NeurIPS 2025 Papers

The m-out-of-n bootstrap—proposed by \cite{bickel1992resampling}—approximates the distribution of a statistic by repeatedly drawing $m$ subsamples ($m \ll n$) without replacement from an original sample of size n; it is now routinely used for robust inference with heavy-tailed data, bandwidth selection, and other large-sample applications. Despite this broad applicability across econometrics, biostatistics, and machine-learning workflows, rigorous parameter-free guarantees for the soundness of the m-out-of-n bootstrap when estimating sample quantiles have remained elusive. This paper establishes such guarantees by analysing the estimator of sample quantiles obtained from m-out-of-n resampling of a dataset of length n. We first prove a central limit theorem for a fully data-driven version of the estimator that holds under a mild moment condition and involves no unknown nuisance parameters. We then show that the moment assumption is essentially tight by constructing a counter-example in which the CLT fails. Strengthening the assumptions slightly, we derive an Edgeworth expansion that delivers exact convergence rates and, as a corollary, a Berry–Esséen bound on the bootstrap approximation error. Finally, we illustrate the scope of our results by obtaining parameter-free asymptotic distributions for practical statistics, including the quantiles for random walk MH, and rewards of ergodic MDP's, thereby demonstrating the usefulness of our theory in modern estimation and learning tasks.

We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy algorithm asymptotically succeeds or fails, in the sense of sublinear vs. linear regret as a function of time. Our characterization identifies a partial identifiability property of the problem instance as the necessary and sufficient condition for the asymptotic success. Notably, once this property holds, the problem becomes easy—\emph{any} algorithm will succeed (in the same sense as above), provided it satisfies a mild non-degeneracy condition. Our characterization extends to contextual bandits and interactive decision-making with arbitrary feedback. Examples demonstrating broad applicability and extensions to infinite reward structures are provided.

Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but they are often complex and fail to highlight the causes underlying this difficulty. In this work, we conduct a series of empirical analyses which suggest that the combination of non-stationarity with gradient pathologies, due to suboptimal architectural choices, underlie the challenges of scale. We propose a series of direct interventions that stabilize gradient flow, enabling robust performance across a range of network depths and widths. Our interventions are simple to implement and compatible with well-established algorithms, and result in an effective mechanism that enables strong performance even at large scales. We validate our findings on a variety of agents and suites of environments.

Prefix caching is a key technique for reducing Large Language Model (LLM) inference costs. However, the prevalent least-recently-used (LRU) eviction algorithm has a large gap to the optimal algorithm. This paper introduces LPC, the first learned method to perform LLM prefix cache eviction. LPC leverages conversational content analysis to provide predictive guidance for eviction, determining which conversations are likely to continue. These insights, combined with last access timestamps, inform more effective cache management. Extensive evaluations across three real-world datasets demonstrate that LPC achieves 18-47% reductions in required cache sizes for equivalent hit ratios and has an 11% improvement in LLM prefilling throughput in an emulated environment.

Robust and unobtrusive in-vehicle physiological monitoring is crucial for ensuring driving safety and user experience. While remote physiological measurement (RPM) offers a promising non-invasive solution, its translation to real-world driving scenarios is critically constrained by the scarcity of comprehensive datasets. Existing resources are often limited in scale, modality diversity, the breadth of biometric annotations, and the range of captured conditions, thereby omitting inherent real-world challenges in driving. Here, we present PhysDrive, the first large-scale multimodal dataset for contactless in-vehicle physiological sensing with dedicated consideration of various modality settings and driving factors. PhysDrive collects data from 48 drivers, including synchronized RGB, near-infrared camera, and raw mmWave radar data, accompanied by six synchronized ground truths (ECG, BVP, Respiration, HR, RR, and SpO2). It covers a wide spectrum of naturalistic driving conditions, including driver motions, dynamic natural light, vehicle types, and road conditions. We extensively evaluate both signal‑processing and deep‑learning methods on PhysDrive, establishing a comprehensive benchmark across all modalities, and release full open‑source code with compatibility for mainstream public toolboxes. We envision PhysDrive will serve as a foundational resource and accelerate research on multimodal driver monitoring and smart‑cockpit systems.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. However, diffusion models that directly work on discrete data space fail to fully exploit the power of iterative refinement, as the signals are lost during transitions between discrete states. Existing continuous diffusion models for discrete data underperform compared to discrete methods, and the lack of a clear connection between the two approaches hinders the development of effective diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on this analogy, introduce a simple diffusion process that generalizes existing discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry, along with a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models.

