NeurIPS 2025 Papers

Multi-view 3D human pose estimation (HPE) leverages complementary information across views to improve accuracy and robustness. Traditional methods rely on camera calibration to establish geometric correspondences, which is sensitive to calibration accuracy and lacks flexibility in dynamic settings. Calibration-free approaches address these limitations by learning adaptive view interactions, typically leveraging expressive and flexible continuous representations. However, as the multiview interaction relationship is learned entirely from data without constraint, they are vulnerable to noisy input, which can propagate, amplify and accumulate errors across all views, severely corrupting the final estimated pose. To mitigate this, we propose a novel framework that integrates a noise-resilient discrete prior into the continuous representation-based model. Specifically, we introduce the \textit{UniCodebook}, a unified, compact, robust, and discrete representation complementary to continuous features, allowing the model to benefit from robustness to noise while preserving regression capability. Furthermore, we further propose an attribute-preserving and complementarity-enhancing Discrete-Continuous Spatial Attention (DCSA) mechanism to facilitate interaction between discrete priors and continuous pose features. Extensive experiments on three representative datasets demonstrate that our approach outperforms both calibration-required and calibration-free methods, achieving state-of-the-art performance.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities through test-time scaling approaches, particularly when fine-tuned with chain-of-thought (CoT) data distilled from more powerful large reasoning models (LRMs). However, these reasoning chains often contain verbose elements that mirror human problem-solving, categorized as progressive reasoning (the essential solution development path) and functional elements (verification processes, alternative solution approaches, and error corrections). While progressive reasoning is crucial, the functional elements significantly increase computational demands during test-time inference. We introduce PIR (Perplexity-based Importance Refinement), a principled framework that quantitatively evaluates the importance of each reasoning step based on its impact on answer prediction confidence. PIR systematically identifies and selectively prunes only low-importance functional steps while preserving all progressive reasoning components, creating optimized training data that maintains the integrity of the core solution path while reducing verbosity. Models fine-tuned on PIR-optimized data exhibit superior test-time scaling properties, generating more concise reasoning chains while achieving improved accuracy (+0.9\% to +6.6\%) with significantly reduced token usage (-3\% to -41\%) across challenging reasoning benchmarks (AIME, AMC, and GPQA Diamond). Our approach demonstrates strong generalizability across different model sizes, data sources, and token budgets, offering a practical solution for deploying reasoning-capable LLMs in scenarios where efficient test-time scaling, response time, and computational efficiency are valuable constraints. Code and dataset are available at the [LIMOPro GitHub repository.](https://github.com/GAIR-NLP/LIMOPro)

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as "delta PDE" and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a >100× lower $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Empowering large language models (LLMs) with chemical intelligence remains a challenge due to the scarcity of high-quality, domain-specific instruction-response datasets and the misalignment of existing synthetic data generation pipelines with the inherently hierarchical and rule-governed structure of chemical information. To address this, we propose ChemOrch, a framework that synthesizes chemically grounded instruction–response pairs through a two-stage process: task-controlled instruction generation and tool-aware response construction. ChemOrch enables controllable diversity and levels of difficulty for the generated tasks and ensures response precision through tool planning \& distillation, and tool-based self-repair mechanisms. The effectiveness of ChemOrch is evaluated based on: 1) the \textbf{high quality} of generated instruction data, demonstrating superior diversity and strong alignment with chemical constraints; 2) the \textbf{dynamic generation of evaluation tasks} that more effectively reveal LLM weaknesses in chemistry; and 3) the significant \textbf{improvement of LLM chemistry capabilities} when the generated instruction data are used for fine-tuning. Our work thus represents a critical step toward scalable and verifiable chemical intelligence in LLMs. The code is available at \url{https://anonymous.4open.science/r/ChemOrch-854A}.

We introduce TAPIP3D, a novel approach for long-term 3D point tracking in monocular RGB and RGB-D videos. TAPIP3D represents videos as camera-stabilized spatio-temporal feature clouds, leveraging depth and camera motion information to lift 2D video features into a 3D world space where camera movement is effectively canceled out. Within this stabilized 3D representation, TAPIP3D iteratively refines multi-frame motion estimates, enabling robust point tracking over long time horizons. To handle the irregular structure of 3D point distributions, we propose a 3D Neighborhood-to-Neighborhood (N2N) attention mechanism—a 3D-aware contextualization strategy that builds informative, spatially coherent feature neighborhoods to support precise trajectory estimation. Our 3D-centric formulation significantly improves performance over existing 3D point tracking methods and even surpasses state-of-the-art 2D pixel trackers in accuracy when reliable depth is available. The model supports inference in both camera-centric (unstabilized) and world-centric (stabilized) coordinates, with experiments showing that compensating for camera motion leads to substantial gains in tracking robustness. By replacing the conventional 2D square correlation windows used in prior 2D and 3D trackers with a spatially grounded 3D attention mechanism, TAPIP3D achieves strong and consistent results across multiple 3D point tracking benchmarks. Our code and trained checkpoints will be public.

