NeurIPS 2025 Papers

Conference on Neural Information Processing Systems

Decision breakdown

5,812papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    931.6%
  • Spotlight
    73912.7%
  • Poster
    4,98085.7%

Browse all papers

Uncover Governing Law of Pathology Propagation Mechanism Through A Mean-Field Game

Tingting Dan, Zhihao Fan, Guorong Wu

Expand abstract

Alzheimer’s disease (AD) is marked by cognitive decline along with the widespread of tau aggregates across the brain cortex. Due to the challenges of imaging pathology spreading flows *in vivo*, however, quantitative analysis on the cortical pathways of tau propagation and its interaction with the cascade of amyloid-beta (A$\beta$) plaques lags behind the experimental insights of underlying pathophysiological mechanisms. To address this challenge, we present a physics-informed neural network, empowered by mean-field theory, to uncover the biologically meaningful spreading pathways of tau aggregates between two longitudinal snapshots. Following the notion of `prion-like' mechanism in AD, we first formulate the dynamics of tau propagation as a mean-field game (MFG), where the spread of tau aggregate at each location (aka. agent) depends on the collective behavior of the surrounding agents as well as the potential field formed by amyloid burden. Given the governing equation of propagation dynamics, MFG reaches an equilibrium that allows us to model the evolution of tau aggregates as an optimal transport with the lowest cost in *Wasserstein* space. By leveraging the variational primal-dual structure in MFG, we propose a *Wasserstein*-1 Lagrangian generative adversarial network (GAN), in which a Lipschitz critic seeks the appropriate transport cost at the population level and a generator parameterizes the flow fields of optimal transport across individuals. Additionally, we incorporate a symbolic regression module to derive an explicit formulation capturing the A$\beta$-tau crosstalk. Experimental results on public neuroimaging datasets demonstrate that our explainable deep model not only yields precise and reliable predictions of future tau progression for unseen new subjects but also provides a new window to uncover new understanding of pathology propagation in AD through learning-based approaches.

Poster
VLMLight: Safety-Critical Traffic Signal Control via Vision-Language Meta-Control and Dual-Branch Reasoning Architecture

Maonan Wang, Yirong Chen, Aoyu Pang, Yuxin Cai, Chung Shue Chen, Yuheng KAN, Man On Pun

Expand abstract

Traffic signal control (TSC) is a core challenge in urban mobility, where real-time decisions must balance efficiency and safety. Existing methods—ranging from rule-based heuristics to reinforcement learning (RL)—often struggle to generalize to complex, dynamic, and safety-critical scenarios. We introduce \textbf{VLMLight}, a novel TSC framework that integrates vision-language meta-control with dual-branch reasoning. At the core of VLMLight is the first image-based traffic simulator that enables multi-view visual perception at intersections, allowing policies to reason over rich cues such as vehicle type, motion, and spatial density. A large language model (LLM) serves as a safety-prioritized meta-controller, selecting between a fast RL policy for routine traffic and a structured reasoning branch for critical cases. In the latter, multiple LLM agents collaborate to assess traffic phases, prioritize emergency vehicles, and verify rule compliance. Experiments show that VLMLight reduces waiting times for emergency vehicles by up to 65% over RL-only systems, while preserving real-time performance in standard conditions with less than 1% degradation. VLMLight offers a scalable, interpretable, and safety-aware solution for next-generation traffic signal control.

Poster
E-MoFlow: Learning Egomotion and Optical Flow from Event Data via Implicit Regularization

Wenpu Li, Bangyan Liao, Yi Zhou, Qi Xu, Pian Wan, Peidong Liu

Expand abstract

The estimation of optical flow and 6-DoF ego-motion—two fundamental tasks in 3-D vision—has typically been addressed independently. For neuromorphic vision (e.g., event cameras), however, the lack of robust data association makes solving the two problems separately an ill-posed challenge, especially in the absence of supervision via ground truth. Existing works mitigate this ill-posedness by either enforcing the smoothness of the flow field via an explicit variational regularizer or leveraging explicit structure-and-motion priors in the parametrization to improve event alignment. The former notably introduces bias in results and computational overhead, while the latter—which parametrizes the optical flow in terms of the scene depth and the camera motion—often converges to suboptimal local minima. To address these issues, we propose an unsupervised pipeline that jointly optimizes egomotion and flow via implicit spatial-temporal and geometric regularization. First, by modeling camera's egomotion as a continuous spline and optical flow as an implicit neural representation, our method inherently embeds spatial-temporal coherence through inductive biases. Second, we incorporate structure-and-motion priors through differential geometric constraints, bypassing explicit depth estimation while maintaining rigorous geometric consistency. As a result, our framework (called \textbf{E-MoFlow}) unifies egomotion and optical flow estimation via implicit regularization under a fully unsupervised paradigm. Experiments demonstrate its versatility to general 6-DoF motion scenarios, achieving state-of-the-art performance among unsupervised methods and competitive even with supervised approaches. Code will be released upon acceptance.

