NeurIPS 2025 Papers

We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention. We show that this reward function is adaptive submodular and provide a greedy policy with a provable near-optimal performance guarantee. A key technical challenge is to efficiently estimate the reward function without having to explicitly enumerate all the graphs in the equivalence class. We propose a sampling-based estimator using random matchings and analyze its bias and concentration behavior. Our simulation results show that performing a small number of interventions guided by our stochastic optimization framework recovers the true underlying causal structure.

Monte Carlo Tree Diffusion (MCTD) integrates diffusion models with structured tree search to enable effective trajectory exploration through stepwise reasoning. However, MCTD remains fundamentally limited by training trajectory lengths. While periodic replanning allows plan concatenation for longer plan generation, the planning process remains locally confined, as MCTD searches within individual trajectories without access to global context. We propose Compositional Monte Carlo Tree Diffusion (C-MCTD), a framework that elevates planning from individual trajectory optimization to reasoning over complete plan compositions. C-MCTD introduces three complementary components: (1) Online Composer, which performs globally-aware planning by searching across entire plan compositions; (2) Distributed Composer, which reduces search complexity through parallel exploration from multiple starting points; and (3) Preplan Composer, which accelerates inference by leveraging cached plan graphs.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of a direct MD approach. We validate FlashMD’s accuracy in reproducing equilibrium and time‐dependent properties, using both system‐specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

Theory of Mind (ToM), the ability to understand people's minds based on their behavior, is key to developing socially intelligent agents. Current approaches to ToM reasoning either rely on prompting Large Language Models (LLMs), which are prone to systematic errors, or use handcrafted, rigid agent models for model-based inference, which are more robust but fail to generalize across domains. In this work, we introduce *AutoToM*, an automated agent modeling method for scalable, robust, and interpretable mental inference. Given a ToM problem, *AutoToM* first proposes an initial agent model and then performs automated Bayesian inverse planning based on this model, leveraging an LLM backend. Guided by inference uncertainty, it iteratively refines the model by introducing additional mental variables and/or incorporating more timesteps in the context. Across five diverse benchmarks, *AutoToM* outperforms existing ToM methods and even large reasoning models. Additionally, we show that *AutoToM* can produce human‐like confidence estimates and enable online mental inference for embodied decision-making.

Learning how the world works is central to building AI agents that can adapt to complex environments. Traditional world models based on deep-learning demand vast amounts of training data, and do not flexibly update their knowledge from sparse observations. Recent advances in program synthesis using Large Language Models (LLMs) give an alternate approach which learns world models represented as source code, supporting strong generalization from little data. To date, application of program-structured world models remains limited to natural language and grid-world domains. We introduce a novel program synthesis method for effectively modeling complex, non-gridworld domains by representing a world model as an exponentially-weighted product of programmatic experts (PoE-World) synthesized by LLMs. We show that this approach can learn complex, stochastic world models from just a few observations. We evaluate the learned world models by embedding them in a model-based planning agent, demonstrating efficient performance and generalization to unseen levels on Atari's Pong and Montezuma's Revenge.

Optical flow estimation has achieved promising results in conventional scenes but faces challenges in high-speed and low-light scenes, which suffer from motion blur and insufficient illumination. These conditions lead to weakened texture and amplified noise and deteriorate the appearance saturation and boundary completeness of frame cameras, which are necessary for motion feature matching. In degraded scenes, the frame camera provides dense appearance saturation but sparse boundary completeness due to its long imaging time and low dynamic range. In contrast, the event camera offers sparse appearance saturation, while its short imaging time and high dynamic range gives rise to dense boundary completeness. Traditionally, existing methods utilize feature fusion or domain adaptation to introduce event to improve boundary completeness. However, the appearance features are still deteriorated, which severely affects the mostly adopted discriminative models that learn the mapping from visual features to motion fields and generative models that generate motion fields based on given visual features. So we introduce diffusion models that learn the mapping from noising flow to clear flow, which is not affected by the deteriorated visual features. Therefore, we propose a novel optical flow estimation framework Diff-ABFlow based on diffusion models with frame-event appearance-boundary fusion. Inspired by the appearance-boundary complementarity of frame and event, we propose an Attention-Guided Appearance-Boundary Fusion module to fuse frame and event. Based on diffusion models, we propose a Multi-Condition Iterative Denoising Decoder. Our proposed method can effectively utilize the respective advantages of frame and event, and shows great robustness to degraded input. In addition, we propose a dual-modal optical flow dataset for generalization experiments. Extensive experiments have verified the superiority of our proposed method. The code is released at <https://github.com/Haonan-Wang-aurora/Diff-ABFlow>.

