NeurIPS 2025 论文列表

Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gröbner and Border bases are fundamental but suffer from high computational costs, which have motivated recent Deep Learning approaches to improve efficiency, albeit at the expense of output correctness. In this work, we introduce the Oracle Border Basis Algorithm, the first Deep Learning approach that accelerates Border basis computation while maintaining output guarantees. To this end, we design and train a Transformer-based oracle that identifies and eliminates computationally expensive reduction steps, which we find to dominate the algorithm's runtime. By selectively invoking this oracle during critical phases of computation, we achieve substantial speedup factors of up to 3.5x compared to the base algorithm, without compromising the correctness of results. To generate the training data, we develop a sampling method and provide the first sampling theorem for border bases. We construct a tokenization and embedding scheme tailored to monomial-centered algebraic computations, resulting in a compact and expressive input representation, which reduces the number of tokens to encode an $n$-variate polynomial by a factor of $O(n)$. Our learning approach is data efficient, stable, and a practical enhancement to traditional computer algebra algorithms and symbolic computation.

We investigate the mechanism underlying a previously identified phenomenon in Vision Transformers -- the emergence of high-norm tokens that lead to noisy attention maps (Darcet et al., 2024). We observe that in multiple models (e.g., CLIP, DINOv2), a sparse set of neurons is responsible for concentrating high-norm activations on outlier tokens, leading to irregular attention patterns and degrading downstream visual processing. While the existing solution for removing these outliers involves retraining models from scratch with additional learned $\textit{register tokens}$, we use our findings to create a training-free approach to mitigate these artifacts. By shifting the high-norm activations from our discovered $\textit{register neurons}$ into an additional untrained token, we can mimic the effect of register tokens on a model already trained without registers. We demonstrate that our method produces cleaner attention and feature maps, enhances performance over base models across multiple downstream visual tasks, and achieves results comparable to models explicitly trained with register tokens. We then extend test-time registers to off-the-shelf vision-language models, yielding cleaner attention-based, text-to-image attribution. Finally, we outline a simple mathematical model that reflects the observed behavior of register neurons and high norm tokens. Our results suggest that test-time registers effectively take on the role of register tokens at test-time, offering a training-free solution for any pre-trained model released without them.

Recent advances in Large Language Models (LLMs) have shown promise in function-level code generation, yet repository-level software engineering tasks remain challenging. Current solutions predominantly rely on proprietary LLM agents, which introduce unpredictability and limit accessibility, raising concerns about data privacy and model customization. This paper investigates whether open-source LLMs can effectively address repository-level tasks without requiring agent-based approaches. We demonstrate this is possible by enabling LLMs to comprehend functions and files within codebases through their semantic information and structural dependencies. To this end, we introduce Code Graph Models (CGMs), which integrate repository code graph structures into the LLM's attention mechanism and map node attributes to the LLM's input space using a specialized adapter. When combined with an agentless graph RAG framework, our approach achieves a 43.00% resolution rate on the SWE-bench Lite benchmark using the open-source Qwen2.5-72B model. This performance ranks first among open weight models, second among methods with open-source systems, and eighth overall, surpassing the previous best open-source model-based method by 12.33%.

In recent years, neural network-guided heuristic search algorithms, such as Monte-Carlo tree search and A$^\*$ search, have achieved significant advancements across diverse practical applications. Due to the challenges stemming from high state-space complexity, sparse training datasets, and incomplete environmental modeling, heuristic estimations manifest uncontrolled inherent biases towards the actual expected evaluations, thereby compromising the decision-making quality of search algorithms. Sampling exploration enhanced A$^\*$ (SeeA$^\*$) was proposed to improve the efficiency of A$^\*$ search by constructing an dynamic candidate subset through random sampling, from which the expanded node was selected. However, uniform sampling strategy utilized by SeeA$^\*$ facilitates exploration exclusively through the injection of randomness, which completely neglects the heuristic knowledge relevant to open nodes. Moreover, the theoretical support of cluster sampling remains ambiguous. Despite the existence of potential biases, heuristic estimations still encapsulate certain valuable information. In this paper, epistemic exploratory A$^\*$ search (KeeA$^\*$) is proposed to integrate heuristic knowledge for calibrating the sampling process. We first theoretically demonstrate that SeeA$^\*$ with cluster sampling outperforms uniform sampling due to the distribution-aware selection with higher variance. Building on this insight, cluster scouting and path-aware sampling are introduced in KeeA$^\*$ to further exploit heuristic knowledge to increase the sampling mean and variance, respectively, thereby generating higher-quality extreme candidates and enhancing overall decision-making performance. Finally, empirical results on retrosynthetic planning and logic synthesis demonstrate superior performance of KeeA$^*$ compared to state-of-the-art heuristic search algorithms.