Poster
BrainMoE: Cognition Joint Embedding via Mixture-of-Expert Towards Robust Brain Foundation Model

Ziquan Wei, Tingting Dan, Tianlong Chen, Guorong Wu

Expand abstract

Given the large scale of public functional Magnetic Resonance Imaging (fMRI), e.g., UK Biobank (UKB) and Human Connectome Projects (HCP), brain foundation models are emerging. Although the amount of samples under rich environmental variables is unprecedented, existing brain foundation models learn from fMRI derived from a narrow range of cognitive states stimulated by similar environments, causing the limited robustness demonstrated in various applications and datasets acquired with different pipelines and limited sample size. By capitalizing on the variety of cognitive status as subjects performing explicit tasks, we present the mixture of brain experts, namely BrainMoE, pre-training on tasking fMRI with rich behavioral tasks in addition to resting fMRI for a robust brain foundation model. Brain experts are designed to produce embeddings for different behavioral tasks related to cognition. Afterward, these cognition embeddings are mixed by a cognition adapter via cross-attention so that BrainMoE can handle orthogonal embeddings and be robust on those boutique downstream datasets. We have pre-trained two existing self-regressive architectures and one new supervised architecture as brain experts on 68,251 fMRI scans among UKB and HCP, containing 12 different cognitive states. Then, BrainMoE is evaluated on a variety of applications, including sex, age prediction, human behavior recognition, disease early diagnosis of Autism, Parkinson's disease, Alzheimer's disease, and Schizophrenia, and fMRI-EEG multimodal applications, where promising results in eight datasets from three different pipelines indicate great potential to facilitate current neuroimaging applications in clinical routines.

Poster
Quantifying Uncertainty in the Presence of Distribution Shifts

Yuli Slavutsky, David Blei

Expand abstract

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially when test-time covariates differ from those seen during training, as occurs with selection bias or shifts over time. To address this, we propose a Bayesian framework for uncertainty estimation that explicitly accounts for covariate shifts. Unlike conventional approaches that rely on fixed priors, a key idea of our method is an adaptive prior, conditioned on both training and new covariates. This prior naturally increases uncertainty for inputs that lie far from the training distribution in regions where predictive performance is likely to degrade. To efficiently approximate the resulting posterior predictive distribution, we employ amortized variational inference. Finally, we construct synthetic environments by drawing small bootstrap samples from the training data, simulating a range of plausible covariate shifts using only the original dataset. We evaluate our method on both synthetic and real-world data, demonstrating that it yields substantially improved uncertainty estimates under distribution shift compared to existing approaches.

Poster
Spik-NeRF: Spiking Neural Networks for Neural Radiance Fields

Gang Wan, Qinlong Lan, LiZihan, Huimin Wang, Wu Yitian, wang zhen, Wanhua Li, Yufei Guo

Expand abstract

Spiking Neural Networks (SNNs), as a biologically inspired neural network architecture, have garnered significant attention due to their exceptional energy efficiency and increasing potential for various applications. In this work, we extend the use of SNNs to neural rendering tasks and introduce Spik-NeRF (Spiking Neural Radiance Fields). We observe that the binary spike activation map of traditional SNNs lacks sufficient information capacity, leading to information loss and a subsequent decline in the performance of spiking neural rendering models. To address this limitation, we propose the use of ternary spike neurons, which enhance the information-carrying capacity in the spiking neural rendering model. With ternary spike neurons, Spik-NeRF achieves performance that is on par with, or nearly identical to, traditional ANN-based rendering models. Additionally, we present a re-parameterization technique for inference that allows Spik-NeRF with ternary spike neurons to retain the event-driven, multiplication-free advantages typical of binary spike neurons. Furthermore, to further boost the performance of Spik-NeRF, we employ a distillation method, using an ANN-based NeRF to guide the training of our Spik-NeRF model, which is more compatible with the ternary neurons compared to the standard binary neurons. We evaluate Spik-NeRF on both realistic and synthetic scenes, and the experimental results demonstrate that Spik-NeRF achieves rendering performance comparable to ANN-based NeRF models.

