NeurIPS 2025 Papers

Data-driven stochastic optimization is ubiquitous in machine learning and operational decision-making problems. Sample average approximation (SAA) and model-based approaches such as estimate-then-optimize (ETO) or integrated estimation-optimization (IEO) are all popular, with model-based approaches being able to circumvent some of the issues with SAA in complex context-dependent problems. Yet the relative performance of these methods is poorly understood, with most results confined to the dichotomous cases of the model-based approach being either well-specified or misspecified. We develop the first results that allow for a more granular analysis of the relative performance of these methods under a local misspecification setting, which models the scenario where the model-based approach is nearly well-specified. By leveraging tools from contiguity theory in statistics, we show that there is a bias-variance tradeoff between SAA, IEO, and ETO under local misspecification, and that the relative importance of the bias and the variance depends on the degree of local misspecification. Moreover, we derive explicit expressions for the decision bias, which allows us to characterize (un)impactful misspecification directions, and provide further geometric understanding of the variance.

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors for positional encoding in MPNNs and Graph Transformers. The expressive power of such Spectrally-enhanced GNNs (SGNNs) is usually evaluated via the $k$-WL graph isomorphism test hierarchy and homomorphism counting. Yet, these frameworks align poorly with the graph spectra, yielding limited insight into SGNNs' expressive power. In this paper, we leverage a well-studied paradigm of classifying graphs by their largest eigenvalue multiplicity to introduce an expressivity hierarchy for SGNNs. We then prove that many SGNNs are incomplete even on graphs with distinct eigenvalues. To mitigate this deficiency, we adapt rotation equivariant neural networks to the graph spectra setting, yielding equiEPNN, a novel SGNN that provably improves upon contemporary SGNNs' expressivity on simple spectrum graphs. We then demonstrate that equiEPNN achieves perfect eigenvector canonicalization on ZINC, and performs favorably on image classification on MNIST-Superpixel and graph property regression on ZINC, compared to leading spectral methods.

Neural operator is considered a popular data-driven alternative to traditional partial differential equation (PDE) solvers. However, most current solutions, whether fulfilling computations in frequency, Laplacian, and wavelet domains, all deviate far from the intrinsic PDE space. While with meticulous network architecture elaborated, the deviation often leads to biased accuracy. To address the issue, we open a new avenue that pioneers leveraging Radon transform to decompose the input space, finalizing a novel Radon neural operator (RNO) to solve PDEs in infinite-dimensional function space. Distinct from previous solutions, we project the input data into the sinogram domain, shrinking the multi-dimensional transformations to a reduced-dimensional counterpart and fitting compactly with the PDE space. Theoretically, we prove that RNO obeys a property of bilipschitz strongly monotonicity under diffeomorphism, providing deeper insights to guarantee the desired accuracy than typical discrete invariance or continuous-discrete equivalence. Within the sinogram domain, we further evidence that different angles contribute unequally to the overall space, thus engineering a reweighting technique to enable more effective PDE solutions. On that basis, a sinogram-domain convolutional layer is crafted, which operates on a fixed $\theta$-grid that is decoupled from the PDE space, further enjoying a natural guarantee of discrete invariance. Extensive experiments demonstrate that RNO sets new state-of-the-art (SOTA) scores across massive standard benchmarks, with superior generalization performance enjoyed. Code is available at <https://github.com/wenbin-lu/Radon-Neural-Operator>.

Mastering fine-grained visual recognition, essential in many expert domains, can require that specialists undergo years of dedicated training. Modeling the progression of such expertize in humans remains challenging, and accurately inferring a human learner’s knowledge state is a key step toward understanding visual learning. We introduce CleverBirds, a large-scale knowledge tracing benchmark for fine-grained bird species recognition. Collected by the citizen-science platform eBird, it offers insight into how individuals acquire expertize in complex fine-grained classification. More than 40,000 participants have engaged in the quiz, answering over 17 million multiple-choice questions spanning over 10,000 bird species, with long-range learning patterns across an average of 400 questions per participant. We release this dataset to support the development and evaluation of new methods for visual knowledge tracing. We show that tracking learners' knowledge is challenging, especially across participant subgroups and question types, with different forms of contextual information offering varying degrees of predictive benefit. CleverBirds is among the largest benchmark of its kind, offering a substantially higher number of learnable concepts. With it, we hope to enable new avenues for studying the development of visual expertize over time and across individuals.

