NeurIPS 2025 Papers

We establish a comprehensive finite-sample and asymptotic theory for stochastic gradient descent (SGD) with constant learning rates. First, we propose a novel linear approximation technique to provide a quenched central limit theorem (CLT) for SGD iterates with refined tail properties, showing that regardless of the chosen initialization, the fluctuations of the algorithm around its target point converge to a multivariate normal distribution. Our conditions are substantially milder than those required in the classical CLTs for SGD, yet offering a stronger convergence result. Furthermore, we derive the first Berry-Esseen bound -- the Gaussian approximation error -- for the constant learning-rate SGD, which is sharp compared to the decaying learning-rate schemes in the literature. Beyond the moment convergence, we also provide the Nagaev-type inequality for the SGD tail probabilities by adopting the autoregressive approximation techniques, which entails non-asymptotic large-deviation guarantees. These results are verified via numerical simulations, paving the way for theoretically grounded uncertainty quantification, especially with non-asymptotic validity.

Optimal transport (OT) provides a powerful framework for comparing and transforming probability distributions, with wide applications in generative modeling, AI4Science and statistical inference. However, existing estimation theory typically requires stringent smoothness conditions on the underlying Brenier potentials and assumes bounded distribution supports, limiting practical applicability. In this paper, we introduce a unified theoretical framework for semi-dual OT map estimation that relaxes both of these restrictions. Building on sieved convex conjugate, our framework has two key contributions: (i) a new map stability bounds that holds without any second-order regularity assumptions on the true Brenier potentials, and (ii) an oracle inequality that cleanly decomposes the estimation error into statistical error, sieved bias, and approximation error. Specifically, our approximation error is measured in the $L^\infty$ norm rather than Sobolev norm in the existing results, aligning more naturally with classical approximation theory. Leveraging these tools, we provide statistical error of semi-dual estimators with mild and verifiable conditions on the true OT map. Moreover, we establish the first theoretical guarantee for deep neural network OT map estimator between general distributions, with Tanh network function class as an example.

The current Federated Recommendation System (FedRS) focuses on personalized recommendation services and assumes clients are personalized IoT devices (e.g., Mobile phones). In this paper, we deeply dive into new but practical FedRS applications within the joint venture ecosystem. Subsidiaries engage as participants with their users and items. However, in such a situation, merely exchanging item embedding is insufficient, as user bases always exhibit both overlaps and exclusive segments, demonstrating the complexity of user information. Meanwhile, directly uploading user information is a violation of privacy and unacceptable. To tackle the above challenges, we propose an efficient and privacy-enhanced federated recommendation for the joint venture ecosystem (FR-JVE) that each client transfers more common knowledge from other clients with a distilled user's \textit{rating preference} from the local dataset. More specifically, we first transform the local data into a new format and apply model inversion techniques to distill the rating preference with frozen user gradients before the federated training. Then, a bridge function is employed on each client side to align the local rating preference and aggregated global preference in a privacy-friendly manner. Finally, each client matches similar users to make a better prediction for overlapped users. From a theoretical perspective, we analyze how effectively FR-JVE can guarantee user privacy. Empirically, we show that FR-JVE achieves superior performance compared to state-of-the-art methods.

In this paper, we address the problem of cost-sensitive hyperparameter optimization (HPO) built upon freeze-thaw Bayesian optimization (BO). Specifically, we assume a scenario where users want to early-stop the HPO process when the expected performance improvement is not satisfactory with respect to the additional computational cost. Motivated by this scenario, we introduce \emph{utility} in the freeze-thaw framework, a function describing the trade-off between the cost and performance that can be estimated from the user's preference data. This utility function, combined with our novel acquisition function and stopping criterion, allows us to dynamically continue training the configuration that we expect to maximally improve the utility in the future, and also automatically stop the HPO process around the maximum utility. Further, we improve the sample efficiency of existing freeze-thaw methods with transfer learning to develop a specialized surrogate model for the cost-sensitive HPO problem. We validate our algorithm on established multi-fidelity HPO benchmarks and show that it outperforms all the previous freeze-thaw BO and transfer-BO baselines we consider, while achieving a significantly better trade-off between the cost and performance.

