NeurIPS 2025 Papers

Rendering produces 2D images from 3D scene representations, yet how continuous variations in camera pose and scenes influence these images—and, consequently, downstream visual models—remains underexplored. We introduce **abstract rendering**, a framework that computes provable bounds on all images rendered under continuously varying camera poses and scenes. The resulting abstract image, expressed as a set of constraints over the image matrix, enables rigorous uncertainty propagation through downstream neural networks and thereby supports certification of model behavior under realistic 3D semantic perturbations, far beyond traditional pixel-level noise models. Our approach propagates camera pose uncertainty through each rendering step using efficient piecewise linear bounds, including custom abstractions for three rendering-specific operations—matrix inversion, sorting-based aggregation, and cumulative product summation—not supported by standard tools. Our implementation, ABSTRACTRENDER, targets two state-of-the-art photorealistic scene representations—3D Gaussian Splats and Neural Radiance Fields (NeRF)—and scales to complex scenes with up to 1M Gaussians. Our computed abstract images achieve up to 3% over-approximation error compared to sampling results (baseline). Through experiments on classification (ResNet), object detection (YOLO), and pose estimation (GATENet) tasks, we demonstrate that abstract rendering enables formal certification of downstream models under realistic 3D variations—an essential step toward safety-critical vision systems.

Test-time adaptation (TTA) methods have gained significant attention for enhancing the performance of vision-language models (VLMs) such as CLIP during inference, without requiring additional labeled data. However, current TTA researches generally suffer from major limitations such as duplication of baseline results, limited evaluation metrics, inconsistent experimental settings, and insufficient analysis. These problems hinder fair comparisons between TTA methods and make it difficult to assess their practical strengths and weaknesses. To address these challenges, we introduce TTA-VLM, a comprehensive benchmark for evaluating TTA methods on VLMs. Our benchmark implements 8 episodic TTA and 7 online TTA methods within a unified and reproducible framework, and evaluates them across 15 widely used datasets. Unlike prior studies focused solely on CLIP, we extend the evaluation to SigLIP—a model trained with a Sigmoid loss—and include training-time tuning methods such as CoOp, MaPLe, and TeCoA to assess generality. Beyond classification accuracy, TTA-VLM incorporates various evaluation metrics, including robustness, calibration, out-of-distribution detection, and stability, enabling a more holistic assessment of TTA methods. Through extensive experiments, we find that 1) existing TTA methods produce limited gains compared to the previous pioneering work; 2) current TTA methods exhibit poor collaboration with training-time fine-tuning methods; 3) accuracy gains frequently come at the cost of reduced model trustworthiness. We release TTA-VLM to provide fair comparison and comprehensive evaluation of TTA methods for VLMs, and we hope it encourages the community to develop more reliable and generalizable TTA strategies. The code is available in https://github.com/TomSheng21/tta-vlm.

Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs fundamentally from the stochastic variant used in practice. Unlike SGD, stochastic Adam does not converge to its full-batch counterpart even with infinitesimal learning rates. We present the first theoretical characterization of how batch size affects Adam's generalization, analyzing two-layer over-parameterized CNNs on image data. Our results reveal that while both Adam and AdamW with proper weight decay $\lambda$ converge to poor test error solutions, their mini-batch variants can achieve near-zero test error. We further prove Adam has a strictly smaller effective weight decay bound than AdamW, theoretically explaining why Adam requires more sensitive $\lambda$ tuning. Extensive experiments validate our findings, demonstrating the critical role of batch size and weight decay in Adam's generalization performance.

