addition, we demonstrate that context-aware pretraining enables more controllable generation than context-free pretraining, in a classifier-free guidance fashion. Although topic and format metadata do not accelerate training, they are effective for steering outputs, offering human-interpretable control over generation.

Poster
Embodied Crowd Counting

Runling Long, Yunlong Wang, Jia Wan, Xiang Deng, Xinting Zhu, Weili Guan, Antoni B. Chan, Liqiang Nie

展开摘要

Occlusion is one of the fundamental challenges in crowd counting. In the community, various data-driven approaches have been developed to address this issue, yet their effectiveness is limited. This is mainly because most existing crowd counting datasets on which the methods are trained are based on passive cameras, restricting their ability to fully sense the environment. Recently, embodied navigation methods have shown significant potential in precise object detection in interactive scenes. These methods incorporate active camera settings, holding promise in addressing the fundamental issues in crowd counting. However, most existing methods are designed for indoor navigation, showing unknown performance in analyzing complex object distribution in large-scale scenes, such as crowds. Besides, most existing embodied navigation datasets are indoor scenes with limited scale and object quantity, preventing them from being introduced into dense crowd analysis. Based on this, a novel task, Embodied Crowd Counting (ECC), is proposed to count the number of persons in a large-scale scene actively. We then build up an interactive simulator, the Embodied Crowd Counting Dataset (ECCD), which enables large-scale scenes and large object quantities. A prior probability distribution approximating a realistic crowd distribution is introduced to generate crowds. Then, a zero-shot navigation method (ZECC) is proposed as a baseline. This method contains an MLLM-driven coarse-to-fine navigation mechanism, enabling active Z-axis exploration, and a normal-line-based crowd distribution analysis method for fine counting. Experimental results show that the proposed method achieves the best trade-off between counting accuracy and navigation cost. Code can be found at https://github.com/longrunling/ECC?.

Poster
Generative Perception of Shape and Material from Differential Motion

Xinran Han, Ko Nishino, Todd Zickler

展开摘要

Perceiving the shape and material of an object from a single image is inherently ambiguous, especially when lighting is unknown and unconstrained. Despite this, humans can often disentangle shape and material, and when they are uncertain, they often move their head slightly or rotate the object to help resolve the ambiguities. Inspired by this behavior, we introduce a novel conditional denoising-diffusion model that generates samples of shape-and-material maps from a short video of an object undergoing differential motions. Our parameter-efficient architecture allows training directly in pixel-space, and it generates many disentangled attributes of an object simultaneously. Trained on a modest number of synthetic object-motion videos with supervision on shape and material, the model exhibits compelling emergent behavior: For static observations, it produces diverse, multimodal predictions of plausible shape-and-material maps that capture the inherent ambiguities; and when objects move, the distributions converge to more accurate explanations. The model also produces high-quality shape-and-material estimates for less ambiguous, real-world objects. By moving beyond single-view to continuous motion observations, and by using generative perception to capture visual ambiguities, our work suggests ways to improve visual reasoning in physically-embodied systems.

Poster
Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes

Hossein Zakerinia, Christoph H. Lampert

展开摘要

We present new fast-rate PAC-Bayesian generalization bounds for multi-task and meta-learning in the unbalanced setting, i.e. when the tasks have training sets of different sizes, as is typically the case in real-world scenarios. Previously, only standard-rate bounds were known for this situation, while fast-rate bounds were limited to the setting where all training sets are of equal size. Our new bounds are numerically computable as well as interpretable, and we demonstrate their flexibility in handling a number of cases where they give stronger guarantees than previous bounds. Besides the bounds themselves, we also make conceptual contributions: we demonstrate that the unbalanced multi-task setting has different statistical properties than the balanced situation, specifically that proofs from the balanced situation do not carry over to the unbalanced setting. Additionally, we shed light on the fact that the unbalanced situation allows two meaningful definitions of multi-task risk, depending on whether all tasks should be considered equally important or if sample-rich tasks should receive more weight than sample-poor ones.

Poster
Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry

Antoine Collas, Ce Ju, Nicolas Salvy, Bertrand Thirion

展开摘要

Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in constrained spaces—such as the set of symmetric positive definite or correlation matrices—that can be modeled as Riemannian manifolds. However, using Riemannian tools typically requires redefining core operations (geodesics, norms, integration), making generative modeling computationally inefficient. In this work, we propose DiffeoCFM, an approach that enables conditional flow matching (CFM) on matrix manifolds by exploiting pullback metrics induced by global diffeomorphisms on Euclidean spaces. We show that Riemannian CFM with such metrics is equivalent to applying standard CFM after data transformation. This equivalence allows efficient vector field learning, and fast sampling with standard ODE solvers. We instantiate DiffeoCFM with two different settings: the matrix logarithm for covariance matrices and the normalized Cholesky decomposition for correlation matrices. We evaluate DiffeoCFM on three large-scale fMRI datasets with more than $4600$ scans from $2800$ subjects (ADNI, ABIDE, OASIS‑3) and two EEG motor imagery datasets with over $30000$ trials from $26$ subjects (BNCI2014‑002 and BNCI2015‑001). It enables fast training and achieves state-of-the-art performance, all while preserving manifold constraints. Code: https://github.com/antoinecollas/DiffeoCFM

Poster
What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimization

Omar Bennouna, Amine Bennouna, Saurabh Amin, Asuman E. Ozdaglar

展开摘要

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions---offering a principled foundation for task-aware data selection.