Engineering design optimization seeks to automatically determine the shapes, topologies, or parameters of components that maximize performance under given conditions. This process often depends on physics-based simulations, which are difficult to install, computationally expensive, and require domain-specific expertise. To mitigate these challenges, we introduce EngiBench, the first open‐source library and datasets spanning diverse domains for data‐driven engineering design. EngiBench provides a unified API and a curated set of benchmarks---covering aeronautics, heat conduction, photonics, and more---that enable fair, reproducible comparisons of optimization and machine learning algorithms, such as generative or surrogate models. We also release EngiOpt, a companion library offering a collection of such algorithms compatible with the EngiBench interface. Both libraries are modular, letting users plug in novel algorithms or problems, automate end-to-end experiment workflows, and leverage built-in utilities for visualization, dataset generation, feasibility checks, and performance analysis. We demonstrate their versatility through experiments comparing state-of-the-art techniques across multiple engineering design problems, an undertaking that was previously prohibitively time-consuming to perform. Finally, we show that these problems pose significant challenges for standard machine learning methods due to highly sensitive and constrained design manifolds.

Operator learning is a powerful paradigm for solving partial differential equations, with Fourier Neural Operators serving as a widely adopted foundation. However, FNOs face significant scalability challenges due to overparameterization and offer no native uncertainty quantification -- a key requirement for reliable scientific and engineering applications. Instead, neural operators rely on post hoc UQ methods that ignore geometric inductive biases. In this work, we introduce DINOZAUR: a diffusion-based neural operator parametrization with uncertainty quantification. Inspired by the structure of the heat kernel, DINOZAUR replaces the dense tensor multiplier in FNOs with a dimensionality-independent diffusion multiplier that has a single learnable time parameter per channel, drastically reducing parameter count and memory footprint without compromising predictive performance. By defining priors over those time parameters, we cast DINOZAUR as a Bayesian neural operator to yield spatially correlated outputs and calibrated uncertainty estimates. Our method achieves competitive or superior performance across several PDE benchmarks while providing efficient uncertainty quantification.

We model sensory streams as observations from high-dimensional stochastic dynamical systems and conceptualize sensory neurons as self-supervised learners of compact representations of such dynamics. From prior experience, neurons learn {\it coherent sets}—regions of stimulus state space whose trajectories evolve cohesively over finite times—and assign membership indices to new stimuli. Coherent sets are identified via spectral clustering of the {\it stochastic Koopman operator (SKO)}, where the sign pattern of a subdominant singular function partitions the state space into minimally coupled regions. For multivariate Ornstein–Uhlenbeck processes, this singular function reduces to a linear projection onto the dominant singular vector of the whitened state-transition matrix. Encoding this singular vector as a receptive field enables neurons to compute membership indices via the projection sign in a biologically plausible manner. Each neuron detects either a {\it predictive} coherent set (stimuli with common futures) or a {\it retrospective} coherent set (stimuli with common pasts), suggesting a functional dichotomy among neurons. Since neurons lack access to explicit dynamical equations, the requisite singular vectors must be estimated directly from data, for example, via past–future canonical correlation analysis on lag-vector representations—an approach that naturally extends to nonlinear dynamics. This framework provides a novel account of neuronal temporal filtering, the ubiquity of rectification in neural responses, and known functional dichotomies. Coherent-set clustering thus emerges as a fundamental computation underlying sensory processing and transferable to bio-inspired artificial systems.

Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically solvable systems. In contrast, many physical phenomena are governed by PDEs, which govern infinite-dimensional fields through Hamiltonian functionals and their functional derivatives. Building on prior work, we represent the Hamiltonian functional as a kernel integral parameterized by a neural field, enabling learnable function-to-scalar mappings and the use of automatic differentiation to calculate functional derivatives. This allows for an extension of Hamiltonian mechanics to neural PDE solvers by predicting a functional and learning in the gradient domain. We show that the resulting Hamiltonian Neural Solver (HNS) can be an effective surrogate model through improved stability and conserving energy-like quantities across 1D and 2D PDEs. This ability to respect conservation laws also allows HNS models to better generalize to longer time horizons or unseen initial conditions.

We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ \emph{Orlicz geometric structure}, leveraging convex functions to capture nuanced geometric relationships and remarkably contribute to advance certain machine learning approaches. However, both OW and GST are restricted to measures with equal total mass, limiting their applicability to real-world scenarios where mass variation is common, and input measures may have noisy supports, or outliers. To address unbalanced measures, OW can either incorporate mass constraints or marginal discrepancy penalization, but this leads to a more complex two-level optimization problem. Additionally, GST provides a scalable yet rigid framework, which poses significant challenges to extend GST to accommodate nonnegative measures. To tackle these challenges, in this work we revisit the entropy partial transport (EPT) problem. By exploiting Caffarelli \& McCann's insights, we develop a novel variant of EPT endowed with Orlicz geometric structure, called \emph{Orlicz-EPT}. We establish theoretical background to solve Orlicz-EPT using a binary search algorithmic approach. Especially, by leveraging the dual EPT and the underlying graph structure, we formulate a novel regularization approach that leads to the proposed \emph{Orlicz-Sobolev transport} (OST). Notably, we demonstrate that OST can be efficiently computed by simply solving a univariate optimization problem, in stark contrast to the intensive computation needed for Orlicz-EPT. Building on this, we derive geometric structures for OST and draw its connections to other transport distances. We empirically illustrate that OST is several-order faster than Orlicz-EPT. Furthermore, we show preliminary evidence on the advantages of OST for measures on a graph in document classification and topological data analysis.

Large recommender models have extended LLMs as powerful recommenders via encoding or item generation, and recent breakthroughs in LLM reasoning synchronously motivate the exploration of reasoning in recommendation. In this work, we propose R$^2$ec, a unified large recommender model with intrinsic reasoning capability. R$^2$ec introduces a dual-head architecture that supports both reasoning chain generation and efficient item prediction in a single model, significantly reducing inference latency. To overcome the lack of annotated reasoning data, we design RecPO, a reinforcement learning framework that optimizes reasoning and recommendation jointly with a novel fused reward mechanism. Extensive experiments on three datasets demonstrate that R$^2$ec outperforms traditional, LLM-based, and reasoning-augmented recommender baselines, while further analyses validate its competitive efficiency among conventional LLM-based recommender baselines and strong adaptability to diverse recommendation scenarios. Code and checkpoints available at https://github.com/YRYangang/RRec.

Adversarial attacks on face recognition systems (FRSs) pose serious security and privacy threats, especially when these systems are used for identity verification. In this paper, we propose a novel method for generating adversarial faces—synthetic facial images that are visually distinct yet recognized as a target identity by the FRS. Unlike iterative optimization-based approaches (e.g., gradient descent or other iterative solvers), our method leverages the structural characteristics of the FRS feature space. We figure out that individuals sharing the same attribute (e.g., gender or race) form an attributed subsphere. By utilizing such subspheres, our method achieves both non-adaptiveness and a remarkably small number of queries. This eliminates the need for relying on transferability and open-source surrogate models, which have been a typical strategy when repeated adaptive queries to commercial FRSs are impossible. Despite requiring only a single non-adaptive query consisting of 100 face images, our method achieves a high success rate of over 93% against AWS’s CompareFaces API at its default threshold. Furthermore, unlike many existing attacks that perturb a given image, our method can deliberately produce adversarial faces that impersonate the target identity while exhibiting high-level attributes chosen by the adversary.