A central challenge in organ transplantation is the extremely low acceptance rate of donor organ offers—typically in the single digits—leading to high discard rates and suboptimal use of available grafts. Current acceptance models embedded in allocation systems are non-causal, trained on observational data, and fail to generalize to policy-relevant counterfactuals. This limits their reliability for both policy evaluation and simulator-based optimization. In this work, we reframe organ offer acceptance as a counterfactual prediction problem and propose a method to learn from routinely recorded—but often overlooked—refusal explanations. These refusal reasons act as direction-only counterfactual signals: for example, a refusal reason such as "old donor age" implies acceptance might have occurred had the donor been younger. We formalize this setting and introduce ClexNet, a novel causal model that learns policy-invariant representations via balanced training and an explanation-guided augmentation loss. On both synthetic and semi-synthetic data, ClexNet outperforms existing acceptance models in predictive performance, generalization, and calibration, offering a robust drop-in improvement for simulators and allocation policy evaluation. Beyond transplantation, our approach provides a general method for incorporating human direction-only explanations as a form of model supervision, improving performance in settings where only observational data is available.

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities in math and coding, often bolstered by post-training on the chain-of-thoughts (CoTs) generated by stronger models. However, existing strategies for curating such training data predominantly rely on heuristics, limiting generalizability and failing to capture subtleties underlying in data. To address these limitations, we leverage influence functions to systematically attribute LLMs' reasoning ability on math and coding to individual training examples, sequences, and tokens, enabling deeper insights into effective data characteristics. Our Influence-based Reasoning Attribution (Infra) uncovers nontrivial cross-domain effects across math and coding tasks: high-difficulty math examples improve both math and code reasoning, while low-difficulty code tasks most effectively benefit code reasoning. Based on these findings, we introduce a simple yet effective dataset reweighting strategy by flipping task difficulty, which doubles AIME24 accuracy from 10\% to 20\% and boosts LiveCodeBench accuracy from 33.8\% to 35.3\% for Qwen2.5-7B-Instruct. Moreover, our fine-grained attribution reveals that the sequence-level exploratory behaviors enhance reasoning performance in both math and code, and the token-level influence patterns are distinct for math and code reasoning: the former prefers natural language logic connectors and the latter emphasizes structural syntax.

Vision-language models (VLMs) excel at descriptive tasks, but whether they truly understand scenes from visual observations remains uncertain. We introduce IR3D-Bench, a benchmark challenging VLMs to demonstrate understanding through active creation rather than passive recognition. Grounded in the analysis-by-synthesis paradigm, IR3D-Bench tasks Vision-Language Agents (VLAs) with actively using programming and rendering tools to recreate the underlying 3D structure of an input image, achieving agentic inverse rendering through tool use. This ''understanding-by-creating'' approach probes the tool-using generative capacity of VLAs, moving beyond the descriptive or conversational capacity measured by traditional scene understanding benchmarks. We provide a comprehensive suite of metrics to evaluate geometric accuracy, spatial relations, appearance attributes, and overall plausibility. Initial experiments on agentic inverse rendering powered by various state-of-the-art VLMs highlight current limitations, particularly in visual precision rather than basic tool usage. IR3D-Bench, including data and evaluation protocols, is released to facilitate systematic study and development of tool-using VLAs towards genuine scene understanding by creating.

Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing methods often suffer from uncontrolled generation, insufficient quality, and limited diversity in reasoning paths. Recent efforts leverage code to enhance CoT by grounding reasoning in executable steps, but such methods are typically constrained to predefined mathematical problems, hindering scalability and generalizability. In this work, we propose \texttt{Caco} (Code-Assisted Chain-of-ThOught), a novel framework that automates the synthesis of high-quality, verifiable, and diverse instruction-CoT reasoning data through code-driven augmentation. Unlike prior work, \texttt{Caco} first fine-tunes a code-based CoT generator on existing math and programming solutions in a unified code format, then scales the data generation to a large amount of diverse reasoning traces. Crucially, we introduce automated validation via code execution and rule-based filtering to ensure logical correctness and structural diversity, followed by reverse-engineering filtered outputs into natural language instructions and language CoTs to enrich task adaptability. This closed-loop process enables fully automated, scalable synthesis of reasoning data with guaranteed executability. Experiments on our created \texttt{Caco}-1.3M dataset demonstrate that \texttt{Caco}-trained models achieve strong competitive performance on mathematical reasoning benchmarks, outperforming existing strong baselines. Further analysis reveals that \texttt{Caco}’s code-anchored verification and instruction diversity contribute to superior generalization across unseen tasks. Our work establishes a paradigm for building self-sustaining, trustworthy reasoning systems without human intervention.

Machine learning-based decision support systems are increasingly deployed in clinical settings, where probabilistic scoring functions are used to inform and prioritize patient management decisions. However, widely used scoring rules, such as accuracy and AUC-ROC, fail to adequately reflect key clinical priorities, including calibration, robustness to distributional shifts, and sensitivity to asymmetric error costs. In this work, we propose a principled yet practical evaluation framework for selecting calibrated thresholded classifiers that explicitly accounts for uncertainty in class prevalences and domain-specific cost asymmetries. Building on the theory of proper scoring rules, particularly the Schervish representation, we derive an adjusted variant of cross-entropy (log score) that averages cost-weighted performance over clinically relevant ranges of class balance. The resulting evaluation is simple to apply, sensitive to clinical deployment conditions, and designed to prioritize models that are both calibrated and robust to real-world variations.

As large language models (LLMs) increasingly underpin technological advancements, the privacy of their training data emerges as a critical concern. Differential Privacy (DP) serves as a rigorous mechanism to protect this data, yet its integration via Differentially Private Stochastic Gradient Descent (DP-SGD) introduces substantial challenges, primarily due to the complexities of per-sample gradient clipping. Current explicit methods, such as Opacus, necessitate extensive storage for per-sample gradients, significantly inflating memory requirements. Conversely, implicit methods like GhostClip reduce storage needs by recalculating gradients multiple times, which leads to inefficiencies due to redundant computations. This paper introduces FlashDP, an innovative cache-friendly per-layer DP-SGD that consolidates necessary operations into a single task, calculating gradients only once in a fused manner. This approach not only diminishes memory movement by up to 50\% but also cuts down redundant computations by 20\%, compared to previous methods. Consequently, FlashDP does not increase memory demands and achieves a 90\% throughput compared to the Non-DP method on a four-A100 system during the pre-training of the Llama-13B model, while maintaining parity with standard per-layer clipped DP-SGD in terms of accuracy. These advancements establish FlashDP as a pivotal development for efficient and privacy-preserving training of LLMs. FlashDP's code has been open-sourced in https://github.com/kaustpradalab/flashdp.

Video aesthetic assessment, a vital area in multimedia computing, integrates computer vision with human cognition. Its progress is limited by the lack of standardized datasets and robust models, as the temporal dynamics of video and multimodal fusion challenges hinder direct application of image-based methods. This study introduces VADB, the largest video aesthetic database with 10,490 diverse videos annotated by 37 professionals across multiple aesthetic dimensions, including overall and attribute-specific aesthetic scores, rich language comments and objective tags. We propose VADB-Net, a dual-modal pre-training framework with a two-stage training strategy, which outperforms existing video quality assessment models in scoring tasks and supports downstream video aesthetic assessment tasks. The dataset and source code are available at https://github.com/BestiVictory/VADB.