Poster
VR-Drive: Viewpoint-Robust End-to-End Driving with Feed-Forward 3D Gaussian Splatting

Hoonhee Cho, Jae-Young Kang, Giwon Lee, Hyemin Yang, Heejun Park, Seokwoo Jung, Kuk-Jin Yoon

展开摘要

End-to-end autonomous driving (E2E-AD) has emerged as a promising paradigm that unifies perception, prediction, and planning into a holistic, data-driven framework. However, achieving robustness to varying camera viewpoints, a common real-world challenge due to diverse vehicle configurations, remains an open problem. In this work, we propose VR-Drive, a novel E2E-AD framework that addresses viewpoint generalization by jointly learning 3D scene reconstruction as an auxiliary task to enable planning-aware view synthesis. Unlike prior scene-specific synthesis approaches, VR-Drive adopts a feed-forward inference strategy that supports online training-time augmentation from sparse views without additional annotations. To further improve viewpoint consistency, we introduce a viewpoint-mixed memory bank that facilitates temporal interaction across multiple viewpoints and a viewpoint-consistent distillation strategy that transfers knowledge from original to synthesized views. Trained in a fully end-to-end manner, VR-Drive effectively mitigates synthesis-induced noise and improves planning under viewpoint shifts. In addition, we release a new benchmark dataset to evaluate E2E-AD performance under novel camera viewpoints, enabling comprehensive analysis. Our results demonstrate that VR-Drive is a scalable and robust solution for the real-world deployment of end-to-end autonomous driving systems.

Poster
PMLF: A Physics-Guided Multiscale Loss Framework for Structurally Heterogeneous Time Series

Xinghong Chen, Weilin Wu, Kunping Yang, Guannan Chen

展开摘要

Forecasting real-world time series requires modeling both short-term fluctuations and long-term evolutions, as these signals typically exhibit multiscale temporal structures. A core challenge lies in reconciling such dynamics: high-frequency seasonality demands local precision, while low-frequency trends require global robustness. However, most existing methods adopt a unified loss function across all temporal components, overlooking their structural differences. This misalignment often causes overfitting to seasonal noise or underfitting of long-term trends, leading to suboptimal forecasting performance. To address this issue, we propose a Physics-guided Multiscale Loss Framework (PMLF) that decomposes time series into seasonal and trend components and assigns component-specific objectives grounded in the distinct energy responses of oscillatory and drift dynamics. Specifically, we assign a quadratic loss to seasonal components, reflecting the quadratic potential energy profile of molecular vibration, while a logarithmic loss is used for trend components to capture the sublinear energy profile of molecular drift under sustained external forces. Furthermore, we introduce a softmax-based strategy that adaptively balances the unequal energetic responses of these two physical processes. Experiments on different public benchmarks show that PMLF improves the performance of diverse baselines, demonstrating the effectiveness of physics-guided loss design in modeling structural heterogeneity in time series forecasting.

Poster
Markov Persuasion Processes: Learning to Persuade From Scratch

Francesco Bacchiocchi, Francesco Emanuele Stradi, Matteo Castiglioni, Alberto Marchesi, Nicola Gatti

展开摘要

In Bayesian persuasion, an informed sender strategically discloses information to a receiver so as to persuade them to undertake desirable actions. Recently, Markov persuasion processes (MPPs) have been introduced to capture sequential scenarios where a sender faces a stream of myopic receivers in a Markovian environment. The MPPs studied so far in the literature suffer from issues that prevent them from being fully operational in practice, e.g., they assume that the sender knows receivers' rewards. We fix such issues by addressing MPPs where the sender has no knowledge about the environment. We design a learning algorithm for the sender, working with partial feedback. We prove that its regret with respect to an optimal information-disclosure policy grows sublinearly in the number of episodes, as it is the case for the loss in persuasiveness cumulated while learning. Moreover, we provide lower bounds for our setting matching the guarantees of our algorithm.

Poster
Space Group Equivariant Crystal Diffusion

Rees Chang, Angela Pak, Alex Guerra, Ni Zhan, Nick Richardson, Elif Ertekin, Ryan P Adams

展开摘要

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiDiff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.