Surrogate models are widely used to approximate complex systems across science and engineering to reduce computational costs. Despite their widespread adoption, the field lacks standardisation across key stages of the modelling pipeline, including data sampling, model selection, evaluation, and downstream analysis. This fragmentation limits reproducibility and cross-domain utility – a challenge further exacerbated by the rapid proliferation of AI-driven surrogate models. We argue for the urgent need to establish a structured reporting standard, the Surrogate Model Reporting Standard (SMRS), that systematically captures essential design and evaluation choices while remaining agnostic to implementation specifics. By promoting a standardised yet flexible framework, we aim to improve the reliability of surrogate modelling, foster interdisciplinary knowledge transfer, and, as a result, accelerate scientific progress in the AI era.

Spike camera with high temporal resolution offers a new perspective on high-speed dynamic scene rendering. Most existing rendering methods rely on Neural Radiance Fields (NeRF) or 3D Gaussian Splatting (3DGS) for static scenes using a monocular spike camera. However, these methods struggle with dynamic motion, while a single camera suffers from limited spatial coverage, making it challenging to reconstruct fine details in high-speed scenes. To address these problems, we propose Spike4DGS, the first high-speed dynamic scene rendering framework with 4D Gaussian Splatting using spike camera arrays. Technically, we first build a multi-view spike camera array to validate our solution, then establish both synthetic and real-world multi-view spike-based reconstruction datasets. Then, we design a multi-view spike-based dense initialization module that obtains dense point clouds and camera poses from continuous spike streams. Finally, we propose a spike-pixel synergy constraint supervision to optimize Spike4DGS, incorporating both rendered image quality loss and dynamic spatiotemporal spike loss. The results show that our Spike4DGS outperforms state-of-the-art methods in terms of novel view rendering quality on both synthetic and real-world datasets. More details are available at https://github.com/Qinghongye/Spike4DGS.

Multimodal federated learning (MMFL) has gained increasing popularity due to its ability to leverage the correlation between various modalities, meanwhile preserving data privacy for different clients. However, recent studies show that correlation between modalities increase the vulnerability of federated learning against Gradient Inversion Attack (GIA). The complicated situation of MMFL privacy preserving can be summarized as follows: 1) different modality transmits different amounts of information, thus requires various protection strength; 2) correlation between modalities should be taken into account. This paper introduces an information theory perspective to analyze the leaked privacy in process of MMFL, and tries to propose a more reasonable protection method \textbf{Sec-MMFL} based on assessing different information leakage possibilities of each modality by conditional mutual information and adjust the corresponding protection strength. Moreover, we use mutual information to reduce the cross-modality information leakage in MMFL. Experiments have proven that our method can bring more balanced and comprehensive protection at an acceptable cost.

Active testing enables label-efficient evaluation of predictive models through careful data acquisition, but it can pose a significant computational cost. We identify cost-saving measures that enable active testing to be scaled up to large language models (LLMs). In particular we show that the surrogate model used to guide data acquisition can be constructed cheaply using in-context learning, does not require updating within an active-testing loop, and can be smaller than the target model. We even find we can make good data-acquisition decisions without making predictions with the target model. As a result we are able to achieve much more accurate evaluations of LLM performance relative to using randomly acquired data. We additionally introduce a bootstrap estimator of evaluation error, which we show to be a useful indicator of how well active testing is working within a single run.