Poster
Reproducing Kernel Banach Space Models for Neural Networks with Application to Rademacher Complexity Analysis

Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh

Expand abstract

This paper explores the use of Hermite transform based reproducing kernel Banach space methods to construct exact or un-approximated models of feedforward neural networks of arbitrary width, depth and topology, including ResNet and Transformers networks, assuming only a feedforward topology, finite energy activations and finite (spectral-) norm weights and biases. Using this model, two straightforward but surprisingly tight bounds on Rademacher complexity are derived, precisely (1) a general bound that is width-independent and scales exponentially with depth; and (2) a width- and depth-independent bound for networks with appropriately constrained (below threshold) weights and biases.

Poster
Parsimonious Predictions for Strategyproof Scheduling

Richard Cole, Anupam Gupta, Pranav Jangir

Expand abstract

We consider the problem of scheduling $m$ jobs on $n$ unrelated strategic machines to minimize the maximum load of any machine, but the machines are strategic and may misreport processing times to minimize their own load. The pioneering work of Nisan and Ronen gave an $n$-approximate deterministic strategyproof mechanism for this setting, and this was recently shown to be best possible by the breakthrough results of Christodoulou et al. This large approxation guarantee begs the question: how can we avoid these large worst-case results. In this work, we use the powerful framework of algorithms with (machine-learned) predictions to bypass these strong impossibility results. We show how we can predict $O(m+n)$ values to obtain a deterministic strategyproof algorithm whose makespan is within a constant factor of the optimal makespan when the predictions are correct, and $O(n)$ times the optimum no matter how poor the predictions are.

Poster
SceneSplat++: A Large Dataset and Comprehensive Benchmark for Language Gaussian Splatting

Mengjiao Ma, Qi Ma, Yue Li, Jiahuan Cheng, Runyi Yang, Bin Ren, Nikola Popovic, Mingqiang Wei, Nicu Sebe, Ender Konukoglu, Luc Van Gool, Theo Gevers, Martin R. Oswald, Danda Pani Paudel

Expand abstract

3D Gaussian Splatting (3DGS) serves as a highly performant and efficient encoding of scene geometry, appearance, and semantics. Moreover, grounding language in 3D scenes has proven to be an effective strategy for 3D scene understanding. Current Language Gaussian Splatting line of work fall into three main groups: (i) per-scene optimization-based, (ii) per-scene optimization-free, and (iii) generalizable approach. However, most of them are evaluated only on rendered 2D views of a handful of scenes and viewpoints close to the training views, limiting ability and insight into holistic 3D understanding. To address this gap, we propose the first large-scale benchmark that systematically assesses these three groups of methods directly in 3D space, evaluating on 1060 scenes across three indoor datasets and one outdoor dataset. Benchmark results demonstrate a clear advantage of the generalizable paradigm, particularly in relaxing the scene-specific limitation, enabling fast feed-forward inference on novel scenes, and achieving superior segmentation performance. We further introduce SceneSplat-49K -- a carefully curated 3DGS dataset comprising of around 49K diverse indoor and outdoor scenes trained from multiple sources, with which we demonstrate generalizable approach could harness strong data priors. Our codes, benchmark, and datasets are available.

Poster
Model-Guided Dual-Role Alignment for High-Fidelity Open-Domain Video-to-Audio Generation

Kang Zhang, Trung X. Pham, Suyeon Lee, Axi Niu, Arda Senocak, Joon Son Chung

Expand abstract

We present MGAudio, a novel flow-based framework for open-domain video-to-audio generation, which introduces model-guided dual-role alignment as a central design principle. Unlike prior approaches that rely on classifier-based or classifier-free guidance, MGAudio enables the generative model to guide itself through a dedicated training objective designed for video-conditioned audio generation. The framework integrates three main components: (1) a scalable flow-based Transformer denoiser, (2) a dual-role alignment mechanism where the audio-visual encoder serves both as a conditioning module and as a feature aligner to improve generation quality, and (3) a model-guided objective that enhances cross-modal coherence and audio realism. MGAudio achieves state-of-the-art performance on VGGSound, reducing FAD to 0.40, substantially surpassing the best classifier-free guidance baselines, and consistently outperforms existing methods across FD, IS, and alignment metrics. It also generalizes well to the challenging UnAV-100 benchmark. These results highlight model-guided dual-role alignment as a powerful and scalable paradigm for conditional video-to-audio generation. Code is available at: https://github.com/pantheon5100/mgaudio