Human cognition is theorized to operate in two modes: fast, intuitive System 1 thinking and slow, deliberate System 2 thinking. While current Large Reasoning Models (LRMs) excel at System 2 thinking, their inability to perform fast thinking leads to high computational overhead and latency. In this work, we enable LRMs to approximate human intelligence through dynamic thinking speed adjustment, optimizing accuracy-efficiency trade-offs. Our approach addresses two key questions: (1) how to control thinking speed in LRMs, and (2) when to adjust it for optimal performance. For the first question, we identify the steering vector that governs slow-fast thinking transitions in LRMs' representation space. Using this vector, we achieve the first representation editing-based test-time scaling effect, outperforming existing prompt-based scaling methods. For the second question, we apply real-time difficulty estimation to signal reasoning segments of varying complexity. Combining these techniques, we propose the first reasoning strategy that enables fast processing of easy steps and deeper analysis for complex reasoning. Without any training or additional cost, our plug-and-play method yields an average +1.3\% accuracy with -8.6\% token usage across leading LRMs and advanced reasoning benchmarks. All of our algorithms are implemented based on vLLM and are expected to support broader applications and inspire future research.

Training data attribution (TDA) methods aim to measure how training data impacts a model's predictions. While gradient-based attribution methods, such as influence functions, offer theoretical grounding, their computational costs make them impractical for large-scale applications. Representation-based approaches are far more scalable, but typically rely on heuristic embeddings that are not optimized for attribution, limiting their fidelity. To address these challenges, we propose AirRep, a scalable, representation-based approach that closes this gap by learning task-specific and model-aligned representations optimized explicitly for TDA. AirRep introduces two key innovations: a trainable encoder tuned for attribution quality, and an attention-based pooling mechanism that enables accurate estimation of group-wise influence. We train AirRep using a ranking objective over automatically constructed training subsets labeled by their empirical effect on target predictions. Experiments on instruction-tuned LLMs demonstrate that AirRep achieves performance on par with state-of-the-art gradient-based approaches while being nearly two orders of magnitude more efficient at inference time. Further analysis highlights its robustness and generalization across tasks and models. Our code is available at https://github.com/sunnweiwei/AirRep.

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts autoencoders to the space of distributions. In GDEs, an encoder acts on sets of samples, and the decoder is replaced by a generator which aims to match the input distribution. This framework enables learning representations of distributions by coupling conditional generative models with encoder networks which satisfy a criterion we call distributional invariance. We show that GDEs learn predictive sufficient statistics embedded in the Wasserstein space, such that latent GDE distances approximately recover the $W_2$ distance, and latent interpolation approximately recovers optimal transport trajectories for Gaussian and Gaussian mixture distributions. We systematically benchmark GDEs against existing approaches on synthetic datasets, demonstrating consistently stronger performance. We then apply GDEs to six key problems in computational biology: learning donor-level representations from single-nuclei RNA sequencing data (6M cells), capturing clonal dynamics in lineage-traced RNA sequencing data (150K cells), predicting perturbation effects on transcriptomes (1M cells), predicting perturbation effects on cellular phenotypes (20M single-cell images), designing synthetic yeast promoters (34M sequences), and spatiotemporal modeling of viral protein sequences (1M sequences).

Recently, reasoning-based MLLMs have achieved a degree of success in generating long-form textual reasoning chains. However, they still struggle with complex tasks that necessitate dynamic and iterative focusing on and revisiting of visual regions to achieve precise grounding of textual reasoning in visual evidence. We introduce VLM-R³ (Visual Language Model with Region Recognition, Reasoning, and Refinement ), a framework that equips an MLLM with the ability to (i) decide when additional visual evidence is needed, (ii) determine where to ground within the image, and (iii) seamlessly weave the relevant sub-image content back into an interleaved chain-of-thought. The core of our method is \textbf{Region-Conditioned Reinforcement Policy Optimization (R-GRPO)}, a training paradigm that rewards the model for selecting informative regions, formulating appropriate transformations (e.g. crop, zoom), and integrating the resulting visual context into subsequent reasoning steps. To bootstrap this policy, we compile a modest but carefully curated Visuo-Lingual Interleaved Rationale (VLIR) corpus that provides step-level supervision on region selection and textual justification. Extensive experiments on MathVista, ScienceQA, and other benchmarks show that VLM-R$^3$ sets a new state of the art in zero-shot and few-shot settings, with the largest gains appearing on questions demanding subtle spatial reasoning or fine-grained visual cue extraction.