Linear RNNs with gating recently demonstrated competitive performance compared to Transformers in language modeling. Although their linear compute scaling in sequence length offers theoretical runtime advantages over Transformers, realizing these benefits in practice requires optimized custom kernels, as Transformers rely on the highly efficient Flash Attention kernels (Dao, 2024). Leveraging the chunkwise-parallel formulation of linear RNNs, Flash Linear Attention (FLA) (Yang & Zhang, 2024) shows that linear RNN kernels are faster than Flash Attention, by parallelizing over chunks of the input sequence. However, since the chunk size of FLA is limited, many intermediate states must be materialized in GPU memory. This leads to low arithmetic intensity and causes high memory consumption and IO cost, especially for long-context pre-training. In this work, we present Tiled Flash Linear Attention (TFLA), a novel kernel algorithm for linear RNNs, that enables arbitrary large chunk sizes and high arithmetic intensity by introducing an additional level of sequence parallelization within each chunk. First, we apply TFLA to the xLSTM with matrix memory, the mLSTM (Beck et al., 2024). Second, we propose an mLSTM variant with sigmoid input gate and reduced computation for even faster kernel runtimes at equal language modeling performance. In our speed benchmarks, we show that our new mLSTM kernels based on TFLA outperform highly optimized Flash Attention, Linear Attention and Mamba kernels, setting a new state of the art for efficient long-context sequence modeling primitives. Our code is available at: https://github.com/NX-AI/mlstm_kernels

In-Context Reinforcement Learning (ICRL) enables agents to learn automatically and on-the-fly from their interactive experiences. However, a major challenge in scaling up ICRL is the lack of scalable task collections. To address this, we propose the procedurally generated tabular Markov Decision Processes, named AnyMDP. Through a carefully designed randomization process, AnyMDP is capable of generating high-quality tasks on a large scale while maintaining relatively low structural biases. To facilitate efficient meta-training at scale, we further introduce decoupled policy distillation and induce prior information in the ICRL framework. Our results demonstrate that, with a sufficiently large scale of AnyMDP tasks, the proposed model can generalize to tasks that were not considered in the training set through versatile in-context learning paradigms. The scalable task set provided by AnyMDP also enables a more thorough empirical investigation of the relationship between data distribution and ICRL performance. We further show that the generalization of ICRL potentially comes at the cost of increased task diversity and longer adaptation periods. This finding carries critical implications for scaling robust ICRL capabilities, highlighting the necessity of diverse and extensive task design, and prioritizing asymptotic performance over few-shot adaptation.

Unlike reasoning, which often entails a deep sequence of deductive steps, complex real-world planning is characterized by the need to synthesize a broad spectrum of parallel and potentially conflicting information and constraints. For example, in travel planning scenarios, it requires the integration of diverse real-world information and user preferences. While LLMs show promise, existing methods with long-horizon thinking struggle with handling multifaceted constraints, leading to suboptimal solutions. Motivated by the challenges of real-world travel planning, this paper introduces the Multiple Aspects of Planning (MAoP), empowering LLMs with "wide-horizon thinking" to solve planning problems with multifaceted constraints. Instead of direct planning, MAoP leverages the strategist to conduct pre-planning from various aspects and provide the planning blueprint for planners, enabling strong inference-time scalability by scaling aspects to consider various constraints. In addition, existing benchmarks for multi-constraint planning are flawed because they assess constraints in isolation, ignoring causal dependencies within the constraints, e.g, travel planning, where past activities dictate future itinerary. To address this, we propose Travel-Sim, an agent-based benchmark assessing plans via real-world simulation, thereby inherently resolving these causal dependencies. This paper advances LLM capabilities in complex planning and offers novel insights for evaluating sophisticated scenarios through simulation.

