NeurIPS 2025 Papers

Retrieval-augmented generation (RAG) systems enhance large language models (LLMs) with external knowledge but are vulnerable to corpus poisoning and contamination attacks, which can compromise output integrity. Existing defenses often apply aggressive filtering, leading to unnecessary loss of valuable information and reduced reliability in generation. To address this problem, we propose a two-stage semantic filtering and conflict-free framework for trustworthy RAG. In the first stage, we perform a joint filter with semantic and cluster-based filtering which is guided by the Entity-intent-relation extractor (EIRE). EIRE extracts entities, latent objectives, and entity relations from both the user query and filtered documents, scores their semantic relevance, and selectively adds valuable documents into the clean retrieval database. In the second stage, we proposed an EIRE-guided conflict-aware filtering module, which analyzes semantic consistency between the query, candidate answers, and retrieved knowledge before final answer generation, filtering out internal and external contradictions that could mislead the model. Through this two-stage process, SeCon-RAG effectively preserves useful knowledge while mitigating conflict contamination, achieving significant improvements in both generation robustness and output trustworthiness. Extensive experiments across various LLMs and datasets demonstrate that the proposed SeCon-RAG markedly outperforms state-of-the-art defense methods.

We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious computational limitations. Although more scalable alternatives such as the Alpha complex or sparse Rips approximations exist, they often still result in a prohibitively large number of simplices. This poses challenges in the complex construction and in the subsequent PH computation, prohibiting their use on large-scale point clouds. To mitigate these issues, we introduce the Flood complex, inspired by the advantages of the Alpha and Witness complex constructions. Informally, at a given filtration value $r\geq 0$, the Flood complex contains all simplices from a Delaunay triangulation of a small subset of a point cloud $X$ that are fully covered by the union of balls of radius $r$ emanating from $X$, a process we call flooding. Our construction allows for efficient PH computation, possesses several desirable theoretical properties, and is amenable to GPU parallelization. Scaling experiments on 3D point cloud data show that we can compute PH of up to dimension 2 on several millions of points. Importantly, when evaluating object classification performance on real-world and synthetic data, we provide evidence that this scaling capability is needed, especially if objects are geometrically or topologically complex, yielding performance superior to other PH-based methods and neural networks for point cloud data. Source code is available on GitHub: https://github.com/plus-rkwitt/flooder

Reward Models (RMs) are crucial to aligning large language models (LLMs), but the degree to which an RM specialized to one task (e.g. writing) generalizes to new tasks (e.g. math) is often not known a priori, often making using only one fixed RM to train LLMs suboptimal. However, optimizing LLMs with multiple RMs simultaneously can incur a prohibitively high computational cost and lead to conflicting signals from different RMs that may degrade performance. To address these challenges, we introduce LASeR (Learning to Adaptively Select Rewards), which frames reward model selection as a multi-armed bandit problem, iteratively and efficiently training LLMs using multiple RMs by selecting the most well-suited RM for each instance. On commonsense and math reasoning tasks, we show that LASeR boosts iterative LLM training, improving the absolute average accuracy of Llama-3-8B over three datasets by $2.67$% over an ensemble of RM scores while also showing superior efficiency (e.g., a $2\times$ speedup). Moreover, on WildChat (open-ended instruction-following tasks), LASeR leads to a $72.69$% AlpacaEval win rate over the RM score ensemble baseline. Extending to long-context generation, LASeR improves by $2.96$ F1 points (avg.) on single-document QA tasks and $2.97$ F1 points on few-shot learning over the RM score ensemble baseline with best-of-$n$ sampling. We include our code in the supplementary.

In recent years, large language models (LLMs) have made significant advancements in arithmetic reasoning. However, the internal mechanism of how LLMs solve arithmetic problems remains unclear. In this paper, we propose explaining arithmetic reasoning in LLMs using game-theoretic interactions. Specifically, we disentangle the output score of the LLM into numerous interactions between the input words. We quantify different types of interactions encoded by LLMs during forward propagation to explore the internal mechanism of LLMs for solving arithmetic problems. We find that (1) the internal mechanism of LLMs for solving simple one-operator arithmetic problems is their capability to encode operand-operator interactions and high-order interactions from input samples. Additionally, we find that LLMs with weak one-operator arithmetic capabilities focus more on background interactions. (2) The internal mechanism of LLMs for solving relatively complex two-operator arithmetic problems is their capability to encode operator interactions and operand interactions from input samples. (3) We explain the task-specific nature of the LoRA method from the perspective of interactions.

