NeurIPS 2025 Papers

Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers offer effective acceleration for diffusion sampling without observations, their application in inverse problems remains limited due to the heterogeneous formulations of inverse algorithms and their prevalent use of approximations and heuristics, which often introduce significant errors that undermine the reliability of analytical solvers. In this work, we begin with an analysis of ODE solvers for inverse problems that reveals a linear combination structure of approximations for the inverse trajectory. Building on this insight, we propose a canonical form that unifies a broad class of diffusion-based inverse algorithms and facilitates the design of more generalizable solvers. Inspired by the linear subspace search strategy, we propose Learnable Linear Extrapolation (LLE), a lightweight approach that universally enhances the performance of any diffusion-based inverse algorithm conforming to our canonical form. LLE optimizes the combination coefficients to refine current predictions using previous estimates, alleviating the sensitivity of analytical solvers for inverse algorithms. Extensive experiments demonstrate consistent improvements of the proposed LLE method across multiple algorithms and tasks, indicating its potential for more efficient solutions and boosted performance of diffusion-based inverse algorithms with limited steps. Codes for reproducing our experiments are available at https://github.com/weigerzan/LLE_inverse_problem.

Estimating hidden states in dynamical systems, also known as optimal filtering, is a long-standing problem in various fields of science and engineering. In this paper, we introduce a general filtering framework, $\textbf{LLM-Filter}$, which leverages large language models (LLMs) for state estimation by embedding noisy observations with text prototypes. In a number of experiments for classical dynamical systems, we find that first, state estimation can significantly benefit from the knowledge embedded in pre-trained LLMs. By achieving proper modality alignment with the frozen LLM, LLM-Filter outperforms the state-of-the-art learning-based approaches. Second, we carefully design the prompt structure, System-as-Prompt (SaP), incorporating task instructions that enable LLMs to understand tasks and adapt to specific systems. Guided by these prompts, LLM-Filter exhibits exceptional generalization, capable of performing filtering tasks accurately in changed or even unseen environments. We further observe a scaling-law behavior in LLM-Filter, where accuracy improves with larger model sizes and longer training times. These findings make LLM-Filter a promising foundation model of filtering.

Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterizes sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. We postulate the *Graphon Limit Hypothesis* and provide empirical evidence to support it. Leveraging this graphon representation, we derive a *Graphon Neural Tangent Kernel (Graphon NTK)* to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. Our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures.

As large language models (LLMs) are increasingly deployed in real-world applications, ensuring the safety of their outputs during decoding has become a critical challenge. However, existing decoding-time interventions, such as Contrastive Decoding, often force a severe trade-off between safety and response quality. In this work, we propose **CARE**, a novel framework for decoding-time safety alignment that integrates three key components: (1) a guard model for real-time safety monitoring, enabling detection of potentially unsafe content; (2) a rollback mechanism with a token buffer to correct unsafe outputs efficiently at an earlier stage without disrupting the user experience; and (3) a novel introspection-based intervention strategy, where the model generates self-reflective critiques of its previous outputs and incorporates these reflections into the context to guide subsequent decoding steps. The framework achieves a superior safety-quality trade-off by using its guard model for precise interventions, its rollback mechanism for timely corrections, and our novel introspection method for effective self-correction. Experimental results demonstrate that our framework achieves a superior balance of safety, quality, and efficiency, attaining a **low harmful response rate** and **minimal disruption to the user experience** while **maintaining high response quality**.

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https://github.com/tensorgi/TPA.

Large language models (LLMs) have achieved state-of-the-art performance in a variety of tasks, but remain largely opaque in terms of their internal mechanisms. Understanding these mechanisms is crucial to improve their reasoning abilities. Drawing inspiration from the interplay between neural processes and human cognition, we propose a novel interpretability framework to systematically analyze the roles and behaviors of attention heads, which are key components of LLMs. We introduce CogQA, a dataset that decomposes complex questions into step-by-step subquestions with a chain-of-thought design, each associated with specific cognitive functions such as retrieval or logical reasoning. By applying a multi-label probing method, we identify the attention heads responsible for these functions. Our analysis across multiple LLM families reveals that attention heads exhibit functional specialization, characterized as cognitive heads. These cognitive heads exhibit several key properties: they are universally sparse, and vary in number and distribution across different cognitive functions, and they display interactive and hierarchical structures. We further show that cognitive heads play a vital role in reasoning tasks—removing them leads to performance degradation, while augmenting them enhances reasoning accuracy. These insights offer a deeper understanding of LLM reasoning and suggest important implications for model design, training and fine-tuning strategies.