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify their predictions' uncertainty, limiting their broader adoption in critical industrial applications. Uncertainty Quantification (UQ) for Deep Learning seeks to address this challenge by providing methodologies to improve the reliability of uncertainty estimates. While numerous techniques have been proposed, a unified tool remains lacking that offers a seamless workflow for evaluating and integrating these methods. To bridge this gap, we introduce **Torch-Uncertainty**, a *PyTorch* and *Lightning* framework designed to streamline the training and evaluation of DNNs with UQ techniques. In this paper, we outline the foundational principles of our library and present comprehensive experimental results that benchmark a diverse set of UQ methods across classification, segmentation, and regression tasks. Our library is available at: https://github.com/ENSTA-U2IS-AI/torch-uncertainty.

Contrastive learning has achieved remarkable success in self-supervised learning by pretraining a generalizable feature representation based on the augmentation invariance. Most existing approaches assume that different augmented views of the same instance (i.e., the *positive pairs*) remain semantically invariant. However, the augmentation results with *varying extent* may introduce semantic discrepancies or even content distortion, and thus the conventional (pseudo) supervision from augmentation invariance may lead to misguided learning objectives. In this paper, we propose a novel method called Contrastive Learning with Variable Similarity (CLVS) to accurately characterize the intrinsic similarity relationships between different augmented views. Our method dynamically adjusts the similarity based on the augmentation extent, and it ensures that strongly augmented views are always assigned lower similarity scores than weakly augmented ones. We provide a theoretical analysis to guarantee the effectiveness of the variable similarity in improving model generalizability. Extensive experiments demonstrate the superiority of our approach, achieving gains of 2.1\% on ImageNet-100 and 1.4\% on ImageNet-1k compared with the state-of-the-art methods.

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through *rewiring* or make use of *Graph Transformers*, which compromise the computational efficiency that characterized early spatial message passing architectures, and typically disregard the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNet model allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring. Across several benchmarks, Stable-ChebNet achieves near state-of-the-art performance.

Maritime object detection is essential for navigation safety, surveillance, and autonomous operations, yet constrained by two key challenges: the scarcity of annotated maritime data and poor generalization across various maritime attributes (e.g., object category, viewpoint, location, and imaging environment). To address these challenges, we propose Neptune-X, a data-centric generative-selection framework that enhances training effectiveness by leveraging synthetic data generation with task-aware sample selection. From the generation perspective, we develop X-to-Maritime, a multi-modality-conditioned generative model that synthesizes diverse and realistic maritime scenes. A key component is the Bidirectional Object-Water Attention module, which captures boundary interactions between objects and their aquatic surroundings to improve visual fidelity. To further improve downstream tasking performance, we propose Attribute-correlated Active Sampling, which dynamically selects synthetic samples based on their task relevance. To support robust benchmarking, we construct the Maritime Generation Dataset, the first dataset tailored for generative maritime learning, encompassing a wide range of semantic conditions. Extensive experiments demonstrate that our approach sets a new benchmark in maritime scene synthesis, significantly improving detection accuracy, particularly in challenging and previously underrepresented settings. The code is available at https://github.com/gy65896/Neptune-X.

Handwritten Mathematical Expression Recognition (HMER) remains a persistent challenge in Optical Character Recognition (OCR) due to the inherent freedom of symbol layouts and variability in handwriting styles. Prior methods have faced performance bottlenecks by proposing isolated architectural modifications, making them difficult to integrate coherently into a unified framework. Meanwhile, recent advances in pretrained vision-language models (VLMs) have demonstrated strong cross-task generalization, offering a promising foundation for developing unified solutions. In this paper, we introduce Uni-MuMER, which fully fine-tunes a VLM for the HMER task without modifying its architecture, effectively injecting domain-specific knowledge into a generalist framework. Our method integrates three data-driven tasks: Tree-Aware Chain-of-Thought (Tree-CoT) for structured spatial reasoning, Error-Driven Learning (EDL) for reducing confusion among visually similar characters, and Symbol Counting (SC) for improving recognition consistency in long expressions. Experiments on the CROHME and HME100K datasets show that Uni-MuMER achieves super state-of-the-art performance, outperforming the best lightweight specialized model SSAN by 16.31\% and the top-performing VLM Gemini2.5-flash by 24.42\% under zero-shot setting. Our datasets, models, and code are open-sourced at: https://github.com/BFlameSwift/Uni-MuMER

