NeurIPS 2025 Papers

A major goal of neuroscience is to understand brain computations during visual processing in naturalistic settings. A dominant approach is to use image-computable deep neural networks trained with different task objectives as a basis for linear encoding models. However, in addition to requiring estimation of a large number of linear encoding parameters, this approach ignores the structure of the feature maps both in the brain and the models. Recently proposed alternatives factor the linear mapping into separate sets of spatial and feature weights, thus finding static receptive fields for units, which is appropriate only for early visual areas. In this work, we employ the attention mechanism used in the transformer architecture to study how retinotopic visual features can be dynamically routed to category-selective areas in high-level visual processing. We show that this computational motif is significantly more powerful than alternative methods in predicting brain activity during natural scene viewing, across different feature basis models and modalities. We also show that this approach is inherently more interpretable as the attention-routing signals for different high-level categorical areas can be easily visualized for any input image. Given its high performance at predicting brain responses to novel images, the model deserves consideration as a candidate mechanistic model of how visual information from retinotopic maps is routed in the human brain based on the relevance of the input content to different category-selective regions. Our code is available at \href{https://github.com/Hosseinadeli/transformer_brain_encoder/}{https://github.com/Hosseinadeli/transformer\_brain\_encoder/}.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on “hiding” dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test – of which we show the Generalized Covariance Measure underlying many recent tests is _nearly_ a special case – and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type I error.

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.

Understanding neural network' (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (states of density) landscape as a function of training loss and test accuracy. Our experiments in transformers on arithmetic tasks suggests that there is NO entropy barrier in the memorization-to-generalization transition of grokking, challenging previous theory that defines grokking as a first-order phase transition. We identify a high-entropy advantage under grokking, an extension of prior work linking entropy to generalizability but much more significant. Inspired by grokking's far-from-equilibrium nature, we develop a toy optimizer WanD based on Wang-landau molecular dynamics, which can eliminate grokking without any constraints and find high-norm generalizing solutions. This provides strictly-defined counterexamples to theory attributing grokking solely to weight norm evolution towards the Goldilocks zone and also suggests new potential ways for optimizer design.

This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial terms based on the well known integral operator framework. The dominant subgaussian component allows to achieve convergence rates that have previously only been derived under subexponential noise—a prevalent assumption in related work from the last two decades. These rates are optimal under standard eigenvalue decay conditions, demonstrating the asymptotic robustness of regularized least squares against heavy- tailed noise. Our derivations are based on a Fuk–Nagaev inequality for Hilbert-space valued random variables.

In dueling bandits, an agent explores and exploits choices (i.e., arms) by learning from their stochastic feedback in the form of relative preferences. Prior related studies focused on unbiased feedback. In practice, however, the feedback provided by evaluators can be biased. For example, human users are likely to provide biased evaluation towards large language models due to their heterogeneous background. In this work, we aim to minimize the regret in dueling bandits considering evaluators’ biased feedback. We begin with a benchmark case where evaluators’ bias information is known. Solving the known-bias case is nontrivial, because the bias cannot be easily decoupled from the feedback. We overcome this challenge and propose an unbiased arm performance estimator and a bias-sensitive dueling bandits algorithm. We manage to analyze the regret, dealing with the complex form of the estimator, and show that the feedback either matching or opposing the ground-truth reduces the regret. Then, we study the case where evaluators’ bias information is unknown. The associated estimator can hardly be solved in closed-form due to the non-convexity of the estimator solving problem. We address this challenge and propose an extended bias-sensitive algorithm by incorporating block coordinate descent. This algorithm is proven to achieve the same order of regret (as in the known bias case) with a bounded error. Experiments show that when compared with baselines, our algorithms reduces the regret by up to 86.9%.