Poster
The Good, the Bad and the Ugly: Meta-Analysis of Watermarks, Transferable Attacks and Adversarial Defenses

Grzegorz Gluch, Berkant Turan, Sai Ganesh Nagarajan, Sebastian Pokutta

展开摘要

We formalize and analyze the trade-off between backdoor-based watermarks and adversarial defenses, framing it as an interactive protocol between a verifier and a prover. While previous works have primarily focused on this trade-off, our analysis extends it by identifying transferable attacks as a third, counterintuitive but necessary option. Our main result shows that for all learning tasks, at least one of the three exists: a _watermark_, an _adversarial defense_, or a _transferable attack_. By transferable attack, we refer to an efficient algorithm that generates queries indistinguishable from the data distribution and capable of fooling _all_ efficient defenders. Using cryptographic techniques, specifically fully homomorphic encryption, we construct a transferable attack and prove its necessity in this trade-off. Finally, we show that tasks of bounded VC-dimension allow adversarial defenses against all attackers, while a subclass allows watermarks secure against fast adversaries.

Poster
Neural Fractional Attention Differential Equations

Qiyu Kang, Wenjun Cui, Xuhao Li, Yuxin Ma, Xueyang Fu, Wee Peng Tay, Yidong Li, Zheng-Jun Zha

展开摘要

The integration of differential equations with neural networks has created powerful tools for modeling complex dynamics effectively across diverse machine learning applications. While standard integer-order neural ordinary differential equations (ODEs) have shown considerable success, they are limited in their capacity to model systems with memory effects and historical dependencies. Fractional calculus offers a mathematical framework capable of addressing this limitation, yet most current fractional neural networks use static memory weightings that cannot adapt to input-specific contextual requirements. This paper proposes a generalized neural Fractional Attention Differential Equation (FADE), which combines the memory-retention capabilities of fractional calculus with contextual learnable attention mechanisms. Our approach replaces fixed kernel functions in fractional operators with neural attention kernels that adaptively weight historical states based on their contextual relevance to current predictions. This allows our framework to selectively emphasize important temporal dependencies while filtering less relevant historical information. Our theoretical analysis establishes solution boundedness, problem well-posedness, and numerical equation solver convergence properties of the proposed model. Furthermore, through extensive evaluation on tasks such as fluid flow, graph learning problems and spatio-temporal traffic flow forecasting, we demonstrate that our adaptive attention-based fractional framework outperforms both integer-order neural ODE models and existing fractional approaches. The results confirm that our framework provides superior modeling capacity for complex dynamics with varying temporal dependencies. The code is available at \url{https://github.com/cuiwjTech/NeurIPS2025_FADE}.

Poster
BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning

Xuechen Zhang, Zijian Huang, Yingcong Li, Chenshun Ni, Jiasi Chen, Samet Oymak

展开摘要

Small language models (SLMs) struggle to learn complex reasoning behaviors, especially when high-quality traces are scarce or difficult to learn from. A typical approach for training such models combines a supervised fine-tuning (SFT) stage, often to distill reasoning capabilities from a larger model, followed by a reinforcement learning (RL) stage such as Group Relative Policy Optimization (GRPO). In this paper, we investigate the fundamental limitations of this SFT + RL paradigm and propose methods to overcome them. Using a toy student-expert model over Markov chains, we demonstrate that the SFT + RL strategy can fail completely when (1) the expert's traces are too difficult for the small model to express, or (2) the small model's initialization achieves exponentially sparse rewards as task complexity grows. To address these, we introduce BREAD, a GRPO variant that bridges SFT and RL via partial expert guidance and branch rollouts. When self-generated traces fail, BREAD adaptively inserts short expert prefixes/hints, allowing the small model to complete the rest of the reasoning path, and ensuring that each update includes at least one successful trace. This mechanism both densifies the reward signal and induces a natural learning curriculum. BREAD requires fewer than 40\% of ground-truth traces, consistently outperforming standard GRPO while speeding up the training by about 3$\times$. Importantly, we find that BREAD helps the model solve problems that are otherwise unsolvable by the SFT + RL strategy, highlighting how branch rollouts and expert guidance can aid SLM reasoning.

Poster
Attention Mechanism, Max-Affine Partition, and Universal Approximation

Hude Liu, Jerry Yao-Chieh Hu, Zhao Song, Han Liu

展开摘要

We establish the universal approximation capability of single-layer, single-head self- and cross-attention mechanisms with minimal attached structures. Our key insight is to interpret single-head attention as an input domain-partition mechanism that assigns distinct values to subregions. This allows us to engineer the attention weights such that this assignment imitates the target function. Building on this, we prove that a single self-attention layer, preceded by sum-of-linear transformations, is capable of approximating any continuous function on a compact domain under the $L_\infty$-norm. Furthermore, we extend this construction to approximate any Lebesgue integrable function under $L_p$-norm for $1\leq p <\infty$. Lastly, we also extend our techniques and show that, for the first time, single-head cross-attention achieves the same universal approximation guarantees.

Poster