Traditional continuous deep reinforcement learning (RL) algorithms employ deterministic or unimodal Gaussian actors, which cannot express complex multimodal decision distributions. This limitation can hinder their performance in diversity-critical scenarios. There have been some attempts to design online multimodal RL algorithms based on diffusion or amortized actors. However, these actors are intractable, making existing methods struggle with balancing performance, decision diversity, and efficiency simultaneously. To overcome this challenge, we first reformulate existing intractable multimodal actors within a unified framework, and prove that they can be directly optimized by policy gradient via reparameterization. Then, we propose a distance-based diversity regularization that does not explicitly require decision probabilities. We identify two diversity-critical domains, namely multi-goal achieving and generative RL, to demonstrate the advantages of multimodal policies and our method, particularly in terms of few-shot robustness. In conventional MuJoCo benchmarks, our algorithm also shows competitive performance. Moreover, our experiments highlight that the amortized actor is a promising policy model class with strong multimodal expressivity and high performance.

We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using \emph{cross-fluctuations}, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic normal distribution, samples undergo sharp, discrete transitions, eventually forming distinct events of a desired distribution while progressively revealing finer structure. As this process is reversible, these transitions also occur in reverse, where intermediate states progressively merge, tracing a path back to the initial distribution. We demonstrate that these transitions can be detected as discontinuities in $n^{\text{th}}$-order cross-fluctuations. For variance-preserving SDEs, we derive a closed-form for these cross-fluctuations that is efficiently computable for the reverse trajectory. %, thus tying cross-fluctuation dynamics to event formation within the desired distribution. We find that detecting these transitions directly boosts sampling efficiency, accelerates class-conditional and rare-class generation, and improves two zero-shot tasks--image classification and style transfer--without expensive grid search or retraining. We also show that this viewpoint unifies classical coupling and mixing from finite Markov chains with continuous dynamics while extending to stochastic SDEs and non Markovian samplers. Our framework therefore bridges discrete Markov chain theory, phase analysis, and modern generative modeling.

Estimating the geometric median of a dataset is a robust counterpart to mean estimation, and is a fundamental problem in computational geometry. Recently, [HSU24] gave an $(\epsilon, \delta)$-differentially private algorithm obtaining an $\alpha$-multiplicative approximation to the geometric median objective, $\frac 1 n \sum_{i \in [n]} \|\cdot - \mathbf{x}_i\|$, given a dataset $D$ of $x_i$ for $i \in [n]$. Their algorithm requires $n \gtrsim \sqrt d \cdot \frac 1 {\alpha\epsilon}$ samples, which they prove is information-theoretically optimal. This result is surprising because its error scales with the effective radius of $D$ (i.e., of a ball capturing most points), rather than the worst-case radius. We give an improved algorithm that obtains the same approximation quality, also using $n \gtrsim \sqrt d \cdot \frac 1 {\alpha\epsilon}$ samples, but in time $\widetilde{O}(nd + \frac d {\alpha^2})$. Our runtime is nearly-linear, plus the cost of the cheapest non-private first-order method due to [CLMPS16]. To achieve our results, we use subsampling and geometric aggregation tools inspired by FriendlyCore [TCKMS22] to speed up the "warm start" component of the [HSU24] algorithm, combined with a careful custom analysis of DP-SGD's sensitivity for the geometric median objective.

Kolmogorov-Arnold Networks (KANs) have demonstrated remarkable expressive capacity and predictive power in symbolic learning. However, existing generalization errors of KANs primarily focus on approximation errors while neglecting estimation errors, leading to a suboptimal bias-variance trade-off and poor generalization performance. Meanwhile, the unclear generalization mechanism hinders the design of more effective KANs variants. As the authors of KANs highlighted, they ``would like to explore ways to restrict KANs' hypothesis space so that they can achieve good performance''. To address these challenges, we explore the generalization mechanism of KANs and design more effective KANs with lower model complexity and better generalization. We define \textit{Lipschitz complexity} as the first structural measure for deep functions represented by KANs and derive novel generalization bounds based on \textit{Lipschitz complexity}, establishing a theoretical foundation for understanding their generalization behavior. To reduce \textit{Lipschitz complexity} and boost the generalization mechanism of KANs, we propose Lipschitz-Enhanced KANs ($\textbf{LipKANs}$) by integrating the Lip layer and pioneering the $L_{1.5}$-regularized loss, contributing to tighter generalization bounds. Empirical experiments validate that the proposed LipKANs enhance the generalization mechanism of KANs when modeling complex distributions. We hope our theoretical bounds and LipKANs lay a foundation for the future development of KANs.