Recent advances in Large Language Models (LLMs) have propelled intelligent agents from reactive responses to proactive support. While promising, existing proactive agents either rely exclusively on observations from enclosed environments (e.g., desktop UIs) with direct LLM inference or employ rule-based proactive notifications, leading to suboptimal user intent understanding and limited functionality for proactive service. In this paper, we introduce ContextAgent, the first context-aware proactive agent that incorporates extensive sensory contexts surrounding humans to enhance the proactivity of LLM agents. ContextAgent first extracts multi-dimensional contexts from massive sensory perceptions on wearables (e.g., video and audio) to understand user intentions. ContextAgent then leverages the sensory contexts and personas from historical data to predict the necessity for proactive services. When proactive assistance is needed, ContextAgent further automatically calls the necessary tools to assist users unobtrusively. To evaluate this new task, we curate ContextAgentBench, the first benchmark for evaluating context-aware proactive LLM agents, covering 1,000 samples across nine daily scenarios and twenty tools. Experiments on ContextAgentBench show that ContextAgent outperforms baselines by achieving up to 8.5% and 6.0% higher accuracy in proactive predictions and tool calling, respectively. We hope our research can inspire the development of more advanced, human-centric, proactive AI assistants. The code and dataset are publicly available at https://github.com/openaiotlab/ContextAgent.

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing statistical theory for OT map estimation is quite restricted, hinging on Brenier's theorem (quadratic cost, absolutely continuous source) to guarantee existence and uniqueness of a deterministic OT map, on which various additional regularity assumptions are imposed to obtain quantitative error bounds. In many real‐world problems these conditions fail or cannot be certified, in which case optimal transportation is possible only via stochastic maps that can split mass. To broaden the scope of map estimation theory to such settings, this work introduces a novel metric for evaluating the transportation quality of stochastic maps. Under this metric, we develop computationally efficient map estimators with near-optimal finite-sample risk bounds, subject to easy-to-verify minimal assumptions. Our analysis further accommodates common forms of adversarial sample contamination, yielding estimators with robust estimation guarantees. Empirical experiments are provided which validate our theory and demonstrate the utility of the proposed framework in settings where existing theory fails. These contributions constitute the first general-purpose theory for map estimation, compatible with a wide spectrum of real-world applications where optimal transport may be intrinsically stochastic.

Large Language Models (LLMs) are typically trained on data mixtures: most data come from web scrapes, while a small portion is curated from high-quality sources with dense domain-specific knowledge. In this paper, we show that when training LLMs on such data mixtures, knowledge acquisition from knowledge-dense datasets—unlike training exclusively on knowledge-dense data—does not always follow a smooth scaling law but can exhibit phase transitions with respect to the mixing ratio and model size. Through controlled experiments on a synthetic biography dataset mixed with web-scraped data, we demonstrate that: (1) as we increase the model size to a critical value, the model suddenly transitions from memorizing very few to most of the biographies; (2) below a critical mixing ratio, the model memorizes almost nothing even with extensive training, but beyond this threshold, it rapidly memorizes more biographies. We attribute these phase transitions to a capacity allocation phenomenon: a model with bounded capacity must act like a knapsack problem solver to minimize the overall test loss, and the optimal allocation across datasets can change discontinuously as the model size or mixing ratio varies. We formalize this intuition in an information-theoretic framework and reveal that these phase transitions are predictable, with the critical mixing ratio following a power-law relationship with the model size. Our findings highlight a concrete case where a good mixing recipe for large models may not be optimal for small models, and vice versa.

Understanding how the human brain progresses from processing simple linguistic inputs to performing high-level reasoning is a fundamental challenge in neuroscience. While modern large language models (LLMs) are increasingly used to model neural responses to language, their internal representations are highly "entangled," mixing information about lexicon, syntax, meaning, and reasoning. This entanglement biases conventional brain encoding analyses toward linguistically shallow features (e.g., lexicon and syntax), making it difficult to isolate the neural substrates of cognitively deeper processes. Here, we introduce a residual disentanglement method that computationally isolates these components. By first probing an LM to identify feature-specific layers, our method iteratively regresses out lower-level representations to produce four nearly orthogonal embeddings for lexicon, syntax, meaning, and, critically, reasoning. We used these disentangled embeddings to model intracranial (ECoG) brain recordings from neurosurgical patients listening to natural speech. We show that: 1) This isolated reasoning embedding exhibits unique predictive power, accounting for variance in neural activity not explained by other linguistic features and even extending to the recruitment of visual regions beyond classical language areas. 2) The neural signature for reasoning is temporally distinct, peaking later (~350-400ms) than signals related to lexicon, syntax, and meaning, consistent with its position atop a processing hierarchy. 3) Standard, non-disentangled LLM embeddings can be misleading, as their predictive success is primarily attributable to linguistically shallow features, masking the more subtle contributions of deeper cognitive processing. Our work provides compelling neural evidence for an abstract reasoning computation during language comprehension and offers a robust framework for mapping distinct cognitive functions from artificial models to the human brain.