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the topological descriptors - the Euler characteristic (EC) and persistent homology (PH). In particular, we establish a complete characterization of the expressive power of EC on general color-based filtrations. We also show that the PH descriptors of (virtual) graph products contain strictly more information than the computation on individual graphs, whereas EC does not. Additionally, we provide algorithms to compute the PH diagrams of the product of vertex- and edge-level filtrations on the graph product. We also substantiate our theoretical analysis with empirical investigations on runtime analysis, expressivity, and graph classification performance. Overall, this work paves way for powerful graph persistent descriptors via product filtrations. Code is available at https://github.com/Aalto-QuML/tda_graph_product.

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.

Channel permutation is a powerful technique for enhancing the accuracy of N:M sparse models by reordering the channels of weight matrices to prioritize the retention of important weights. However, traditional channel permutation methods rely on handcrafted quality metrics, which often fail to accurately capture the true impact of pruning on model performance. To address this limitation, we propose PermLLM, a novel post-training pruning framework that introduces learnable channel permutation (LCP) for N:M sparsity. LCP leverages Sinkhorn normalization to transform discrete permutation matrices into differentiable soft permutation matrices, enabling end-to-end optimization. Additionally, PermLLM incorporates an efficient block-wise channel permutation strategy, which significantly reduces the number of learnable parameters and computational complexity. PermLLM seamlessly integrates with existing one-shot pruning methods to adaptively optimize channel permutations, effectively mitigating pruning-induced errors. Extensive experiments on the LLaMA series, Qwen, and OPT models demonstrate that PermLLM achieves superior performance in optimizing N:M sparse models.

Strategic classification (SC) explores how individuals or entities modify their features strategically to achieve favorable classification outcomes. However, existing SC methods, which are largely based on linear models or shallow neural networks, face significant limitations in terms of scalability and capacity when applied to real-world datasets with significantly increasing scale, especially in financial services and the internet sector. In this paper, we investigate how to leverage large language models to design a more scalable and efficient SC framework, especially in the case of growing individuals engaged with decision-making processes. Specifically, we introduce GLIM, a gradient-free SC method grounded in in-context learning. During the feed-forward process of self-attention, GLIM implicitly simulates the typical bi-level optimization process of SC, including both the feature manipulation and decision rule optimization. Without fine-tuning the LLMs, our proposed GLIM enjoys the advantage of cost-effective adaptation in dynamic strategic environments. Theoretically, we prove GLIM can support pre-trained LLMs to adapt to a broad range of strategic manipulations. We validate our approach through experiments with a collection of pre-trained LLMs on real-world and synthetic datasets in financial and internet domains, demonstrating that our GLIM exhibits both robustness and efficiency, and offering an effective solution for large-scale SC tasks.

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of observed entries; they may fail under overparametrization, when their assumed rank is higher than the correct one; and many of them fail to recover even mildly ill-conditioned matrices. In this paper we propose a novel RMC method, denoted $\texttt{RGNMR}$, which overcomes these limitations. $\texttt{RGNMR}$ is a simple factorization-based iterative algorithm, which combines a Gauss–Newton linearization with removal of entries suspected to be outliers. On the theoretical front, we prove that under suitable assumptions, $\texttt{RGNMR}$ is guaranteed exact recovery of the underlying low rank matrix. Our theoretical results improve upon the best currently known for factorization-based methods. On the empirical front, we show via several simulations the advantages of $\texttt{RGNMR}$ over existing RMC methods, and in particular its ability to handle a small number of observed entries, overparameterization of the rank and ill-conditioned matrices. In addition, we propose a novel scheme for estimating the number of corrupted entries. This scheme may be used by other RMC methods that require as input the number of corrupted entries.