In this paper, we propose Tortoise and Hare Guidance (THG), a training-free strategy that accelerates diffusion sampling while maintaining high-fidelity generation. We demonstrate that the noise estimate and the additional guidance term exhibit markedly different sensitivity to numerical error by reformulating the classifier-free guidance (CFG) ODE as a multirate system of ODEs. Our error-bound analysis shows that the additional guidance branch is more robust to approximation, revealing substantial redundancy that conventional solvers fail to exploit. Building on this insight, THG significantly reduces the computation of the additional guidance: the noise estimate is integrated with the tortoise equation on the original, fine-grained timestep grid, while the additional guidance is integrated with the hare equation only on a coarse grid. We also introduce (i) an error-bound-aware timestep sampler that adaptively selects step sizes and (ii) a guidance-scale scheduler that stabilizes large extrapolation spans. THG reduces the number of function evaluations (NFE) by up to 30% with virtually no loss in generation fidelity (∆ImageReward ≤ 0.032) and outperforms state-of-the-art CFG-based training-free accelerators under identical computation budgets. Our findings highlight the potential of multirate formulations for diffusion solvers, paving the way for real-time high-quality image synthesis without any model retraining. The source code is available at https://github.com/yhlee-add/THG.

Encoding models based on word embeddings or artificial neural network (ANN) features reliably predict brain responses to naturalistic stimuli but remain difficult to interpret. A central limitation is superposition—the entanglement of distinct semantic features along correlated directions in dense embeddings, which arises when latent features outnumber the embedding dimensions. This entanglement renders regression weights non-identifiable: different combinations of semantic directions can produce identical predicted brain activity, preventing principled interpretation of voxel selectivity. To overcome this, we introduce the Sparse Concept Encoding Model, which transforms dense embeddings into a higher-dimensional, sparse, and non-negative space of learned concept atoms. This transformation yields an axis-aligned semantic basis where each dimension corresponds to an interpretable concept, enabling direct readout of conceptual selectivity from voxel weights. When applied to fMRI data collected during story listening, our model matches the prediction performance of conventional dense models while substantially enhancing interpretability. It enables novel neuroscientific analyses such as disentangling overlapping cortical representations of time, space, and number, and revealing structured similarity among distributed conceptual maps. This framework offers a scalable and interpretable bridge between ANN-derived features and human conceptual representations in the brain.

In decision-making processes, an intelligent agent with causal knowledge can optimize action spaces to avoid unnecessary exploration. A *structural causal bandit* framework provides guidance on how to prune actions that are unable to maximize reward by leveraging prior knowledge of the underlying causal structure among actions. A key assumption of this framework is that the agent has access to a fully-specified causal diagram representing the target system. In this paper, we extend the structural causal bandits to scenarios where the agent leverages a Markov equivalence class. In such cases, the causal structure is provided to the agent in the form of a *partial ancestral graph* (PAG). We propose a generalized framework for identifying potentially optimal actions within this graph structure, thereby broadening the applicability of structural causal bandits.

Current transformer-based imitation learning approaches introduce discrete action representations and train an autoregressive transformer decoder on the resulting latent code. However, the initial quantization breaks the continuous structure of the action space thereby limiting the capabilities of the generative model. We propose a quantization-free method instead that leverages Generative Infinite-Vocabulary Transformers (GIVT) as a direct, continuous policy parametrization for autoregressive transformers. This simplifies the imitation learning pipeline while achieving state-of-the-art performance on a variety of popular simulated robotics tasks. We enhance our policy roll-outs by carefully studying sampling algorithms, further improving the results.

