NeurIPS 2025 Papers

$k$-means++ and the related greedy $k$-means++ algorithm are celebrated algorithms that efficiently compute seeds for Lloyd's algorithm. Greedy $k$-means++ is a generalization of $k$-means++ where, in each iteration, a new seed is greedily chosen among multiple $\ell \geq 2$ points sampled, as opposed to a single seed being sampled in $k$-means++. While empirical studies consistently show the superior performance of greedy $k$-means++, making it a preferred method in practice, a discrepancy exists between theory and practice. No theoretical justification currently explains this improved performance. Indeed, the prevailing theory suggests that greedy $k$-means++ exhibits worse performance than $k$-means++ in worst-case scenarios. This paper presents an analysis demonstrating the outperformance of the greedy algorithm compared to $k$-means++ for a natural class of well-separated instances with exponentially decaying distributions, such as Gaussian, specifically when $\ell = \Theta(\log k)$, a common parameter setting in practical applications.

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature’s label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to drift noisy samples back to label-consistent representations. During adaptation, we sample from each target feature’s latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier’s accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve. Code is available on our Github: https://github.com/JingWang18/DVD-SFDA.

We investigate the universal approximation property (UAP) of transformer-type architectures, providing a unified theoretical framework that extends prior results on residual networks to models incorporating attention mechanisms. Our work identifies token distinguishability as a fundamental requirement for UAP and introduces a general sufficient condition that applies to a broad class of architectures. Leveraging an analyticity assumption on the attention layer, we can significantly simplify the verification of this condition, providing a non-constructive approach in establishing UAP for such architectures. We demonstrate the applicability of our framework by proving UAP for transformers with various attention mechanisms, including kernel-based and sparse ones. The corollaries of our results either generalize prior works or establish UAP for architectures not previously covered. Furthermore, our framework offers a principled foundation for designing novel transformer architectures with inherent UAP guarantees, including those with specific functional symmetries. We propose examples to illustrate these insights.

Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics. Current implementations rely on specialized layers, limiting architectural choices. We introduce Lorentz Local Canonicalization (LLoCa), a general framework that renders any backbone network exactly Lorentz-equivariant. Using equivariantly predicted local reference frames, we construct LLoCa-transformers and graph networks. We adapt a recent approach for geometric message passing to the non-compact Lorentz group, allowing propagation of space-time tensorial features. Data augmentation emerges from LLoCa as a special choice of reference frame. Our models achieve competitive and state-of-the-art accuracy on relevant particle physics tasks, while being $4\times$ faster and using $10\times$ fewer FLOPs.

Video Large Language Models have demonstrated strong video understanding capabilities, yet their practical deployment is hindered by substantial inference costs caused by redundant video tokens. Existing pruning techniques fail to effectively exploit the spatiotemporal redundancy present in video data. To bridge this gap, we perform a systematic analysis of video redundancy from two perspectives: temporal context and visual context. Leveraging these insights, we propose Dynamic Density Pruning for Fast Video LLMs termed FastVID. Specifically, FastVID dynamically partitions videos into temporally ordered segments to preserve temporal structure and applies a density-based token pruning strategy to maintain essential spatial and temporal information. Our method significantly reduces computational overhead while maintaining temporal and visual integrity. Extensive evaluations show that FastVID achieves state-of-the-art performance across various short- and long-video benchmarks on leading Video LLMs, including LLaVA-OneVision, LLaVA-Video, Qwen2-VL, and Qwen2.5-VL. Notably, on LLaVA-OneVision-7B, FastVID effectively prunes $\textbf{90.3\%}$ of video tokens, reduces FLOPs to $\textbf{8.3\%}$, and accelerates the prefilling stage by $\textbf{7.1}\times$, while maintaining $\textbf{98.0\%}$ of the original accuracy. The code is available at https://github.com/LunarShen/FastVID.

Current text-to-image diffusion generation typically employs complete-text conditioning. Due to the intricate syntax, diffusion transformers (DiTs) inherently suffer from a comprehension defect of complete-text captions. One-fly complete-text input either overlooks critical semantic details or causes semantic confusion by simultaneously modeling diverse semantic primitive types. To mitigate this defect of DiTs, we propose a novel split-text conditioning framework named DiT-ST. This framework converts a complete-text caption into a split-text caption, a collection of simplified sentences, to explicitly express various semantic primitives and their interconnections. The split-text caption is then injected into different denoising stages of DiT-ST in a hierarchical and incremental manner. Specifically, DiT-ST leverages Large Language Models to parse captions, extracting diverse primitives and hierarchically sorting out and constructing these primitives into a split-text input. Moreover, we partition the diffusion denoising process according to its differential sensitivities to diverse semantic primitive types and determine the appropriate timesteps to incrementally inject tokens of diverse semantic primitive types into input tokens via cross-attention. In this way, DiT-ST enhances the representation learning of specific semantic primitive types across different stages. Extensive experiments validate the effectiveness of our proposed DiT-ST in mitigating the complete-text comprehension defect. Datasets and models are available.