Poster
ALTER: All-in-One Layer Pruning and Temporal Expert Routing for Efficient Diffusion Generation

Xiaomeng Yang, LEI LU, Qihui Fan, Changdi Yang, Juyi Lin, Yanzhi Wang, Xuan Zhang, Shangqian Gao

Expand abstract

Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images. However, their iterative denoising process results in significant computational overhead during inference, limiting their practical deployment in resource-constrained environments. Existing acceleration methods often adopt uniform strategies that fail to capture the temporal variations during diffusion generation, while the commonly adopted sequential $\textit{pruning-then-fine-tuning strategy}$ suffers from sub-optimality due to the misalignment between pruning decisions made on pretrained weights and the model’s final parameters. To address these limitations, we introduce $\textbf{ALTER}$: $\textbf{A}$ll-in-One $\textbf{L}$ayer Pruning and $\textbf{T}$emporal $\textbf{E}$xpoert $\textbf{R}$outing, a unified framework that transforms diffusion models into a mixture of efficient temporal experts. ALTER achieves a single-stage optimization that unifies layer pruning, expert routing, and model fine-tuning by employing a trainable hypernetwork, which dynamically generates layer pruning decisions and manages timestep routing to specialized, pruned expert sub-networks throughout the ongoing fine-tuning of the UNet. This unified co-optimization strategy enables significant efficiency gains while preserving high generative quality. Specifically, ALTER achieves same-level visual fidelity to the original 50-step Stable Diffusion v2.1 model while utilizing only 25.9\% of its total MACs with just 20 inference steps and delivering a 3.64$\times$ speedup through 35\% sparsity.

Poster
Who You Are Matters: Bridging Interests and Social Roles via LLM-Enhanced Logic Recommendation

Qing Yu, Xiaobei Wang, Shuchang Liu, cheng.feng, Xiaoyu Yang, Xueliang Wang, Chang Meng, Shanshan Wu, HailanYang, Bin Wen, Huihui Xiao, Xiang Li, Fan Yang, Xiaoqiang Feng, Lantao Hu, Han Li, Kun Gai, Lixin Zou

Expand abstract

Recommender systems filter contents/items valuable to users by inferring preferences from user features and historical behaviors. Mainstream approaches follow the learning-to-rank paradigm, which focus on discovering and modeling item topics (e.g., categories), and capturing user preferences on these topics based on historical interactions. However, this paradigm often neglects the modeling of user characteristics and their social roles, which are logical confounders influencing the correlated interest and user preference transition. To bridge this gap, we introduce the user role identification task and the behavioral logic modeling task that aim to explicitly model user roles and learn the logical relations between item topics and user social roles. We show that it is possible to explicitly solve these tasks through an efficient integration framework of Large Language Model (LLM) and recommendation systems, for which we propose TagCF. On the one hand, TagCF exploits the (Multi-modal) LLM's world knowledge and logic inference ability to extract realistic tag-based virtual logic graphs that reveal dynamic and expressive knowledge of users, refining our understanding of user behaviors. On the other hand, TagCF presents empirically effective integration modules that take advantage of the extracted tag-logic information, augmenting the recommendation performance. We conduct both online experiments and offline experiments with industrial and public datasets as verification of TagCF's effectiveness, and we empirically show that the user role modeling strategy is potentially a better choice than the modeling of item topics. Additionally, we provide evidence that the extracted logic graphs are empirically a general and transferable knowledge that can benefit a wide range of recommendation tasks. Our code is available in https://github.com/Code2Q/TagCF.

Poster
KL Penalty Control via Perturbation for Direct Preference Optimization

Sangkyu Lee, Janghoon Han, Hosung Song, Stanley Jungkyu Choi, Honglak Lee, Youngjae Yu