This paper introduces VeriThoughts, a novel dataset designed for reasoning-based Verilog code generation. We establish a new benchmark framework grounded in formal verification methods to evaluate the quality and correctness of generated hardware descriptions. Additionally, we present a suite of specialized small-scale models optimized specifically for Verilog generation. Our work addresses the growing need for automated hardware design tools that can produce verifiably correct implementations from high-level specifications, potentially accelerating the hardware development process while maintaining rigorous correctness guarantees.

We present STARFlow, a scalable generative model based on normalizing flows that achieves strong performance on high-resolution image synthesis. STARFlow's main building block is Transformer Autoregressive Flow (TARFlow), which combines normalizing flows with Autoregressive Transformer architectures and has recently achieved impressive results in image modeling. In this work, we first establish the theoretical universality of TARFlow for modeling continuous distributions. Building on this foundation, we introduce a set of architectural and algorithmic innovations that significantly enhance the scalability: (1) a deep-shallow design where a deep Transformer block captures most of the model’s capacity, followed by a few shallow Transformer blocks that are computationally cheap yet contribute non-negligibly, (2) learning in the latent space of pretrained autoencoders, which proves far more effective than modeling pixels directly, and (3) a novel guidance algorithm that substantially improves sample quality. Crucially, our model remains a single, end-to-end normalizing flow, allowing exact maximum likelihood training in continuous space without discretization. STARFlow achieves competitive results in both class- and text-conditional image generation, with sample quality approaching that of state-of-the-art diffusion models. To our knowledge, this is the **first** successful demonstration of normalizing flows at this scale and resolution. Code and weights available at https://github.com/apple/ml-starflow.

Effective robotic exploration in continuous domains requires planning trajectories that maximize coverage over a predefined region. A recent development, Stein Variational Ergodic Search (SVES), proposed parallel ergodic exploration (a key approach within the field of robotic exploration), via Stein variational inference that computes a set of candidate trajectories approximating the posterior distribution over the solution space trajectories. While this approach leverages GPU parallelism well, the trajectories in the set might not be distinct enough, leading to a suboptimal set. In this paper, we propose two key methods to diversify the solution set of this approach. First, we leverage the signature kernel within the SVES framework, introducing a pathwise, sequence-sensitive interaction that preserves the Markovian structure of the trajectories and naturally spreads paths across distinct regions of the search space. Second, we propose a derivative-free evolution-strategy interpretation of SVES that exploits batched, GPU-friendly fitness evaluations and can be paired with approximate gradients whenever analytic gradients of the kernel are unavailable or computationally intractable. The resulting method both retains SVES’s advantages while diversifying the solution set and extending its reach to black-box objectives. Across planar forest search, 3D quadrotor coverage, and model-predictive control benchmarks, our approach consistently reduces ergodic cost and produces markedly richer trajectory sets than SVES without significant extra tuning effort.

Vision-Language Models (VLMs) excel at visual understanding but often suffer from visual hallucinations, where they generate descriptions of nonexistent objects, actions, or concepts, posing significant risks in safety-critical applications. Existing hallucination mitigation methods typically follow one of two paradigms: generation adjustment, which modifies decoding behavior to align text with visual inputs, and post-hoc verification, where external models assess and correct outputs. While effective, generation adjustment methods often rely on heuristics and lack correction mechanisms, while post-hoc verification is complicated, typically requiring multiple models and tending to reject outputs rather than refine them. In this work, we introduce REVERSE, a unified framework that integrates hallucination-aware training with on-the-fly self-verification. By leveraging a new hallucination-verification dataset containing over 1.3M semi-synthetic samples, along with a novel inference-time retrospective resampling technique, our approach enables VLMs to both detect hallucinations during generation and dynamically revise those hallucinations. Our evaluations show that REVERSE achieves state-of-the-art hallucination reduction, outperforming the best existing methods by up to 12% on CHAIR-MSCOCO and 34% on HaloQuest.