This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to the identity matrix, and estimators derived from data augmentation (DA). Here, DA refers to the common practice of enriching a dataset with artificial samples—typically generated via a generative model or through random transformations of the original data—prior to model fitting. For both classes of estimators, we derive estimators and provide concentration bounds for their quadratic error. This allows for both method comparison and hyperparameter tuning, such as selecting the optimal proportion of artificial samples. On the technical side, our analysis relies on tools from random matrix theory. We introduce a novel deterministic equivalent for generalized resolvent matrices, accommodating dependent samples with specific structure. We support our theoretical results with numerical experiments.

Out-of-distribution (OOD) 3D relighting requires novel view synthesis under unseen lighting conditions that differ significantly from the observed images. Existing relighting methods, which assume consistent light source distributions between training and testing, often degrade in OOD scenarios. We introduce **MetaGS** to tackle this challenge from two perspectives. First, we propose a meta-learning approach to train 3D Gaussian splatting, which explicitly promotes learning generalizable Gaussian geometries and appearance attributes across diverse lighting conditions, even with biased training data. Second, we embed fundamental physical priors from the *Blinn-Phong* reflection model into Gaussian splatting, which enhances the decoupling of shading components and leads to more accurate 3D scene reconstruction. Results on both synthetic and real-world datasets demonstrate the effectiveness of MetaGS in challenging OOD relighting tasks, supporting efficient point-light relighting and generalizing well to unseen environment lighting maps.

Reconstruction and joint-embedding have emerged as two leading paradigms in Self‑Supervised Learning (SSL). Reconstruction methods focus on recovering the original sample from a different view in input space. On the other hand, joint-embedding methods align the representations of different views in latent space. Both approaches offer compelling advantages, yet practitioners lack clear guidelines for choosing between them. In this work, we unveil the core mechanisms that distinguish each paradigm. By leveraging closed-form solutions for both approaches, we precisely characterize how the view generation process, e.g. data augmentation, impacts the learned representations. We then demonstrate that, unlike supervised learning, both SSL paradigms require a minimal alignment between augmentations and irrelevant features to achieve asymptotic optimality with increasing sample size. Our findings indicate that in scenarios where these irrelevant features have a large magnitude, joint-embedding methods are preferable because they impose a strictly weaker alignment condition compared to reconstruction-based methods. These results not only clarify the trade-offs between the two paradigms but also substantiate the empirical success of joint-embedding approaches on real-world challenging datasets.

For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's principle of optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning (RL). Although recent advances in RL successfully leverage this formulation, the existing methods typically assume the underlying dynamics are known a priori because they need explicit access to the coefficient functions of dynamical equations to update the value function following the HJB equation. We address this inherent limitation of HJB-based RL; we propose a model-free approach still targeting the HJB equation and propose the corresponding temporal difference method. We establish exponential convergence of the idealized continuous-time dynamics and empirically demonstrate its potential advantages over transition–kernel–based formulations. The proposed formulation paves the way toward bridging stochastic control and model-free reinforcement learning.

The influence function serves as an efficient post-hoc interpretability tool that quantifies the impact of training data modifications on model parameters, enabling enhanced model performance, improved generalization, and interpretability insights without the need for expensive retraining processes. Recently, Multivariate Time Series (MTS) analysis has become an important yet challenging task, attracting significant attention. While channel extremely matters to MTS tasks, channel-centric methods are still largely under-explored for MTS. Particularly, no previous work studied the effects of channel information of MTS in order to explore counterfactual effects between these channels and model performance. To fill this gap, we propose a novel Channel-wise Influence (ChInf) method that is the first to estimate the influence of different channels in MTS. Based on ChInf, we naturally derived two channel-wise algorithms by incorporating ChInf into classic MTS tasks. Extensive experiments demonstrate the effectiveness of ChInf and ChInf-based methods in critical MTS analysis tasks, such as MTS anomaly detection and MTS data pruning. Specifically, our ChInf-based methods rank top-1 among all methods for comparison, while previous influence functions do not perform well on MTS anomaly detection tasks and MTS data pruning problem. This fully supports the superiority and necessity of ChInf.