The rapid extension of context windows in large vision-language models has given rise to long-context vision-language models (LCVLMs), which are capable of handling hundreds of images with interleaved text tokens in a single forward pass. In this work, we introduce MMLongBench, the first benchmark covering a diverse set of long-context vision-language tasks, to evaluate LCVLMs effectively and thoroughly. MMLongBench is composed of 13,331 examples spanning five different categories of downstream tasks, such as Visual RAG and Many-Shot ICL. It also provides broad coverage of image types, including various natural and synthetic images. To assess the robustness of the models to different input lengths, all examples are delivered at five standardized input lengths (8K-128K tokens) via a cross-modal tokenization scheme that combines vision patches and text tokens. Through a thorough benchmarking of 46 closed-source and open-source LCVLMs, we provide a comprehensive analysis of the current models' vision-language long-context ability. Our results show that: i) performance on a single task is a weak proxy for overall long-context capability; ii) both closed-source and open-source models face challenges in long-context vision-language tasks, indicating substantial room for future improvement; iii) models with stronger reasoning ability tend to exhibit better long-context performance. By offering wide task coverage, various image types, and rigorous length control, MMLongBench provides the missing foundation for diagnosing and advancing the next generation of LCVLMs.

Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete constraints. We design an end-to-end differentiable framework that enables us to solve discrete constrained optimization problems with neural networks. Concretely, we leverage algorithmic techniques from the literature on convex geometry and Carathéodory's theorem to decompose neural network outputs into convex combinations of polytope corners that correspond to feasible sets. This decomposition-based approach enables self-supervised training but also ensures efficient quality-preserving rounding of the neural net output into feasible solutions. Extensive experiments in cardinality-constrained optimization show that our approach can consistently outperform neural baselines. We further provide worked-out examples of how our method can be applied beyond cardinality-constrained problems to a diverse set of combinatorial optimization tasks, including finding independent sets in graphs, and solving matroid-constrained problems.

Estimating causal effects from spatiotemporal observational data is essential in public health, environmental science, and policy evaluation, where randomized experiments are often infeasible. Existing approaches, however, either rely on strong structural assumptions or fail to handle key challenges such as interference, spatial confounding, temporal carryover, and *time-varying confounding*—where covariates are influenced by past treatments and, in turn, affect future ones. We introduce the **GST-UNet** (**G**-computation **S**patio-**T**emporal **UNet**), a theoretically grounded neural framework that combines a U-Net-based spatiotemporal encoder with regression-based iterative G-computation to estimate location-specific potential outcomes under complex intervention sequences. GST-UNet explicitly adjusts for time-varying confounders and captures non-linear spatial and temporal dependencies, enabling valid causal inference from a *single* observed trajectory in data-scarce settings. We validate its effectiveness in synthetic experiments and in a real-world analysis of wildfire smoke exposure and respiratory hospitalizations during the 2018 California Camp Fire. Together, these results position GST-UNet as a **principled and ready-to-use framework** for spatiotemporal causal inference, advancing reliable estimation in policy-relevant and scientific domains.

Text-to-image diffusion models excel at translating language prompts into photorealistic images by implicitly grounding textual concepts through their cross-modal attention mechanisms. Recent multi-modal diffusion transformers extend this by introducing joint self-attention over concatenated image and text tokens, enabling richer and more scalable cross-modal alignment. However, a detailed understanding of how and where these attention maps contribute to image generation remains limited. In this paper, we introduce Seg4Diff (Segmentation for Diffusion), a systematic framework for analyzing the attention structures of MM-DiT, with a focus on how specific layers propagate semantic information from text to image. Through comprehensive analysis, we identify a semantic grounding expert layer, a specific MM-DiT block that consistently aligns text tokens with spatially coherent image regions, naturally producing high-quality semantic segmentation masks. We further demonstrate that applying a lightweight fine-tuning scheme with mask-annotated image data enhances the semantic grouping capabilities of these layers and thereby improves both segmentation performance and generated image fidelity. Our findings demonstrate that semantic grouping is an emergent property of diffusion transformers and can be selectively amplified to advance both segmentation and generation performance, paving the way for unified models that bridge visual perception and generation.