The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting $\eta\in(0,1]$ as the fraction of data with correctly matched modalities among $n$ paired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: $(i)$ the error without filtering is upper and lower bounded by $\frac{1}{\eta \sqrt{n}}$, and $(ii)$ the error with teacher-based filtering is upper bounded by $\frac{1}{\sqrt{\eta n}}$ in the large $\eta$ regime, and by $\frac{1}{\sqrt{n}}$ in the small $\eta$ regime.

Machine learning (ML) algorithms deployed in real-world environments are often faced with the challenge of adapting models to concept drift, where the task data distributions are shifting over time. The problem becomes even more difficult when model performance must be maintained under adherence to strict resource constraints. Existing solutions often depend on drift-detection methods that produce high computational overhead for resource-constrained environments, and fail to provide strict guarantees on resource usage or theoretical performance assurances. To address these shortcomings, we propose RCCDA: a dynamic model update policy that optimizes ML training dynamics while ensuring compliance to predefined resource constraints, utilizing only past loss information and a tunable drift threshold. In developing our policy, we analytically characterize the evolution of model loss under concept drift with arbitrary training update decisions. Integrating these results into a Lyapunov drift-plus-penalty framework produces a lightweight greedy-optimal policy that provably limits update frequency and cost. Experimental results on four domain generalization datasets demonstrate that our policy outperforms baseline methods in inference accuracy while adhering to strict resource constraints under several schedules of concept drift, making our solution uniquely suited for real-time ML deployments.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical ``what if?'' scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes -- blackbox and concept-based predictors -- and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

Open-World Object Detection (OWOD) enriches traditional object detectors by enabling continual discovery and integration of unknown objects via human guidance. However, existing OWOD approaches frequently suffer from semantic confusion between known and unknown classes, alongside catastrophic forgetting, leading to diminished unknown recall and degraded known-class accuracy. To overcome these challenges, we propose **C**ombinato**r**ial **O**pen-**W**orld **D**etection (**CROWD**), a unified framework reformulating unknown object discovery and adaptation as an interwoven combinatorial (set-based) data-discovery (CROWD-Discover) and representation learning (CROWD-Learn) task. CROWD-Discover strategically mines unknown instances by maximizing Submodular Conditional Gain (SCG) functions, selecting representative examples distinctly dissimilar from known objects. Subsequently, CROWD-Learn employs novel combinatorial objectives that jointly disentangle known and unknown representations while maintaining discriminative coherence among known classes, thus mitigating confusion and forgetting. Extensive evaluations on OWOD benchmarks illustrate that CROWD achieves improvements of 2.83% and 2.05% in known-class accuracy on M-OWODB and S-OWODB, respectively, and nearly 2.4$\times$ unknown recall compared to leading baselines.

In human-AI interaction, effective communication relies on aligning the AI agent’s model with the human user’s mental model -- a process known as model reconciliation. However, existing model reconciliation approaches predominantly assume deterministic models, overlooking the fact that human knowledge is often uncertain or probabilistic. To bridge this gap, we present a probabilistic model reconciliation framework that resolves inconsistencies in MPE outcome probabilities between an agent’s and a user’s models. Our approach is built on probabilistic logic programming (PLP) using ProbLog, where explanations are generated as cost-optimal model updates that reconcile these probabilistic differences. We develop two search algorithms - a generic baseline and an optimized version. The latter is guided by theoretical insights and further extended with greedy and weighted variants to enhance scalability and efficiency. Our approach is validated through a user study on explanation types and computational experiments showing that the optimized version consistently outperforms the generic baseline.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the linegraph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. The complete code is available at https://github.com/ml-jku/plstm_experiments.

This paper introduces a general method for the exploration of equivalence classes in the input space of Transformer models. The proposed approach is based on sound mathematical theory which describes the internal layers of a Transformer architecture as sequential deformations of the input manifold. Using eigendecomposition of the pullback of the distance metric defined on the output space through the Jacobian of the model, we are able to reconstruct equivalence classes in the input space and navigate across them. Our method enables two complementary exploration procedures: the first retrieves input instances that produce the same class probability distribution as the original instance—thus identifying elements within the same equivalence class—while the second discovers instances that yield a different class probability distribution, effectively navigating toward distinct equivalence classes. Finally, we demonstrate how the retrieved instances can be meaningfully interpreted by projecting their embeddings back into a human-readable format.