We present **Brain Harmony (BrainHarmonix)**, the first multimodal brain foundation model that unifies structural morphology and functional dynamics into compact 1D token representations. The model was pretrained on two of the largest neuroimaging datasets to date, encompassing 64,594 T1-weighted structural MRI 3D volumes (～ 14 million images) and 70,933 functional MRI (fMRI) time series. BrainHarmonix is grounded in two foundational neuroscience principles: *structure complements function* - structural and functional modalities offer distinct yet synergistic insights into brain organization; *function follows structure* - brain functional dynamics are shaped by cortical morphology. The modular pretraining process involves single-modality training with geometric pre-alignment followed by modality fusion through shared brain hub tokens. Notably, our dynamics encoder uniquely handles fMRI time series with heterogeneous repetition times (TRs), addressing a major limitation in existing models. BrainHarmonix is also the first to deeply compress high-dimensional neuroimaging signals into unified, continuous 1D tokens, forming a compact latent space of the human brain. BrainHarmonix achieves strong generalization across diverse downstream tasks, including neurodevelopmental and neurodegenerative disorder classification and cognition prediction - consistently outperforming previous approaches. Our models - pretrained on 8 H100 GPUs - aim to catalyze a new era of AI-driven neuroscience powered by large-scale multimodal neuroimaging.

Over the past decades, pansharpening has contributed greatly to numerous remote sensing applications, with methods evolving from theoretically grounded models to deep learning approaches and their hybrids. Though promising, existing methods rarely address pansharpening through the lens of underlying physical imaging processes. In this work, we revisit the spectral imaging mechanism and propose a novel physics‐informed neural operator framework for pansharpening, termed PINO, which faithfully models the end‐to‐end electro‐optical sensor process. Specifically, PINO operates as: (1) First, a spatial-spectral encoder pair is introduced to aggregate multi-granularity high-resolution panchromatic (PAN) and low-resolution multispectral (LRMS) features. (2) Subsequently, an iterative neural integral process utilizes these fused spatial-spectral characteristics to learn a continuous radiance field $L_i(x, y, \lambda)$ over spatial coordinates and wavelength, effectively emulating band-wise spectral integration. (3) Finally, the learned radiance field is modulated by the sensor’s spectral responsivity $R_b(\lambda)$ to produce physically consistent spatial–spectral fusion products. This physics-grounded fusion paradigm offers a principled solution for reconstructing high-resolution multispectral and hyperspectral images in accordance with sensor imaging physics, effectively harnessing the unique advantages of spectral data to better uncover real-world characteristics. Experiments on multiple benchmark datasets show that our method surpasses state-of-the-art fusion algorithms, achieving reduced spectral aberrations and finer spatial textures. Furthermore, extension to hyperspectral (HS) data demonstrates its generalizability and universality. The code will be available upon potential acceptance.

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. Under standard spectral decay assumptions, we develop a novel blockwise decomposition method that enables precise concentration analysis for dependent data. Using this technique, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

Watermarking, the practice of embedding imperceptible information into media such as images, videos, audio, and text, is essential for intellectual property protection, content provenance and attribution. The growing complexity of digital ecosystems necessitates watermarks for different uses to be embedded in the same media. However, to detect and decode all watermarks, they need to coexist well with one another. We perform the first study of coexistence of deep image watermarking methods and, contrary to intuition, we find that various open-source watermarks can coexist with only minor impacts on image quality and decoding robustness. The coexistence of watermarks also opens the avenue for ensembling watermarking methods. We show how ensembling can increase the overall message capacity and enable new trade-offs between capacity, accuracy, robustness and image quality, without needing to retrain the base models.