Characterizing a large language model's (LLM's) knowledge of a given question is challenging. As a result, prior work has primarily examined LLM behavior under knowledge conflicts, where the model's internal parametric memory contradicts information in the external context. However, this does not fully reflect how well the model knows the answer to the question. In this paper, we first introduce a taxonomy of five knowledge statuses based on the consistency and correctness of LLM knowledge modes. We then propose KScope, a hierarchical framework of statistical tests that progressively refines hypotheses about knowledge modes and characterizes LLM knowledge into one of these five statuses. We apply KScope to nine LLMs across four datasets and systematically establish: (1) Supporting context narrows knowledge gaps across models. (2) Context features related to difficulty, relevance, and familiarity drive successful knowledge updates. (3) LLMs exhibit similar feature preferences when partially correct or conflicted, but diverge sharply when consistently wrong. (4) Context summarization constrained by our feature analysis, together with enhanced credibility, further improves update effectiveness and generalizes across LLMs.

We present LrcSSM, a $\textit{non-linear}$ recurrent model that processes long sequences as fast as today's linear state-space layers. By forcing its Jacobian matrix to be diagonal, the full sequence can be solved in parallel, giving $\mathcal{O}(TD)$ time and memory and only $\mathcal{O}(\log T)$ sequential depth, for input-sequence length $T$ and a state dimension $D$. Moreover, LrcSSM offers a formal gradient-stability guarantee that other input-varying systems such as Liquid-S4 and Mamba do not provide. Importantly, the diagonal Jacobian structure of our model results in no performance loss compared to the original model with dense Jacobian, and the approach can be generalized to other non-linear recurrent models, demonstrating broader applicability. On a suite of long-range forecasting tasks, we demonstrate that LrcSSM outperforms Transformers, LRU, S5, and Mamba.

In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model. Two main strategies have emerged for learning invariant distributions: designing equivariant network architectures and using data augmentation to approximate equivariance. While equivariant architectures preserve symmetry by design, they often involve greater complexity and pose optimization challenges. Data augmentation, on the other hand, offers flexibility but may fall short in fully capturing symmetries. Our framework enhances both approaches by reducing training variance and providing a provably lower-variance gradient estimator. We achieve this by interpreting data augmentation as a Monte Carlo estimator of the training gradient and applying Rao–Blackwellization. This leads to more stable optimization, faster convergence, and reduced variance, all while requiring only a single forward and backward pass per sample. We also present a practical implementation of this estimator—incorporating the loss and sampling procedure—through a method we call Orbit Diffusion. Theoretically, we guarantee that our loss admits equivariant minimizers. Empirically, Orbit Diffusion achieves state-of-the-art results on GEOM-QM9 for molecular conformation generation, improves crystal structure prediction, and advances text-guided crystal generation on the Perov-5 and MP-20 benchmarks. Additionally, it enhances protein designability in protein structure generation. Code is available at https://github.com/vinhsuhi/Orbit-Diffusion.git.

Overparameterized neural networks can interpolate a given dataset in many different ways, prompting the fundamental question: which among these solutions should we prefer, and what explicit regularization strategies will provably yield these solutions? This paper addresses the challenge of finding the sparsest interpolating ReLU network—i.e., the network with the fewest nonzero parameters or neurons—a goal with wide-ranging implications for efficiency, generalization, interpretability, theory, and model compression. Unlike post hoc pruning approaches, we propose a continuous, almost-everywhere differentiable training objective whose global minima are guaranteed to correspond to the sparsest single-hidden-layer ReLU networks that fit the data. This result marks a conceptual advance: it recasts the combinatorial problem of sparse interpolation as a smooth optimization task, potentially enabling the use of gradient-based training methods. Our objective is based on minimizing $\ell^p$ quasinorms of the weights for $0 < p < 1$, a classical sparsity-promoting strategy in finite-dimensional settings. However, applying these ideas to neural networks presents new challenges: the function class is infinite-dimensional, and the weights are learned using a highly nonconvex objective. We prove that, under our formulation, global minimizers correspond exactly to sparsest solutions. Our work lays a foundation for understanding when and how continuous sparsity-inducing objectives can be leveraged to recover sparse networks through training.