The growing use of generative models in daily life calls for efficient mechanisms to control their generation, to e.g. produce safe content or provide users with tools to explore style changes. Ideally, such mechanisms should require low volume of unpaired data (\ie without explicit preference), and should be cheap, both at train and inference time, while preserving output quality. Recent research has shown that such mechanisms can be obtained by intervening exclusively on model activations, with the goal of correcting distributional differences between activations seen when using prompts from a source vs. a target set (e.g. toxic and non-toxic sentences). While cheap, these fast methods are inherently crude: their maps are tuned locally, not accounting for their impact on downstream layers, resulting in interventions that cause unintended shifts when used out-of-sample. We propose in this work linear end-to-end activation steering (LinEAS), an approach trained with a global loss that accounts simultaneously for all layer-wise distributional shifts. In addition to being more robust, the loss used to train LinEAS can be regularized with sparsifying norms, which can automatically carry out neuron selection. LinEAS only requires a handful of unpaired samples to be effective, and beats similar baselines on toxicity mitigation in language models, becoming competitive with oracle-dependent methods that have access to strong supervision. LinEAS is modality-agnostic and we empirically find that it outperforms existing activation steering methods at mitigating and including new concepts at the output of single-step text-to-image generation models.

Spatial transcriptomics (ST) technologies provide gene expression measurements with spatial resolution, enabling the dissection of tissue structure and function. A fundamental challenge in ST analysis is clustering spatial spots into coherent functional regions. While existing models effectively integrate expression and spatial signals, they largely overlook sequence-level biological priors encoded in the DNA sequences of expressed genes. To bridge this gap, we propose SAINT (Sequence-Aware Integration for Nucleotide-informed Transcriptomics), a unified framework that augments spatial representation learning with nucleotide-derived features. We construct sequence-augmented datasets across 14 tissue sections from three widely used ST benchmarks (DLPFC, HBC, and MBA), retrieving reference DNA sequences for each expressed gene and encoding them using a pretrained Nucleotide Transformer. For each spot, gene-level embeddings are aggregated via expression-weighted and attention-based pooling, then fused with spatial-expression representations through a late fusion module. Extensive experiments demonstrate that SAINT consistently improves clustering performance across multiple datasets. Experiments validate the superiority, effectiveness, sensitivity, and transferability of our framework, confirming the complementary value of incorporating sequence-level priors into spatial transcriptomics clustering.

Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving state-of-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets. To bridge this gap, we present ShapeX, an innovative framework that segments time series into meaningful shapelet-driven segments and employs Shapley values to assess their saliency. At the core of ShapeX lies the Shapelet Describe-and-Detect (SDD) framework, which effectively learns a diverse set of shapelets essential for classification. We further demonstrate that ShapeX produces explanations which reveal causal relationships instead of just correlations, owing to the atomicity properties of shapelets. Experimental results on both synthetic and real-world datasets demonstrate that ShapeX outperforms existing methods in identifying the most relevant subsequences, enhancing both the precision and causal fidelity of time series explanations.

Visual In-Context Learning (VICL) has emerged as a prominent approach for adapting visual foundation models to novel tasks, by effectively exploiting contextual information embedded in in-context examples, which can be formulated as a global ranking problem of potential candidates. Current VICL methods, such as Partial2Global and VPR, are grounded in the similarity-priority assumption that images more visually similar to a query image serve as better in-context examples. This foundational assumption, while intuitive, lacks sufficient justification for its efficacy in selecting optimal in-context examples. Furthermore, Partial2Global constructs its global ranking from a series of randomly sampled pairwise preference predictions. Such a reliance on random sampling can lead to incomplete coverage and redundant samplings of comparisons, thus further adversely impacting the final global ranking. To address these issues, this paper introduces an enhanced variant of Partial2Global designed for reliable and holistic selection of in-context examples in VICL. Our proposed method, dubbed RH-Partial2Global, leverages a jackknife conformal prediction-guided strategy to construct reliable alternative sets and a covering design-based sampling approach to ensure comprehensive and uniform coverage of pairwise preferences. Extensive experiments demonstrate that RH-Partial2Global achieves excellent performance and outperforms Partial2Global across diverse visual tasks.