For an LLM to correctly respond to an instruction it must understand both the semantics and the domain (i.e., subject area) of a given task-instruction pair. However, syntax can also convey implicit information. Recent work shows that \textit{syntactic templates}---frequent sequences of Part-of-Speech (PoS) tags---are prevalent in training data and often appear in model outputs. In this work we characterize syntactic templates, domain, and semantics in task-instruction pairs. We identify cases of spurious correlations between syntax and domain, where models learn to associate a domain with syntax during training; this can sometimes override prompt semantics. Using a synthetic training dataset, we find that the syntactic-domain correlation can lower performance (mean 0.51 +/- 0.06) on entity knowledge tasks in OLMo-2 models (1B-13B). We introduce an evaluation framework to detect this phenomenon in trained models, and show that it occurs on a subset of the FlanV2 dataset in open (OLMo-2-7B; Llama-4-Maverick), and closed (GPT-4o) models. Finally, we present a case study on the implications for LLM security, showing that unintended syntactic-domain correlations can be used to bypass refusals in OLMo-2-7B Instruct and GPT-4o. Our findings highlight two needs: (1) to explicitly test for syntactic-domain correlations, and (2) to ensure \textit{syntactic} diversity in training data, specifically within domains, to prevent such spurious correlations.

Few-shot segmentation aims to segment unseen categories from just a handful of annotated examples. This requires mechanisms to identify semantically related objects across images and accurately produce masks. We note that Segment Anything 2 (SAM2), with its prompt-and-propagate mechanism, provides strong segmentation capabilities and a built-in feature matching process. However, we show that its representations are entangled with task-specific cues optimized for object tracking, which impairs its use for tasks requiring higher level semantic understanding. Our key insight is that, despite its class-agnostic pretraining, SAM2 already encodes rich semantic structure in its features. We propose SANSA (Semantically AligNed Segment Anything 2), a framework that makes this latent structure explicit, and repurposes SAM2 for few-shot segmentation through minimal task-specific modifications. SANSA achieves state-of-the-art on few-shot segmentation benchmarks designed to assess generalization and outperforms generalist methods in the popular in-context setting. Additionally, it supports flexible promptable interaction via points, boxes, or scribbles, and remains significantly faster and more compact than prior approaches. Code at: https://github.com/ClaudiaCuttano/SANSA.

Current image generation methods are based on a two-stage training approach. In stage 1, an auto-encoder is trained to compress an image into a latent space; in stage 2, a generative model is trained to learn a distribution over that latent space. This reveals a fundamental trade-off, do we compress more aggressively to make the latent distribution easier for the stage 2 model to learn even if it makes reconstruction worse? We study this problem in the context of discrete, auto-regressive image generation. Through the lens of scaling laws, we show that smaller stage 2 models can benefit from more compressed stage 1 latents even if reconstruction performance worsens, demonstrating that generation modeling capacity plays a role in this trade-off. Diving deeper, we rigorously study the connection between compute scaling and the stage 1 rate-distortion trade-off. Next, we introduce Causally Regularized Tokenization (CRT), which uses knowledge of the stage 2 generation modeling procedure to embed useful inductive biases in stage 1 latents. This regularization improves stage 2 generation performance better by making the tokens easier to model without affecting the stage 1 compression rate and marginally affecting distortion: we are able to improve compute efficiency 2-3$\times$ over baseline. Finally, we use CRT with further optimizations to the visual tokenizer setup to result in a generative pipeline that matches LlamaGen-3B generation performance (2.18 FID) with half the tokens per image (256 vs. 576) and a fourth the total model parameters (775M vs. 3.1B) while using the same architecture and inference procedure.

Proportional fairness criteria inspired by democratic ideals of proportional representation have received growing attention in the clustering literature. Prior work has investigated them in two separate paradigms. Chen et al. [ICML 2019] study _centroid clustering_, in which each data point's loss is determined by its distance to a representative point (centroid) chosen in its cluster. Caragiannis et al. [NeurIPS 2024] study _non-centroid clustering_, in which each data point's loss is determined by its maximum distance to any other data point in its cluster. We generalize both paradigms to introduce _semi-centroid clustering_, in which each data point's loss is a combination of its centroid and non-centroid losses, and study two proportional fairness criteria---the core and, its relaxation, fully justified representation (FJR). Our main result is a novel algorithm which achieves a constant approximation to the core, in polynomial time, even when the distance metrics used for centroid and non-centroid loss measurements are different. We also derive improved results for more restricted loss functions and the weaker FJR criterion, and establish lower bounds in each case.