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices. We begin by deriving an upper bound on the KL divergence of the forward process, introducing a surrogate initialization distribution to address the challenge posed by the absorbing stationary distribution, which is a singleton and causes the KL divergence to be ill-defined. We then establish the first convergence guarantees for both the $\tau$-leaping and uniformization samplers under absorbing rate matrices, demonstrating improved rates over their counterparts using uniform rate matrices. Furthermore, under suitable assumptions, we provide convergence guarantees without early stopping. Our analysis introduces several new technical tools to address challenges unique to absorbing rate matrices. These include a Jensen-type argument for bounding forward process convergence, novel techniques for bounding absorbing score functions, and a non-divergent upper bound on the score near initialization that removes the need of early-stopping.

Breast cancer remains a leading cause of death among women, with early detection significantly improving prognosis. Non-contrast computed tomography (NCCT) scans of the chest, routinely acquired for thoracic assessments, often capture the breast region incidentally, presenting an underexplored opportunity for opportunistic breast lesion detection without additional imaging cost or radiation. However, the subtle appearance of lesions in NCCT and the difficulty of jointly modeling lesion detection and malignancy classification pose unique challenges. In this work, we propose Dual-Res Tandem Mamba-3D (DRT-M3D), a novel multitask framework for opportunistic breast cancer analysis on NCCT scans. DRT-M3D introduces a dual-resolution architecture, which captures fine-grained spatial details for segmentation-based lesion detection and global contextual features for breast-level cancer classification. It further incorporates a tandem input mechanism that models bilateral breast regions jointly through Mamba-3D blocks, enabling cross-breast feature interaction by leveraging subtle asymmetries between the two sides. Our approach achieves state-of-the-art performance in both tasks across multi-institutional NCCT datasets spanning four medical centers. Extensive experiments and ablation studies validate the effectiveness of each key component.

Accurate visual localization from aerial views is a fundamental problem with applications in mapping, large-area inspection, and search-and-rescue operations. In many scenarios, these systems require high-precision localization while operating with limited resources (e.g., no internet connection or GNSS/GPS support), making large image databases or heavy 3D models impractical. Surprisingly, little attention has been given to leveraging orthographic geodata as an alternative paradigm, which is lightweight and increasingly available through free releases by governmental authorities (e.g., the European Union). To fill this gap, we propose OrthoLoC, the first large-scale dataset comprising 16,425 UAV images from Germany and the United States with multiple modalities. The dataset addresses domain shifts between UAV imagery and geospatial data. Its paired structure enables fair benchmarking of existing solutions by decoupling image retrieval from feature matching, allowing isolated evaluation of localization and calibration performance. Through comprehensive evaluation, we examine the impact of domain shifts, data resolutions, and covisibility on localization accuracy. Finally, we introduce a refinement technique called AdHoP, which can be integrated with any feature matcher, improving matching by up to 95% and reducing translation error by up to 63%. The dataset and code are available at: https://deepscenario.github.io/OrthoLoC .

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness---that is, the universal approximation property over the space of equivariant functions---the network must effectively capture the intricate multi-body interactions among different nodes. Prior methods attain this via deeper architectures, augmented body orders, or increased degrees of steerable features, often at high computational cost and without polynomial-time solutions. In this work, we present a theoretically grounded framework for constructing complete equivariant GNNs that is both efficient and practical. We prove that a complete equivariant GNN can be achieved through two key components: 1) a complete scalar function, referred to as the canonical form of the geometric graph; and 2) a full-rank steerable basis set. Leveraging this finding, we propose an efficient algorithm for constructing complete equivariant GNNs based on two common models: EGNN and TFN. Empirical results demonstrate that our model demonstrates superior completeness and excellent performance with only a few layers, thereby significantly reducing computational overhead while maintaining strong practical efficacy.

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies. In this paper, we present an $\textbf{U}$nsupervised and $\textbf{G}$eneralizable $\textbf{M}$esh $\textbf{M}$ovement $\textbf{N}$etwork (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level. Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in low-overlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, a novel two-stage method that combines geometric, color, and Gaussian information for robust registration. Our approach incorporates a dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the Geometric-3DGS module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometric-color context. Leveraging LORA optimization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process, leading to improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap. We validate our method by colorizing the Kitti dataset as ColorKitti and testing on both Color3DMatch and Color3DLoMatch datasets. Our method achieves state-of-the-art performance with Registration Recall at 99.9%, Relative Rotation Error as low as 0.013, and Relative Translation Error as low as 0.024, improving precision by at least a factor of 2.