Event cameras are bio-inspired sensors that capture intensity changes asynchronously with distinct advantages, such as high temporal resolution. Existing methods for event-based object/action recognition predominantly sample and convert event representation at every fixed temporal interval (or frequency). However, they are constrained to processing a limited number of event lengths and show poor frequency generalization, thus not fully leveraging the event's high temporal resolution. In this paper, we present our PASS framework, exhibiting superior capacity for spatiotemporal event modeling towards a larger number of event lengths and generalization across varying inference temporal frequencies. Our key insight is to learn adaptively encoded event features via the state space models (SSMs), whose linear complexity and generalization on input frequency make them ideal for processing high temporal resolution events. Specifically, we propose a Path-selective Event Aggregation and Scan (PEAS) module to encode events into features with fixed dimensions by adaptively scanning and selecting aggregated event presentation. On top of it, we introduce a novel Multi-faceted Selection Guiding (MSG) loss to minimize the randomness and redundancy of the encoded features during the PEAS selection process. Our method outperforms prior methods on five public datasets and shows strong generalization across varying inference frequencies with less accuracy drop (ours -8.62% v.s. -20.69% for the baseline). Moreover, our model exhibits strong long spatiotemporal modeling for a broader distribution of event length (1-10^9), precise temporal perception, and effective generalization for real-world scenarios. Code and checkpoints will be released upon acceptance.

Large language models (LLMs) have demonstrated remarkable performance on various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for embedding tokens in LLMs. In this study, we investigate the non-Euclidean characteristics of LLMs. Our findings reveal that token frequency follows a power-law distribution, with high-frequency tokens clustering near the origin and low-frequency tokens positioned farther away. Additionally, token embeddings exhibit a high degree of hyperbolicity, indicating a latent tree-like structure in the embedding space. Motivated by these observations, we propose to efficiently fine-tune LLMs in hyperbolic space to better exploit the underlying complex structures. However, we find that this hyperbolic fine-tuning cannot be achieved through the naive application of exponential and logarithmic maps when the embedding and weight matrices both reside in Euclidean space. To address this technical issue, we introduce hyperbolic low-rank efficient fine-tuning, HypLoRA, which performs low-rank adaptation directly on the hyperbolic manifold, preventing the cancellation effect produced by consecutive exponential and logarithmic maps and thereby preserving hyperbolic modeling capabilities. Extensive experiments across various base models and two different reasoning benchmarks, specifically arithmetic and commonsense reasoning tasks, demonstrate that HypLoRA substantially improves LLM performance.

Key-Value (KV) cache eviction---which retains the KV pairs of the most important tokens while discarding less important ones---is a critical technique for optimizing both memory usage and inference latency in large language models (LLMs). However, existing approaches often rely on simple heuristics---such as attention weights---to measure token importance, overlooking the spatial relationships between token value states in the vector space. This often leads to suboptimal token selections and thus performance degradation. To tackle this problem, we propose a novel method, namely **AnDPro** (**An**chor **D**irection **Pro**jection), which introduces a projection-based scoring function to more accurately measure token importance. Specifically, AnDPro operates in the space of value vectors and leverages the projections of these vectors onto an *``Anchor Direction''*---the direction of the pre-eviction output---to measure token importance and guide more accurate token selection. Experiments on $16$ datasets from the LongBench benchmark demonstrate that AnDPro can maintain $96.07\\%$ of the full cache accuracy using only $3.44\\%$ KV cache budget, reducing KV cache budget size by $46.0\\%$ without compromising quality compared to previous state-of-the-arts.