Synthetic data is crucial for advancing autonomous driving (AD) systems, yet current state-of-the-art video generation models, despite their visual realism, suffer from subtle geometric distortions that limit their utility for downstream perception tasks. We identify and quantify this critical issue, demonstrating a significant performance gap in 3D object detection when using synthetic versus real data. To address this, we introduce Reinforcement Learning with Geometric Feedback (RLGF), RLGF uniquely refines video diffusion models by incorporating rewards from specialized latent-space AD perception models. Its core components include an efficient Latent-Space Windowing Optimization technique for targeted feedback during diffusion, and a Hierarchical Geometric Reward (HGR) system providing multi-level rewards for point-line-plane alignment, and scene occupancy coherence. To quantify these distortions, we propose GeoScores. Applied to models like DiVE on nuScenes, RLGF substantially reduces geometric errors (e.g., VP error by 21\%, Depth error by 57\%) and dramatically improves 3D object detection mAP by 12.7\%, narrowing the gap to real-data performance. RLGF offers a plug-and-play solution for generating geometrically sound and reliable synthetic videos for AD development.

Preference-based reinforcement learning (PbRL) bypasses complex reward engineering by learning from human feedback. However, due to the high cost of obtaining feedback, PbRL typically relies on a limited set of preference-labeled samples. This data scarcity introduces two key inefficiencies: (1) the reward model overfits to the limited feedback, leading to poor generalization to unseen samples, and (2) the agent exploits the learned reward model, exacerbating overestimation of action values in temporal difference (TD) learning. To address these issues, we propose STAR, an efficient PbRL method that integrates preference margin regularization and policy regularization. Preference margin regularization mitigates overfitting by introducing a bounded margin in reward optimization, preventing excessive bias toward specific feedback. Policy regularization bootstraps a conservative estimate $\widehat{Q}$ from well-supported state-action pairs in the replay memory, reducing overestimation during policy learning. Experimental results show that STAR improves feedback efficiency, achieving 34.8\% higher performance in online settings and 29.7\% in offline settings compared to state-of-the-art methods. Ablation studies confirm that STAR facilitates more robust reward and value function learning. The videos of this project are released at https://sites.google.com/view/pbrl-star.

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both *likelihood modeling* and *generated text quality*. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the *Anchored Diffusion Language Model (ADLM)*, a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4\% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches. Please see our project page: [anchored-diffusion-llm.github.io](https://anchored-diffusion-llm.github.io/) for code and demo.

Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called *iterative polynomial filtering* and show a number of striking applications for supervised learning with contamination: (1) We show that any function class that can be approximated by low-degree polynomials with respect to a hypercontractive distribution can be efficiently learned under bounded contamination (also known as *nasty noise*). This is a surprising resolution to a longstanding gap between the complexity of agnostic learning and learning with contamination, as it was widely believed that low-degree approximators only implied tolerance to label noise. (2) For any function class that admits the (stronger) notion of sandwiching approximators, we obtain near-optimal learning guarantees even with respect to heavy additive contamination, where far more than $1/2$ of the training set may be added adversarially. Prior related work held only for regression and in a list-decodable setting. (3) We obtain the first efficient algorithms for tolerant testable learning of functions of halfspaces with respect to any fixed log-concave distribution. Even the non-tolerant case for a single halfspace in this setting had remained open. These results significantly advance our understanding of efficient supervised learning under contamination, a setting that has been much less studied than its unsupervised counterpart.

Recent endeavors in Multimodal Large Language Models (MLLMs) aim to unify visual comprehension and generation. However, these two capabilities remain largely independent, as if they are two separate functions encapsulated within the same model. Consequently, visual comprehension does not enhance visual generation, and the reasoning mechanisms of LLMs have not been fully integrated to revolutionize image generation. In this paper, we propose to enable the collaborative co-evolution of visual comprehension and generation, advancing image generation into an iterative introspective process. We introduce a two-stage training approach: supervised fine-tuning teaches the MLLM with the foundational ability to generate genuine CoT for visual generation, while reinforcement learning activates its full potential via an exploration-exploitation trade-off. Ultimately, we unlock the Aha moment in visual generation, advancing MLLMs from text-to-image tasks to unified image generation. Extensive experiments demonstrate that our model not only excels in text-to-image generation and image editing, but also functions as a superior image semantic evaluator with enhanced visual comprehension capabilities. Project Page: \url{https://janus-pro-r1.github.io}.