In the incentivized exploration model, a principal aims to explore and learn over time by interacting with a sequence of self-interested agents. It has been recently understood that the main challenge in designing incentive-compatible algorithms for this problem is to gather a moderate amount of initial data, after which one can obtain near-optimal regret via posterior sampling. With high-dimensional contexts, however, this \emph{initial exploration} phase requires exponential sample complexity in some cases, which prevents efficient learning unless initial data can be acquired exogenously. We show that these barriers to exploration disappear under mild geometric conditions on the set of available actions, in which case incentive-compatibility does not preclude regret-optimality. Namely, we consider the linear bandit model with actions in the Euclidean unit ball, and give an incentive-compatible exploration algorithm with sample complexity that scales polynomially with the dimension and other parameters.

The real world is dynamic, yet most image fusion methods process static frames independently, ignoring temporal correlations in videos and leading to flickering and temporal inconsistency. To address this, we propose Unified Video Fusion (UniVF), a novel and unified framework for video fusion that leverages multi-frame learning and optical flow-based feature warping for informative, temporally coherent video fusion. To support its development, we also introduce Video Fusion Benchmark (VF-Bench), the first comprehensive benchmark covering four video fusion tasks: multi-exposure, multi-focus, infrared-visible, and medical fusion. VF-Bench provides high-quality, well-aligned video pairs obtained through synthetic data generation and rigorous curation from existing datasets, with a unified evaluation protocol that jointly assesses the spatial quality and temporal consistency of video fusion. Extensive experiments show that UniVF achieves state-of-the-art results across all tasks on VF-Bench. Project page: [vfbench.github.io](https://vfbench.github.io).

Selecting artificial intelligence (AI) models, such as large language models (LLMs), from multiple candidates requires accurate performance estimation. This is ideally achieved through empirical evaluations involving abundant real-world data. However, such evaluations are costly and impractical at scale. To address this challenge, autoevaluation methods leverage synthetic data produced by automated evaluators, such as LLMs-as-judges, reducing variance but potentially introducing bias. Recent approaches have employed semi-supervised prediction-powered inference ($\texttt{PPI}$) to correct for the bias of autoevaluators. However, the use of autoevaluators may lead in practice to a degradation in sample efficiency compared to conventional methods using only real-world data. In this paper, we propose $\texttt{R-AutoEval+}$, a novel framework that provides finite-sample reliability guarantees on the model evaluation, while also ensuring an enhanced (or at least no worse) sample efficiency compared to conventional methods. The key innovation of $\texttt{R-AutoEval+}$ is an adaptive construction of the model evaluation variable, which dynamically tunes its reliance on synthetic data, reverting to conventional methods when the autoevaluator is insufficiently accurate. Experiments on the use of LLMs-as-judges for the optimization of quantization settings for the weights of an LLM, for prompt design in LLMs, and for test-time reasoning budget allocation in LLMs confirm the reliability and efficiency of $\texttt{R-AutoEval+}$.

Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning capabilities of large language models by learning directly from rule-based outcome rewards. Recent RLVR works that operate under the zero setting avoid supervision in labeling the reasoning process, but still depend on manually curated collections of questions and answers for training. The scarcity of high-quality, human-produced examples raises concerns about the long-term scalability of relying on human supervision, a challenge already evident in the domain of language model pretraining. Furthermore, in a hypothetical future where AI surpasses human intelligence, tasks provided by humans may offer limited learning potential for a superintelligent system. To address these concerns, we propose a new RLVR paradigm called Absolute Zero, in which a single model learns to propose tasks that maximize its own learning progress and improves reasoning by solving them, without relying on any external human or distillation data. Under this paradigm, we introduce the Absolute Zero Reasoner (AZR), a system that self-evolves its training curriculum and reasoning ability. AZR uses a code executor to both validate self-proposed code reasoning tasks and verify answers, serving as an unified source of verifiable feedback to guide open-ended yet grounded learning. Despite being trained entirely without external data, AZR achieves overall SOTA performance on coding and mathematical reasoning tasks, outperforming existing zero-setting models that rely on tens of thousands of in-domain human-curated examples. Furthermore, we demonstrate that AZR can be effectively applied across different model scales and is compatible with various model classes.