Generation of images containing multiple humans, performing complex actions, while preserving their facial identities, is a significant challenge. A major factor contributing to this is the lack of a a dedicated benchmark. To address this, we introduce MultiHuman-Testbench, a novel benchmark for rigorously evaluating generative models for multi-human generation. The benchmark comprises 1800 samples, including carefully curated text prompts, describing a range of simple to complex human actions. These prompts are matched with a total of 5,550 unique human face images, sampled uniformly to ensure diversity across age, ethnic background, and gender. Alongside captions, we provide human-selected pose conditioning images which accurately match the prompt. We propose a multi-faceted evaluation suite employing four key metrics to quantify face count, ID similarity, prompt alignment, and action detection. We conduct a thorough evaluation of a diverse set of models, including zero-shot approaches and training-based methods, with and without regional priors. We also propose novel techniques to incorporate image and region isolation using human segmentation and Hungarian matching, significantly improving ID similarity. Our proposed benchmark and key findings provide valuable insights and a standardized tool for advancing research in multi-human image generation.

Leveraging the power of Large Language Models (LLMs) through preference optimization is crucial for aligning model outputs with human values. Direct Preference Optimization (DPO) has recently emerged as a simple yet effective method by directly optimizing on preference data without the need for explicit reward models. However, DPO typically relies on human-labeled preference data, which can limit its scalability. Self-Play Fine-Tuning (SPIN) addresses this by allowing models to generate their own rejected samples, reducing the dependence on human annotations. Nevertheless, SPIN uniformly applies learning signals across all tokens, ignoring the fine-grained quality variations within responses. As the model improves, rejected samples increasingly contain high-quality tokens, making the uniform treatment of tokens suboptimal. In this paper, we propose SWIFT (Self-Play Weighted Fine-Tuning), a fine-grained self-refinement method that assigns token-level importance weights estimated from a stronger teacher model. Beyond alignment, we also demonstrate that SWIFT serves as an effective knowledge distillation strategy by using the teacher not for logits matching, but for reward-guided token weighting. Extensive experiments on diverse benchmarks and settings demonstrate that SWIFT consistently surpasses both existing alignment approaches and conventional knowledge distillation methods.

Neural networks are powered by an implicit bias: a tendency of gradient descent to fit training data in a way that generalizes to unseen data. A recent class of neural network models gaining increasing popularity is structured state space models (SSMs). Prior work argued that the implicit bias of SSMs leads to generalization in a setting where data is generated by a low dimensional teacher. In this paper, we revisit the latter setting, and formally establish a phenomenon entirely undetected by prior work on the implicit bias of SSMs. Namely, we prove that while implicit bias leads to generalization under many choices of training data, there exist special examples whose inclusion in training completely distorts the implicit bias, to a point where generalization fails. This failure occurs despite the special training examples being labeled by the teacher, i.e., having clean labels! We empirically demonstrate the phenomenon, with SSMs trained independently and as part of non-linear neural networks. In the area of adversarial machine learning, disrupting generalization with cleanly labeled training examples is known as clean-label poisoning. Given the proliferation of SSMs, we believe that delineating their susceptibility to clean-label poisoning, and developing methods for overcoming this susceptibility, are critical research directions to pursue.

Modeling boiling---an inherently chaotic, multiphase process central to energy and thermal systems---remains a significant challenge for neural PDE surrogates. Existing models require future input (e.g., bubble positions) during inference because they fail to learn nucleation from past states, limiting their ability to autonomously forecast boiling dynamics. They also fail to model flow boiling velocity fields, where sharp interface–momentum coupling demands long-range and directional inductive biases. We introduce Bubbleformer, a transformer-based spatiotemporal model that forecasts stable and long-range boiling dynamics including nucleation, interface evolution, and heat transfer without dependence on simulation data during inference. Bubbleformer integrates factorized axial attention, frequency-aware scaling, and conditions on thermophysical parameters to generalize across fluids, geometries, and operating conditions.To evaluate physical fidelity in chaotic systems, we propose interpretable physics-based metrics that evaluate heat flux consistency, interface geometry, and mass conservation. We also release BubbleML 2.0, a high-fidelity dataset that spans diverse working fluids (cryogens, refrigerants, dielectrics), boiling configurations (pool and flow boiling), flow regimes (bubbly, slug, annular), and boundary conditions. Bubbleformer sets new benchmark results in both prediction and forecasting of two-phase boiling flows.