Neural networks generally prefer simple and easy-to-learn features. When these features are spuriously correlated with the labels, the network's performance can suffer, particularly for underrepresented classes or concepts. Self-supervised representation learning methods, such as contrastive learning, are especially prone to this issue, often resulting in worse performance on downstream tasks. We identify a key spectral signature of this failure: early reliance on dominant singular modes of the learned feature matrix. To mitigate this, we propose a novel framework that promotes a uniform eigenspectrum of the feature covariance matrix, encouraging diverse and semantically rich representations. Our method operates in a fully self-supervised setting, without relying on ground-truth labels or any additional information. Empirical results on SimCLR and SimSiam demonstrate consistent gains in robustness and transfer performance, suggesting broad applicability across self-supervised learning paradigms. Code: https://github.com/NaghmehGh/SpuriousCorrelation_SSRL

Video Temporal Grounding (VTG) aims to retrieve precise temporal segments in a video conditioned on natural language queries. Unlike conventional neural frameworks that rely heavily on computationally expensive dense matrix multiplications, Spiking Neural Networks (SNNs)—previously underexplored in this domain—offer a unique opportunity to tackle VTG tasks through bio-plausible spike-based communication and an event-driven accumulation-based computational paradigm. We introduce SpikingVTG, a multi-modal spiking detection transformer, designed to harness the computational simplicity and sparsity of SNNs for VTG tasks. Leveraging the temporal dynamics of SNNs, our model introduces a Saliency Feedback Gating (SFG) mechanism that assigns dynamic saliency scores to video clips and applies multiplicative gating to highlight relevant clips while suppressing less informative ones. SFG enhances performance and reduces computational overhead by minimizing neural activity. We analyze the layer-wise convergence dynamics of SFG-enabled model and apply implicit differentiation at equilibrium to enable efficient, BPTT-free training. To improve generalization and maximize performance, we enable knowledge transfer by optimizing a Cos-L2 representation matching loss that aligns the layer-wise representation and attention maps of a non-spiking teacher with those of our student SpikingVTG. Additionally, we present Normalization-Free (NF)-SpikingVTG, which eliminates non-local operations like softmax and layer normalization, and an extremely quantized 1-bit (NF)-SpikingVTG variant for potential deployment on edge devices. Our models achieve competitive results on QVHighlights, Charades-STA, TACoS, and YouTube Highlights, establishing a strong baseline for multi-modal spiking VTG solutions.

Bayesian Optimization (BO) is a widely used method for optimizing expensive black-box functions, relying on probabilistic surrogate models such as Gaussian Processes (GPs). The quality of the surrogate model is crucial for good optimization performance, especially in the few-shot setting where only a small number of batches of points can be evaluated. In this setting, the initialization plays a critical role in shaping the surrogate's predictive quality and guiding subsequent optimization. Despite this, practitioners typically rely on (quasi-)random designs to cover the input space. However, such approaches neglect two key factors: (a) random designs may not be space-filling, and (b) efficient hyperparameter learning during initialization is essential for high-quality prediction, which may conflict with space-filling designs. To address these limitations, we propose Hyperparameter-Informed Predictive Exploration (HIPE), a novel acquisition strategy that balances space-filling exploration with hyperparameter learning using information-theoretic principles. We derive a closed-form expression for HIPE in the GP setting and demonstrate its effectiveness through extensive experiments in active learning and few-shot BO. Our results show that HIPE outperforms standard initialization strategies in terms of predictive accuracy, hyperparameter identification, and optimization performance, particularly in large-batch, few-shot settings relevant to many real-world BO applications.

Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if } F(S)\leq F(T) $. We call functions satisfying this property \emph{Monotone and Separating (MAS)} set functions. We establish lower and upper bounds for the vector dimension necessary to obtain MAS functions, as a function of the cardinality of the multisets and the underlying ground set. In the important case of an infinite ground set, we show that MAS functions do not exist, but provide a model called \our\ which provably enjoys a relaxed MAS property we name 'weakly MAS' and is stable in the sense of Holder continuity. We also show that MAS functions can be used to construct universal models which are monotone by construction, and can approximate all monotone set functions. Experimentally, we consider a variety of set containtment tasks. The experiments show the benefit of using our \our\ model, in comparsion with standard set models which do not incorporate set containment as an inductive bias.