We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at a rate that is nearly independent of explicit dimension dependence. Specifically, for a $d$-dimensional strongly log-concave and log-smooth target, the number of iterations for BBVI with a sub-Gaussian family to obtain a solution $\epsilon$-close to the global optimum has a dimension dependence of $\mathrm{O}(\log d)$. This is a significant improvement over the $\mathrm{O}(d)$ dependence of full-rank location-scale families. For heavy-tailed families, we prove a weaker $\mathrm{O}(d^{2/k})$ dependence, where $k$ is the number of finite moments of the family. Additionally, if the Hessian of the target log-density is constant, the complexity is free of any explicit dimension dependence. We also prove that our bound on the gradient variance, which is key to our result, cannot be improved using only spectral bounds on the Hessian of the target log-density.

We propose **GAM-Agent**, a game-theoretic multi-agent framework for enhancing vision-language reasoning. Unlike prior single-agent or monolithic models, GAM-Agent formulates the reasoning process as a non-zero-sum game between base agents—each specializing in visual perception subtasks—and a critical agent that verifies logic consistency and factual correctness. Agents communicate via structured claims, evidence, and uncertainty estimates. The framework introduces an uncertainty-aware controller to dynamically adjust agent collaboration, triggering multi-round debates when disagreement or ambiguity is detected. This process yields more robust and interpretable predictions. Experiments on four challenging benchmarks—MMMU, MMBench, MVBench, and V*Bench—demonstrate that GAM-Agent significantly improves performance across various VLM backbones. Notably, GAM-Agent boosts the accuracy of small-to-mid scale models (e.g., Qwen2.5-VL-7B, InternVL3-14B) by 5–6\%, and still enhances strong models like GPT-4o by up to 2–3\%. Our approach is modular, scalable, and generalizable, offering a path toward reliable and explainable multi-agent multimodal reasoning.

Panoramic video generation aims to synthesize 360-degree immersive videos, holding significant importance in the fields of VR, world models, and spatial intelligence. Existing works fail to synthesize high-quality panoramic videos due to the inherent modality gap between panoramic data and perspective data, which constitutes the majority of the training data for modern diffusion models. In this paper, we propose a novel framework utilizing pretrained perspective video models for generating panoramic videos. Specifically, we design a novel panorama representation named ViewPoint map, which possesses global spatial continuity and fine-grained visual details simultaneously. With our proposed Pano-Perspective attention mechanism, the model benefits from pretrained perspective priors and captures the panoramic spatial correlations of the ViewPoint map effectively. Extensive experiments demonstrate that our method can synthesize highly dynamic and spatially consistent panoramic videos, achieving state-of-the-art performance and surpassing previous methods.

Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification, which can be used to improve the accuracy of quantum computation and communication. We formulate a rigorous paradigm for identifying the purest quantum state among $K$ unknown $n$-qubit quantum states using total $N$ quantum state copies. For incoherent strategies, we derive the first adaptive algorithm achieving error probability $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, fundamentally improving quantum property learning through measurement optimization. By developing a coherent measurement protocol with error bound $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, we demonstrate a significant separation from incoherent strategies, formally quantifying the power of quantum memory and coherent measurement. Furthermore, we establish a lower bound by demonstrating that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This research advances the characterization of quantum noise through efficient learning frameworks. Our results establish theoretical foundations for noise-adaptive quantum property learning while delivering practical protocols for enhancing the reliability of quantum hardware.