Modern large-language models often face communication bottlenecks on current hardware rather than computational limitations. *Multi-head latent attention (MLA)* addresses this by compressing the key-value cache using low-rank matrices, while the Absorb operation prevents the KV cache from reverting to its original size, significantly boosting both training and inference speed. Despite the success of DeepSeek V2/V3/R1, most model providers have heavily invested in optimizing GQA-based models and, therefore, lack strong incentives to retrain MLA-based models from scratch. This paper demonstrates that MLA provides superior expressive power compared to GQA with the same KV cache overhead, thereby offering a rationale for transitioning from GQA to MLA. In addition, we introduce TransMLA, a framework that seamlessly converts any GQA-based pre-trained model (e.g., LLaMA, Qwen, Gemma, Mistral/Mixtral) into an MLA-based model. For the first time, our method enables *direct conversion of these models into a format compatible with DeepSeek's codebase*, allowing them to fully leverage the existing, highly-optimized support for the DeepSeek architecture within inference engines like vLLM and SGlang. By compressing 93\% of the KV cache in LLaMA-2-7B, we achieve a **10x speedup** with an 8K context length while maintaining meaningful output. Moreover, the model requires only **6B tokens** for fine-tuning to recover comparable performance across multiple benchmarks. TransMLA provides a practical path for migrating GQA-based models to the MLA structure, and when combined with DeepSeek’s advanced optimizations—such as FP8 quantization and Multi-Token Prediction—further inference acceleration can be achieved.

Robust Federated Graph Learning (FGL) provides an effective decentralized framework for training Graph Neural Networks (GNNs) in noisy-label environments. However, the subtlety of noise during training presents formidable obstacles for developing robust FGL systems. Previous robust FL approaches neither adequately constrain edge-mediated error propagation nor account for intra-class topological differences. At the client level, we innovatively demonstrate that hyperspherical embedding can effectively capture graph structures in a fine-grained manner. Correspondingly, our method effectively addresses the aforementioned issues through fine-grained hypersphere alignment. Moreover, we uncover undetected noise arising from localized perspective constraints and propose the geometric-aware hyperspherical purification module at the server level. Combining both level strategies, we present our robust FGL framework,**HYPERION**, which operates all components within a unified hyperspherical space. **HYPERION** demonstrates remarkable robustness across multiple datasets, for instance, achieving a 29.7\% $\uparrow$ F1-macro score with 50\%-pair noise on Cora. The code is available for anonymous access at \url{https://anonymous.4open.science/r/Hyperion-NeurIPS/}.

One of the chronic problems of deep-learning models is shortcut learning. In a case where the majority of training data are dominated by a certain feature, neural networks prefer to learn such a feature even if the feature is not generalizable outside the training set. Based on the framework of Neural Tangent Kernel (NTK), we analyzed the case of linear neural networks to derive some important properties of shortcut learning. We defined a “feature” of a neural network as an eigenfunction of NTK. Then, we found that shortcut features correspond to features with larger eigenvalues when the shortcuts stem from the imbalanced number of samples in the clustered distribution. We also showed that the features with larger eigenvalues still have a large influence on the neural network output even after training, due to data variances in the clusters. Such a preference for certain features remains even when a margin of a neural network output is controlled, which shows that the max-margin bias is not the only major reason for shortcut learning. These properties of linear neural networks are empirically extended for more complex neural networks as a two-layer ReLU FC network and a ResNet-18.

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and test data differ, presenting additional challenges for learning. Although kernel methods have optimal statistical properties, their high computational demands in terms of time and, particularly, memory, limit their scalability to large datasets. To address this limitation, the main focus of this paper is to explore the trade-off between computational efficiency and statistical accuracy under covariate shift. We investigate the use of random projections where the hypothesis space consists of a random subspace within a given RKHS. Our results show that, even in the presence of covariate shift, significant computational savings can be achieved without compromising learning performance.

We study the finite-horizon Restless Multi-Armed Bandit (RMAB) problem with $N$ homogeneous arms. Prior work has shown that when an RMAB satisfies a non-degeneracy condition, Linear-Programming-based (LP-based) policies derived from the fluid approximation, which captures the mean dynamics of the system, achieve an exponentially small optimality gap. However, it is common for RMABs to be degenerate, in which case LP-based policies can result in a $\Theta(1/\sqrt{N})$ optimality gap per arm. In this paper, we propose a novel Stochastic-Programming-based (SP-based) policy that, under a uniqueness assumption, achieves an $\tilde{\mathcal{O}}(1/N)$ optimality gap for degenerate RMABs. Our approach is based on the construction of a Gaussian stochastic system that captures not only the mean but also the variance of the RMAB dynamics, resulting in a more accurate approximation than the fluid approximation. We then solve a stochastic program for this system to obtain our policy. This is the first result to establish an $\tilde{\mathcal{O}}(1/N)$ optimality gap for degenerate RMABs.