Process reward model (PRM) has been proven effective in test-time scaling of LLM on challenging reasoning tasks. However, the reward hacking induced by PRM hinders its successful applications in reinforcement fine-tuning. We find the primary cause of reward hacking induced by PRM is that: the canonical summation-form credit assignment in reinforcement learning (RL), i.e. cumulative gamma-decayed future rewards, causes the LLM to hack steps with high rewards. Therefore, to unleashing the power of PRM in training-time, we propose PURE: Process sUpervised Reinforcement lEarning. The core of PURE is the min-form credit assignment that defines the value function as the minimum future rewards. This method unifies the optimization objective with respect to process rewards during test-time and training-time, and significantly alleviates reward hacking due to the limits on the range of values of value function and more rational assignment of advantages. Through extensively experiments on 3 base models, we achieve similar reasoning performance using PRM-based approach compared with verifiable reward-based approach if enabling min-form credit assignment. In contrast, the canonical sum-form credit assignment even collapses training at the beginning. Moreover, when we incorporate 1/10th verifiable rewards to auxiliary the PRM-based fine-tuning, it further alleviate reward hacking and results in the best fine-tuned model based on Qwen2.5-Math-7B with 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Furthermore, we summary the reward hacking cases we encountered during training and analysis the cause of training collapse.

Regression models are crucial in recommender systems. However, retransformation bias problem has been conspicuously neglected within the community. While many works in other fields have devised effective bias correction methods, all of them are post-hoc cures externally to the model, facing practical challenges when applied to real-world recommender systems. Hence, we propose a preemptive paradigm to eradicate the bias intrinsically from the models via minor model refinement. Specifically, a novel TranSUN method is proposed with a joint bias learning manner to offer theoretically guaranteed unbiasedness under empirical superior convergence. It is further generalized into a novel generic regression model family, termed Generalized TranSUN (GTS), which not only offers more theoretical insights but also serves as a generic framework for flexibly developing various bias-free models. Comprehensive experimental results demonstrate the superiority of our methods across data from various domains, which have been successfully deployed in two real-world industrial recommendation scenarios, i.e. product and short video recommendation scenarios in Guess What You Like business domain in the homepage of Taobao App (a leading e-commerce platform with DAU > 300M), to serve the major online traffic.

Causal mediation analysis is crucial for deconstructing complex mechanisms of action. However, in current mediation analysis, complex structures derived from causal discovery lack direct interpretation of mediation pathways, while traditional mediation analysis and effect estimation are limited by the reliance on pre-specified pathways, leading to a disconnection between structure discovery and causal mechanism understanding. Therefore, a unified framework integrating structure discovery, pathway identification, and effect estimation systematically quantifies mediation pathways under structural uncertainty, enabling automated identification and inference of mediation pathways. To this end, we propose Structure-Informed Guided Mediation Analysis (SIGMA), which guides automated mediation pathway identification through probabilistic causal structure discovery and uncertainty quantification, enabling end-to-end propagation of structural uncertainty from structure learning to effect estimation. Specifically, SIGMA employs differentiable Flow-Structural Equation Models to learn structural posteriors, generating diverse Directed Acyclic Graphs (DAGs) to quantify structural uncertainty. Based on these DAGs, we introduce the Path Stability Score to evaluate the marginal probability of pathways, identifying high-confidence mediation paths. For identified mediation pathways, we integrate Efficient Influence Functions with Bayesian model averaging to fuse within-structure estimation uncertainty and between-structure effect variation, propagating uncertainty to the final effect estimates. In synthetic data experiments, SIGMA achieves state-of-the-art performance in pathway identification accuracy and effect quantification precision under structures uncertainty, concurrent multiple pathways, and nonlinear scenarios. In real-world applications using Human Phenotype Project data, SIGMA identifies mediation effects of sleep quality on cardiovascular health through inflammatory and metabolic pathways, uncovering previously unspecified multiple mediation paths.