Recent advancements underscore the significant role of Reinforcement Learning (RL) in enhancing the Chain-of-Thought (CoT) reasoning capabilities of large language models (LLMs). Two prominent RL algorithms, Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO), are central to these developments, showcasing different pros and cons. Autoregressive image generation, also interpretable as a sequential CoT reasoning process, presents unique challenges distinct from LLM-based CoT reasoning. These encompass ensuring text-image consistency, improving image aesthetic quality, and designing sophisticated reward models, rather than relying on simpler rule-based rewards. While recent efforts have extended RL to this domain, these explorations typically lack an in-depth analysis of the domain-specific challenges and the characteristics of different RL strategies. To bridge this gap, we provide the first comprehensive investigation of the GRPO and DPO algorithms in autoregressive image generation, evaluating their ***in-domain*** performance and ***out-of-domain*** generalization, while scrutinizing the impact of ***different reward models*** on their respective capabilities. Our findings reveal that GRPO and DPO exhibit distinct advantages, and crucially, that reward models possessing stronger intrinsic generalization capabilities potentially enhance the generalization potential of the applied RL algorithms. Furthermore, we systematically explore ***three prevalent scaling strategies*** to enhance both their in-domain and out-of-domain proficiency, deriving unique insights into efficiently scaling performance for each paradigm. We hope our study paves a new path for inspiring future work on developing more effective RL algorithms to achieve robust CoT reasoning in the realm of autoregressive image generation.

Coordinate denoising has emerged as a promising method for 3D molecular pretraining due to its theoretical connection to learning molecular force field. However, existing denoising methods rely on oversimplied molecular dynamics that assume atomic motions to be isotropic and homoscedastic. To address these limitations, we propose a novel denoising framework AniDS: Anisotropic Variational Autoencoder for 3D Molecular Denoising. AniDS introduces a structure-aware anisotropic noise generator that can produce atom-specific, full covariance matrices for Gaussian noise distributions to better reflect directional and structural variability in molecular systems. These covariances are derived from pairwise atomic interactions as anisotropic corrections to an isotropic base. Our design ensures that the resulting covariance matrices are symmetric, positive semi-definite, and SO(3)-equivariant, while providing greater capacity to model complex molecular dynamics. Extensive experiments show that AniDS outperforms prior isotropic and homoscedastic denoising models and other leading methods on the MD17 and OC22 benchmarks, achieving average relative improvements of 8.9% and 6.2% in force prediction accuracy. Our case study on a crystal and molecule structure shows that AniDS adaptively suppresses noise along the bonding direction, consistent with physicochemical principles. Our code is available at https://github.com/ZeroKnighting/AniDS.

This paper proposes the Dual-Stage Sparse Attention (DuSA) mechanism for attention acceleration of transformers. In the first stage, DuSA performs intrablock sparse attention to aggregate local inductive biases. In the second stage, DuSA performs interblock sparse attention to obtain long-range dependencies. Both stages have low computational complexity and can be further accelerated by memory acceleration attention mechanisms directly, which makes DuSA faster than some extremely fast attention mechanisms. The dual-stage sparse attention design provides a lower error in approximating vanilla scaled-dot product attention than the basic single-stage sparse attention mechanisms and further advances the basic sparse attention mechanisms to match or even outperform vanilla scaled-dot product attention. Even in some plug and play situations, DuSA can still maintain low performance loss. DuSA can be used in both training and inference acceleration. DuSA achieves leading performance in different benchmarks: long range arena, image classification, semantic segmentation, object detection, text to video generation, and long context understanding, and accelerates models of different sizes.

Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as $\Theta(d)$, leading to dimension-dependent convergence rates without further assumptions on the objective function, which is prohibitive for large-scale LLM parameters. To address this problem, we present a Pseudo-Zeroth-Order (PseuZO) framework for optimizing composite objective functions, especially large-scale models: $ \min_{\mathbf{x} \in \mathcal{X}} \mathcal{F}(\mathbf{x})= \bbE_{\mathbf{z}} g\circ h(\mathbf{x};\mathbf{z}) $, where $h$ represents complex, high-dimensional representations and $g$ is a task-specific loss. While existing zeroth-order methods estimate gradients with final loss functions, our PseuZO algorithm estimate the Jacobian matrix of $h(\mathbf{x})$ with the model output $\mathbf{o}= h(\mathbf{x})$, and the gradient of the loss function on model output $\mathbf{e} = \nabla_{\mathbf{o}} g(\mathbf{o})$, and apply exponential moving average on Jacobian estimators to reduce the variance. Moreover, we use the sliding window technique to reduce memory costs. Our algorithm achieves an $O( \max \lbrace \alpha_1 L\epsilon^{-2}, \alpha_1 L \sigma_2^2\epsilon^{-4} \rbrace )$ convergence rate, where $\alpha_1$ is the effective dimension of $\mathcal{F}$. Experimental results demonstrate that PseuZO outperforms MeZO and MeZO-SVRG in classification, multiple choice and generation tasks in both full-parameter and PEFT fine-tuning settings by boosting convergence in the early stages of training. For instance, under the same computation time, with respect to SST2 task, PesuZO gets 9.8\% higher accuracy than MeZO (91.2\% v.s. 82.4\%). With the sliding window technique, our PseuZO achieves $70\%\sim80\%$ memory reduction compared to FO-SGD for different model sizes as PseuZO only introduced a small dimension-independent memory overhead, which enables efficient scaling of the model size. The code is available at https://github.com/YangBigMn/PseuZO. $\newcommand{\bbE}{\mathbb{E}}$