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce \textbf{Test3R}, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets ($I_1,I_2,I_3$), Test3R generates reconstructions from pairs ($I_1,I_2$) and ($I_1,I_3$). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image $I_1$. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

As large language models increasingly gain popularity in real-world applications, processing extremely long contexts, often exceeding the model’s pre-trained context limits, has emerged as a critical challenge. While existing approaches to efficient long-context processing show promise, recurrent compression-based methods struggle with information preservation, whereas random access approaches require substantial memory resources. We introduce REFORM, a novel inference framework that efficiently handles long contexts through a two-phase approach. First, it incrementally processes input chunks while maintaining a compressed KV cache, constructs cross-layer context embeddings, and utilizes early exit strategy for improved efficiency. Second, it identifies and gathers essential tokens via similarity matching and selectively recomputes the KV cache. Compared to baselines, REFORM achieves over 50% and 27% performance gains on RULER and BABILong respectively at 1M context length. It also outperforms baselines on ∞-Bench, RepoEval, and MM-NIAH, demonstrating flexibility across diverse tasks and domains. Additionally, REFORM reduces inference time by 30% and peak memory usage by 5%, achieving both efficiency and superior performance.

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Bandeira et al. (2022) introduced the Franz-Parisi (FP) criterion for characterizing the computational hard phases in statistical detection problems. The FP criterion, based on an annealed version of the celebrated Franz-Parisi potential from statistical physics, was shown to be equivalent to low-degree polynomial (LDP) lower bounds for Gaussian additive models, thereby connecting two distinct approaches to understanding the computational hardness in statistical inference. In this paper, we propose a refined FP criterion that aims to better capture the geometric ``overlap" structure of statistical models. Our main result establishes that this optimized FP criterion is equivalent to Statistical Query (SQ) lower bounds---another foundational framework in computational complexity of statistical inference. Crucially, this equivalence holds under a mild, verifiable assumption satisfied by a broad class of statistical models, including Gaussian additive models, planted sparse models, as well as non-Gaussian component analysis (NGCA), single-index (SI) models, and convex truncation detection settings. For instance, in the case of convex truncation tasks, the assumption is equivalent with the Gaussian correlation inequality (Royen, 2014) from convex geometry. In addition to the above, our equivalence not only unifies and simplifies the derivation of several known SQ lower bounds—such as for the NGCA model (Diakonikolas et al., 2017) and the SI model (Damian et al., 2024)—but also yields new SQ lower bounds of independent interest, including for the computational gaps in mixed sparse linear regression (Arpino et al., 2023) and convex truncation (De et al., 2023).

Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as powerful priors for solving such problems. However, existing methods either rely on projection-based techniques that enforce measurement consistency through heuristic updates, or they approximate the likelihood $p(\boldsymbol{y} \mid \boldsymbol{x})$, often resulting in artifacts and instability under complex or high-noise conditions. To address these limitations, we propose a novel framework called coupled data and measurement space diffusion posterior sampling (C-DPS), which eliminates the need for constraint tuning or likelihood approximation. C-DPS introduces a forward stochastic process in the measurement space $\{\boldsymbol{y}_t\}$, evolving in parallel with the data-space diffusion $\{\boldsymbol{x}_t\}$, which enables the derivation of a closed-form posterior $p(\boldsymbol{x}_{t-1} \mid \boldsymbol{x}_t, \boldsymbol{y}_{t-1})$. This coupling allows for accurate and recursive sampling based on a well-defined posterior distribution. Empirical results demonstrate that C-DPS consistently outperforms existing baselines, both qualitatively and quantitatively, across multiple inverse problem benchmarks.

The integration of machine learning (ML) into the physical sciences is reshaping computational paradigms, offering the potential to accelerate demanding simulations such as computational fluid dynamics (CFD). Yet, persistent challenges in accuracy, generalization, and physical consistency hinder the practical deployment of ML models in scientific domains. To address these limitations and systematically benchmark progress, we organized the ML4CFD competition, centered on surrogate modeling for aerodynamic simulations over two-dimensional airfoils. The competition attracted over 240 teams, who were provided with a curated dataset generated via OpenFOAM and evaluated through a multi-criteria framework encompassing predictive accuracy, physical fidelity, computational efficiency, and out-of-distribution generalization. This retrospective analysis reviews the competition outcomes, highlighting several approaches that outperformed baselines under our global evaluation score. Notably, the top entry exceeded the performance of the original OpenFOAM solver on aggregate metrics, illustrating the promise of ML based surrogates to outperform traditional solvers under tailored criteria. However, this does not imply that the winning solution could replace the OpenFOAM solver or that it was overall superior, even for this specific task. Drawing from these results, we analyze the key design principles of top submissions, assess the robustness of our evaluation framework, and offer guidance for future scientific ML challenges.

We present *Plenodium* (*plenoptic medium*), an effective and efficient 3D representation framework capable of jointly modeling both objects and the participating medium. In contrast to existing medium representations that rely solely on view-dependent modeling, our novel plenoptic medium representation incorporates both directional and positional information through spherical harmonics encoding, enabling highly accurate underwater scene reconstruction. To address the initialization challenge in degraded underwater environments, we propose the pseudo-depth Gaussian complementation to augment COLMAP-derived point clouds with robust depth priors. In addition, a depth ranking regularized loss is developed to optimize the geometry of the scene and improve the ordinal consistency of the depth maps. Extensive experiments on real-world underwater datasets demonstrate that our method achieves significant improvements in 3D reconstruction. Furthermore, we construct a simulated dataset with GT and the controllable scattering medium to demonstrate the restoration capability of our method in underwater scenarios.