In this paper, we explore the universal properties underlying causal inference by formulating it in terms of a topos. More concretely, we introduce topos causal models (TCMs), a strict generalization of the popular structural causal models (SCMs). A topos category has several properties that make it attractive: a general theory for how to combine local functions that define ``independent causal mechanisms" into a consistent global function building on the theory of sheaves in a topos; a generic way to define causal interventions using a subobject classifier in a topos category; and finally, an internal logical language for causal and counterfactual reasoning that emerges from the topos itself. A striking characteristic of subobject classifiers is that they induce an intuitionistic logic, whose semantics is based on the partially ordered lattice of subobjects. We show that the underlying subobject classifier for causal inference is not Boolean in general, but forms a Heyting algebra. We define the internal Mitchell-B\'enabou language, a typed local set theory, associated with causal models, and its associated Kripke-Joyal intuitionistic semantics. We prove a universal property of TCM, namely that any causal functor mapping decomposable structure to probabilistic semantics factors uniquely through a TCM representation.

Efficient optimization is essential for training large language models. Although intra-layer selective updates have been explored, a general mechanism that enables fine-grained control while ensuring convergence guarantees is still lacking. To bridge this gap, we propose \textbf{MGUP}, a novel mechanism for selective updates. \textbf{MGUP} augments standard momentum-based optimizers by applying larger step-sizes to a selected fixed proportion of parameters in each iteration, while applying smaller, non-zero step-sizes to the rest. As a nearly {plug-and-play} module, \textbf{MGUP} seamlessly integrates with optimizers such as AdamW, Lion, and Muon. This yields powerful variants such as \textbf{MGUP-AdamW}, \textbf{MGUP-Lion}, and \textbf{MGUP-Muon}. Under standard assumptions, we provide theoretical convergence guarantees for \textbf{MGUP-AdamW} (without weight decay) in stochastic optimization. Extensive experiments across diverse tasks, including MAE pretraining, LLM pretraining, and downstream fine-tuning, demonstrate that our \textbf{MGUP}-enhanced optimizers achieve superior or more stable performance compared to their original base optimizers. We offer a principled, versatile, and theoretically grounded strategy for efficient intra-layer selective updates, accelerating and stabilizing the training of large-scale models. The code is publicly available at https://github.com/MaeChd/MGUP.

Previous dominant methods for scene flow estimation focus mainly on input from two consecutive frames, neglecting valuable information in the temporal domain. While recent trends shift towards multi-frame reasoning, they suffer from rapidly escalating computational costs as the number of frames grows. To leverage temporal information more efficiently, we propose DeltaFlow ($\Delta$Flow), a lightweight 3D framework that captures motion cues via a $\Delta$ scheme, extracting temporal features with minimal computational cost, regardless of the number of frames. Additionally, scene flow estimation faces challenges such as imbalanced object class distributions and motion inconsistency. To tackle these issues, we introduce a Category-Balanced Loss to enhance learning across underrepresented classes and an Instance Consistency Loss to enforce coherent object motion, improving flow accuracy. Extensive evaluations on the Argoverse 2, Waymo and nuScenes datasets show that $\Delta$Flow achieves state-of-the-art performance with up to 22\% lower error and $2\times$ faster inference compared to the next-best multi-frame supervised method, while also demonstrating a strong cross-domain generalization ability. The code is open-sourced at https://github.com/Kin-Zhang/DeltaFlow along with trained model weights.