Recent trends in test-time scaling for reasoning models (e.g., OpenAI o1, DeepSeek R1) have led to a popular belief that extending thinking traces using prompts like “Wait” or “Let me rethink” can improve performance. This raises a natural question: Does thinking more at test-time truly lead to better reasoning? To answer this question, we perform a detailed empirical study across models and benchmarks, which reveals a consistent pattern of initial performance improvements from additional thinking followed by a decline, due to "overthinking". To understand this non-monotonic trend, we consider a simple probabilistic model, which reveals that additional thinking increases output variance—creating an illusion of improved reasoning while ultimately undermining precision. Thus, observed gains from "more thinking" are not true indicators of improved reasoning, but artifacts stemming from the connection between model uncertainty and evaluation metric. This suggests that test-time scaling through extended thinking is not an effective way to utilize the inference thinking budget. Recognizing these limitations, we introduce an alternative test-time scaling approach, parallel thinking, inspired by Best-of-N sampling. Our method generates multiple independent reasoning paths within the same inference budget and selects the most consistent response via majority vote, achieving up to 20% higher accuracy compared to extended thinking. This provides a simple yet effective mechanism for test-time scaling of reasoning models.

Math reasoning has been one crucial ability of large language models (LLMs), where significant advancements have been achieved in recent years. However, most efforts focus on LLMs by curating high-quality annotation data and intricate training (or inference) paradigms, while the math reasoning performance of multi-modal LLMs (MLLMs) remains lagging behind. Since the MLLM typically consists of an LLM and vision block, we wonder: \textit{Can MLLMs directly absorb math reasoning abilities from off-the-shelf math LLMs without tuning?} Recent model-merging approaches may offer insights into this question. However, they overlook the alignment between the MLLM and LLM, where we find that there is a large gap between their parameter spaces, resulting in lower performance. Our empirical evidence reveals two key factors behind this issue: the identification of crucial reasoning-associated layers in the model and the mitigation of the gaps in parameter space. Based on the empirical insights, we propose \textbf{IP-Merging} that first \textbf{I}dentifies the reasoning-associated parameters in both MLLM and Math LLM, then \textbf{P}rojects them into the subspace of MLLM aiming to maintain the alignment, finally merges parameters in this subspace. IP-Merging is a tuning-free approach since parameters are directly adjusted. Extensive experiments demonstrate that our IP-Merging method can enhance the math reasoning ability of MLLMs directly from Math LLMs without compromising their other capabilities.

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by outliers, standard GPs and their sparse approximations struggle with computational tractability and robustness. We introduce Robust Computation-aware Gaussian Process (RCaGP), a novel GP model that jointly addresses these challenges by combining a principled treatment of approximation-induced uncertainty with robust generalized Bayesian updating. The key insight is that robustness and approximation-awareness are not orthogonal but intertwined: approximations can exacerbate the impact of outliers, and mitigating one without the other is insufficient. Unlike previous work that focuses narrowly on either robustness or approximation quality, RCaGP combines both in a principled and scalable framework, thus effectively managing both outliers and computational uncertainties introduced by approximations such as low-rank matrix multiplications. Our model ensures more conservative and reliable uncertainty estimates, a property we rigorously demonstrate. Additionally, we establish a robustness property and show that the mean function is key to preserving it, motivating a tailored model selection scheme for robust mean functions. Empirical results confirm that solving these challenges jointly leads to superior performance across both clean and outlier-contaminated settings, both on regression and high-throughput Bayesian optimization benchmarks.