The diffusion inversion problem seeks to recover the latent generative trajectory of a diffusion model given a real image. Faithful inversion is critical for ensuring consistency in diffusion-based image editing. Prior works formulate this task as a fixed-point problem and solve it using numerical methods. However, achieving both accuracy and efficiency remains challenging, especially for few-step models and novel samples. In this paper, we propose ***PreciseInv***, a general-purpose test-time optimization framework that enables fast and faithful inversion in as few as two inference steps. Unlike root-finding methods, we reformulate inversion as a learning problem and introduce a dynamic programming-inspired strategy to recursively estimate a parameterized sequence of noise embeddings. This design leverages the smoothness of the diffusion latent space for accurate gradient-based optimization and ensures memory efficiency via recursive subproblem construction. We further provide a theoretical analysis of ***PreciseInv***'s convergence and derive a provable upper bound on its reconstruction error. Extensive experiments on COCO 2017, DarkFace, and a stylized cartoon dataset show that ***PreciseInv*** achieves state-of-the-art performance in both reconstruction quality and inference speed. Improvements are especially notable for few-step models and under distribution shifts. Moreover, precise inversion yields substantial gains in editing consistency for text-driven image manipulation tasks. Code is available at: https://github.com/panda7777777/PreciseInv

Prediction with expert advice serves as a fundamental model in online learning and sequential decision-making. However, in many real-world settings, this classical model proves insufficient as the feedback available to the decision-maker is often subject to noise, errors, or communication constraints. This paper provides fundamental limits on performance, quantified by the regret, in the case when the feedback is corrupted by an additive noise. Our general analysis achieves sharp regret bounds for canonical examples of such additive noise as the Gaussian distribution, the uniform distribution, and a general noise with a log-concave density. This analysis demonstrates how different noise characteristics affect regret bounds and identifies how the regret fundamentally scales as a function of the properties of the noise distribution.

In modern optimization methods used in deep learning, each update depends on the history of previous iterations, often referred to as memory, and this dependence decays fast as the iterates go further into the past. For example, gradient descent with momentum has exponentially decaying memory through exponentially averaged past gradients. We introduce a general technique for identifying a memoryless algorithm that approximates an optimization algorithm with memory. It is obtained by replacing all past iterates in the update by the current one, and then adding a correction term arising from memory (also a function of the current iterate). This correction term can be interpreted as a perturbation of the loss, and the nature of this perturbation can inform how memory implicitly (anti-)regularizes the optimization dynamics. As an application of our theory, we find that Lion does not have the kind of implicit anti-regularization induced by memory that AdamW does, providing a theory-based explanation for Lion’s better generalization performance recently documented. Empirical evaluations confirm our theoretical findings.

In spite of their prevalence, the behaviour of Neural Networks when extrapolating far from the training distribution remains poorly understood, with existing results limited to specific cases. In this work, we prove general results---the first of their kind---by applying Neural Tangent Kernel (NTK) theory to analyse infinitely-wide neural networks trained until convergence and prove that the inclusion of just one Layer Norm (LN) fundamentally alters the induced NTK, transforming it into a bounded-variance kernel. As a result, the output of an infinitely wide network with at least one LN remains bounded, even on inputs far from the training data. In contrast, we show that a broad class of networks without LN can produce pathologically large outputs for certain inputs. We support these theoretical findings with empirical experiments on finite-width networks, demonstrating that while standard NNs often exhibit uncontrolled growth outside the training domain, a single LN layer effectively mitigates this instability. Finally, we explore real-world implications of this extrapolatory stability, including applications to predicting residue sizes in proteins larger than those seen during training and estimating age from facial images of underrepresented ethnicities absent from the training set.

Options markets represent one of the most sophisticated segments of the financial ecosystem, with prices that directly reflect market uncertainty. In this paper, we introduce the first reinforcement learning (RL) framework specifically designed for volatility trading through options, focusing on profit from the difference between implied volatility and realized volatility. Our multi-agent architecture consists of an Option Position Agent (OP-Agent) responsible for volatility timing by controlling long/short volatility positions, and a Hedger Routing Agent (HR-Agent) that manages risk and maximizes path-dependent profits by selecting optimal hedging strategies with different risk preferences. Evaluating our approach using cryptocurrency options data from 2021-2024, we demonstrate superior performance on BTC and ETH, significantly outperforming traditional strategies and machine learning baselines across all profit and risk-adjusted metrics while exhibiting sophisticated trading behavior. The code framework and sample data of this paper have been released on https://github.com/Edwicn/OPHR-MasteringVolatilityTradingwithMultiAgentDeepReinforcementLearning

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from **Thought Leaps** due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called **ScaleQM+**, based on the structured ScaleQuestMath dataset, and trained **CoT-Bridge** to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87\% on NuminaMath. Our approach effectively enhances distilled data (+3.02\%) and provides better starting points for reinforcement learning (+3.1\%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrates improved generalization to out-of-domain logical reasoning tasks, confirming that enhancing reasoning completeness yields broadly applicable benefits.