Expand abstract

Direct Preference Optimization (DPO) demonstrates the advantage of aligning a large language model with human preference using only an offline dataset. However, DPO has the limitation that the KL penalty, which prevents excessive deviation from the reference model, is static throughout the training process. Several methods claim to change this static KL penalty of DPO into a dynamic one, but no approach can adaptively assign different KL penalties for each preference pair. In this paper, we propose $\varepsilon$-Direct Preference Optimization ($\varepsilon$-DPO), which allows adaptive control of the KL penalty strength $\beta$ for each preference pair. Specifically, $\varepsilon$-DPO adaptively controls $\beta$ for each preference pair based on the monotonicity of logits as a preference model under the perturbation of $\beta$ during training. This is equivalent to adjusting the KL penalty by checking whether the change in training-time temperature can lead to better preference confidence as preference models by simply reusing the logit of the current policy and the reference policy. Experimental results show that the simple criterion of $\varepsilon$-DPO for KL penalty relaxation significantly improves DPO compared to most existing direct alignment algorithms on general chatbot benchmarks and reveal that this KL penalty control criterion can reflect confusion as a preference model and provide an efficient KL trade-off, highlighting the significance of instance-level adaptive KL penalty control in DPO.

Poster
Uncertainty-Sensitive Privileged Learning

Fan-Ming Luo, Lei Yuan, Yang Yu

Expand abstract

Privileged learning efficiently tackles high-dimensional, partially observable decision-making problems by first training a privileged policy (PP) on low-dimensional privileged observations, and then deriving a deployment policy (DP) either by imitating the PP or coupling it with an observation encoder. However, since the DP relies on local and partial observations, a behavioral divergence (BD) often emerges between the DP and the PP, ultimately degrading deployment performance. A promising strategy is to train a PP to learn the optimal behaviors attainable under the DP’s observation space by applying reward penalties in regions with large BD. However, producing these behaviors is challenging for the PP because they rely on the DP’s information-gathering progress, which is invisible to the PP. In this paper, we quantify the DP’s information-gathering progress by estimating the prediction uncertainty of privileged observations reconstructed from partial observations, and accordingly propose the framework of Uncertainty-Sensitive Privileged Learning (USPL). USPL feeds this uncertainty estimation to the PP and combines reward transformation with privileged-observation blurring, driving the PP to choose actions that actively reduce uncertainty and thus gather the necessary information. Experiments across nine tasks demonstrate that USPL significantly reduces the behavioral discrepancies, achieving superior deployment performance compared to baselines. Additional visualization results show that the DP accurately quantifies its uncertainty, and the PP effectively adapts to uncertainty variations. Code is available at https://github.com/FanmingL/USPL.

Poster
Fairshare Data Pricing via Data Valuation for Large Language Models

Luyang Zhang, Cathy Jiao, Beibei Li, Chenyan Xiong

Expand abstract

Training data is the backbone of large language models (LLMs), yet today’s data markets often operate under exploitative pricing -- sourcing data from marginalized groups with little pay or recognition. This paper introduces a theoretical framework for LLM data markets, modeling the strategic interactions between buyers (LLM builders) and sellers (human annotators). We begin with theoretical and empirical analysis showing how exploitative pricing drives high-quality sellers out of the market, degrading data quality and long-term model performance. Then we introduce fairshare, a pricing mechanism grounded in data valuation that quantifies each data’s contribution. It aligns incentives by sustaining seller participation and optimizing utility for both buyers and sellers. Theoretically, we show that fairshare yields mutually optimal outcomes: maximizing long-term buyer utility and seller profit while sustaining market participation. Empirically when training open-source LLMs on complex NLP tasks, including math problems, medical diagnosis, and physical reasoning, fairshare boosts seller earnings and ensures a stable supply of high-quality data, while improving buyers’ performance-per-dollar and long-term welfare. Our findings offer a concrete path toward fair, transparent, and economically sustainable data markets for LLM. Our code will be open sourced.

Poster
Distributional Autoencoders Know the Score

Andrej Leban

Expand abstract

The Distributional Principal Autoencoder (DPA) combines distributionally correct reconstruction with principal-component-like interpretability of the encodings. In this work, we provide exact theoretical guarantees on both fronts. First, we derive a closed-form relation linking each optimal level-set geometry to the data-distribution score. This result explains DPA's empirical ability to disentangle factors of variation of the data, as well as allows the score to be recovered directly from samples. When the data follows the Boltzmann distribution, we demonstrate that this relation yields an approximation of the minimum free-energy path for the Müller–Brown potential in a single fit. Second, we prove that if the data lies on a manifold that can be approximated by the encoder, latent components beyond the manifold dimension are conditionally independent of the data distribution - carrying no additional information - and thus reveal the intrinsic dimension. Together, these results show that a single model can learn the data distribution and its intrinsic dimension with exact guarantees simultaneously, unifying two longstanding goals of unsupervised learning.