Recent advances in generative modeling have shown significant promise in designing novel periodic crystal structures. Existing approaches typically rely on either large language models (LLMs) or equivariant denoising models, each with complementary strengths: LLMs excel at handling discrete atomic types but often struggle with continuous features such as atomic positions and lattice parameters, while denoising models are effective at modeling continuous variables but encounter difficulties in generating accurate atomic compositions. To bridge this gap, we propose CrysLLMGen, a hybrid framework that integrates an LLM with a diffusion model to leverage their complementary strengths for crystal material generation. During sampling, CrysLLMGen first employs a fine-tuned LLM to produce an intermediate representation of atom types, atomic coordinates, and lattice structure. While retaining the predicted atom types, it passes the atomic coordinates and lattice structure to a pre-trained equivariant diffusion model for refinement. Our framework outperforms state-of-the-art generative models across several benchmark tasks and datasets. Specifically, CrysLLMGen not only achieves a balanced performance in terms of structural and compositional validity but also generates more stable and novel materials compared to LLM-based and denoising-based models Furthermore, CrysLLMGen exhibits strong conditional generation capabilities, effectively producing materials that satisfy user-defined constraints. Code is available at \url{https://github.com/kdmsit/crysllmgen}

Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a $\textit{landmark-based approximation}$: influence is precisely computed for a small subset of "landmark" samples and then efficiently propagated to all other samples to determine their weights. We validate Influence Distillation by applying it to instruction tuning on the Tulu V2 dataset, targeting a range of tasks including GSM8k, SQuAD, and MMLU, across several models from the Llama and Qwen families. Experiments show that Influence Distillation matches or outperforms state-of-the-art performance while achieving up to $3.5\times$ faster selection.

In this paper, we introduce FedMGP, a new paradigm for personalized federated prompt learning in vision-language models (VLMs). Existing federated prompt learning (FPL) methods often rely on a single, text-only prompt representation, which leads to client-specific overfitting and unstable aggregation under heterogeneous data distributions. Toward this end, FedMGP equips each client with multiple groups of paired textual and visual prompts, enabling the model to capture diverse, fine-grained semantic and instance-level cues. A diversity loss is introduced to drive each prompt group to specialize in distinct and complementary semantic aspects, ensuring that the groups collectively cover a broader range of local characteristics.During communication, FedMGP employs a dynamic prompt aggregation strategy based on similarity-guided probabilistic sampling: each client computes the cosine similarity between its prompt groups and the global prompts from the previous round, then samples s groups via a softmax-weighted distribution. This soft selection mechanism preferentially aggregates semantically aligned knowledge while still enabling exploration of underrepresented patterns—effectively balancing the preservation of common knowledge with client-specific features. Notably, FedMGP maintains parameter efficiency by redistributing a fixed prompt capacity across multiple groups, achieving state-of-the-art performance with the lowest communication parameters (5.1k) among all federated prompt learning methods. Theoretical analysis shows that our dynamic aggregation strategy promotes robust global representation learning by reinforcing shared semantics while suppressing client-specific noise. Extensive experiments demonstrate that FedMGP consistently outperforms prior approaches in both personalization and domain generalization across diverse federated vision-language benchmarks.The code will be released on https://github.com/weihao-bo/FedMGP.git.

Benchmarks are essential for quantitatively tracking progress in AI. As AI agents become increasingly capable, researchers and practitioners have introduced agentic benchmarks to evaluate agents on complex, real-world tasks. These benchmarks typically measure agent capabilities by evaluating task outcomes via specific reward designs. However, we show that many agentic benchmarks have issues in task setup or reward design. For example, SWE-bench-Verified uses insufficient test cases, while $\tau$-bench counts empty responses as successes. Such issues can lead to under- or overestimation of agents’ performance by up to 100% in relative terms. To make agentic evaluation rigorous, we introduce the Agentic Benchmark Checklist (ABC), a set of guidelines that we synthesized from our benchmark-building experience, a survey of best practices, and previously reported issues. When applied to CVE-Bench, a benchmark with a particularly complex evaluation design, ABC reduces performance overestimation by 33%.