Existing test-time adaptation (TTA) methods primarily focus on scenarios involving domain shifts in a single modality. However, they often prove ineffective when multiple modalities simultaneously undergo domain shifts, as they struggle to identify and utilize reliable samples within testing batches amid severe prediction bias. To address this problem, we propose Partition-Then-Adapt (PTA), a novel approach combating prediction bias for TTA with multi-modal domain shifts. PTA comprises two key components: Partition and Debiased Reweighting (PDR) and multi-modal Attention-Guided Alignment (AGA). Specifically, PDR evaluates each sample’s predicted label frequency relative to the batch average, partitioning the batch into potential reliable and unreliable subsets. It then reweights each sample by jointly assessing its bias and confidence levels through a quantile-based approach. By applying weighted entropy loss, PTA simultaneously promotes learning from reliable subsets and discourages reliance on unreliable ones. Moreover, AGA regularizes PDR to focus on semantically meaningful multi-modal cues. Extensive experiments validate the effectiveness of PTA, surpassing state-of-the-art method by 6.1\% on Kinetics50-MC and 5.8\% on VGGSound-MC, respectively. Code of this paper is available at https://github.com/MPI-Lab/PTA.

Diffusion generative models have become the standard for producing high-quality, coherent video content, yet their slow inference speeds and high computational demands hinder practical deployment. Although both quantization and sparsity can independently accelerate inference while maintaining generation quality, naively combining these techniques in existing training-free approaches leads to significant performance degradation, as they fail to achieve proper joint optimization. We introduce FPSAttention, a novel training-aware co-design of FP8 quantization and Sparsity for video generation, with a focus on the 3D bi-directional attention mechanism. Our approach features three key innovations: 1) A unified 3D tile-wise granularity that simultaneously supports both quantization and sparsity. 2) A denoising step-aware strategy that adapts to the noise schedule, addressing the strong correlation between quantization/sparsity errors and denoising steps. 3) A native, hardware-friendly kernel that leverages FlashAttention and is implemented with optimized Hopper architecture features, enabling highly efficient execution. Trained on Wan2.1's 1.3B and 14B models and evaluated on the vBench benchmark, FPSAttention achieves a 7.09$\times$ kernel speedup for attention operations and a 4.96$\times$ end-to-end speedup for video generation compared to the BF16 baseline at 720p resolution—without sacrificing generation quality.

We study the problem of explainable $k$-medians clustering introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (2020). In this problem, the goal is to construct a threshold decision tree that partitions data into $k$ clusters while minimizing the $k$-medians objective. These trees are interpretable because each internal node makes a simple decision by thresholding a single feature, allowing users to trace and understand how each point is assigned to a cluster. We present the first algorithm for explainable $k$-medians under $\ell_p$ norm for every finite $p \geq 1$. Our algorithm achieves an $\tilde{O}\big(p(\log k)^{1 + 1/p - 1/p^2}\big)$ approximation to the optimal $k$-medians cost for any $p \geq 1$. Previously, algorithms were known only for $p = 1$ and $p = 2$. For $p = 2$, our algorithm improves upon the existing bound of $\tilde O(\log^{3/2}k)$, and for $p = 1$, it matches the tight bound of $\log k + O(1)$ up to a multiplicative $O(\log \log k)$ factor. We show how to implement our algorithm in a dynamic setting. The dynamic algorithm maintains an explainable clustering under a sequence of insertions and deletions, with amortized update time $O(d \log^3 k)$ and $O(\log k)$ recourse, making it suitable for large-scale and evolving datasets.

How can we reliably simulate future driving scenarios under a wide range of ego driving behaviors? Recent driving world models, developed exclusively on real-world driving data composed mainly of safe expert trajectories, struggle to follow hazardous or non-expert behaviors, which are rare in such data. This limitation restricts their applicability to tasks such as policy evaluation. In this work, we address this challenge by enriching real-world human demonstrations with diverse non-expert data collected from a driving simulator (e.g., CARLA), and building a controllable world model trained on this heterogeneous corpus. Starting with a video generator featuring diffusion transformer architecture, we devise several strategies to effectively integrate conditioning signals and improve prediction controllability and fidelity. The resulting model, ReSim, enables Reliable Simulation of diverse open-world driving scenarios under various actions, including hazardous non-expert ones. To close the gap between high-fidelity simulation and applications that require reward signals to judge different actions, we introduce a Video2Reward module that estimates reward from ReSim’s simulated future. Our ReSim paradigm achieves up to 44% higher visual fidelity, improves controllability for both expert and non-expert actions by over 50%, and boosts planning and policy selection performance on NAVSIM by 2% and 25%, respectively.