Poster
CLIPGaussian: Universal and Multimodal Style Transfer Based on Gaussian Splatting

Kornel Howil, Joanna Waczynska, Joanna Waczyńska, Piotr Borycki, Tadeusz Dziarmaga, Marcin Mazur, Przemysław Spurek

Expand abstract

Gaussian Splatting (GS) has recently emerged as an efficient representation for rendering 3D scenes from 2D images and has been extended to images, videos, and dynamic 4D content. However, applying style transfer to GS-based representations, especially beyond simple color changes, remains challenging. In this work, we introduce CLIPGaussian, the first unified style transfer framework that supports text- and image-guided stylization across multiple modalities: 2D images, videos, 3D objects, and 4D scenes. Our method operates directly on Gaussian primitives and integrates into existing GS pipelines as a plug-in module, without requiring large generative models or retraining from scratch. The CLIPGaussian approach enables joint optimization of color and geometry in 3D and 4D settings, and achieves temporal coherence in videos, while preserving the model size. We demonstrate superior style fidelity and consistency across all tasks, validating CLIPGaussian as a universal and efficient solution for multimodal style transfer.

Poster
Binary Quadratic Quantization: Beyond First-Order Quantization for Real-Valued Matrix Compression

Kyo Kuroki, Yasuyuki Okoshi, Thiem Van Chu, Kazushi Kawamura, Masato Motomura

Expand abstract

This paper proposes a novel matrix quantization method, Binary Quadratic Quan- tization (BQQ). In contrast to conventional first-order quantization approaches— such as uniform quantization and binary coding quantization—that approximate real-valued matrices via linear combinations of binary bases, BQQ leverages the expressive power of binary quadratic expressions while maintaining an extremely compact data format. We validate our approach with two experiments: a matrix compression benchmark and post-training quantization (PTQ) on pretrained Vision Transformer-based models. Experimental results demonstrate that BQQ consistently achieves a superior trade-off between memory efficiency and reconstruction error than conventional methods for compressing diverse matrix data. It also delivers strong PTQ performance, even though we neither target state-of-the-art PTQ accuracy under tight memory constraints nor rely on PTQ-specific binary matrix optimization. For example, our proposed method outperforms the state-of- the-art PTQ method by up to 2.2% and 59.1% on the ImageNet dataset under the calibration-based and data-free scenarios, respectively, with quantization equivalent to 2 bits. These findings highlight the surprising effectiveness of binary quadratic expressions for efficient matrix approximation and neural network compression.

Poster
Asymptotics of SGD in Sequence-Single Index Models and Single-Layer Attention Networks

Luca Arnaboldi, Bruno Loureiro, Ludovic STEPHAN, Florent Krzakala, Lenka Zdeborova

Expand abstract

We study the dynamics of stochastic gradient descent (SGD) for a class of sequence models termed Sequence Single-Index (SSI) models, where the target depends on a single direction in input space applied to a sequence of tokens. This setting generalizes classical single-index models to the sequential domain, encompassing simplified one-layer attention architectures. We derive a closed-form expression for the population loss in terms of a pair of sufficient statistics capturing semantic and positional alignment, and characterize the induced high-dimensional SGD dynamics for these coordinates. Our analysis reveals two distinct training phases: escape from uninformative initialization and alignment with the target subspace, and demonstrates how the sequence length and positional encoding influence convergence speed and learning trajectories. These results provide a rigorous and interpretable foundation for understanding how sequential structure in data can be beneficial for learning with attention-based models.

Poster
Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensions

Yizhou Xu, Florent Krzakala, Lenka Zdeborova, Lenka Zdeborová

Expand abstract

The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well understood in cases that essentially reduce to singular value decomposition of the data. Here, we consider the limit of a large dimension of the input space and a constant number of hidden units. In this limit, we simplify the standard RBM training objective into a form that is equivalent to the multi-index model with non-separable regularization. This opens a path to analyze training of the RBM using methods that are established for multi-index models, such as Approximate Message Passing (AMP) and its state evolution, and the analysis of Gradient Descent (GD) via the dynamical mean-field theory. We then give rigorous asymptotics of the training dynamics of RBMs on data generated by the spiked covariance model as a prototype of a structure suitable for unsupervised learning. We show in particular that RBMs reach the optimal computational weak recovery threshold, aligning with the Baik-Ben Arous-Péché (BBP) transition, in the spiked covariance model.

Poster