NeurIPS 2025 Papers

Simplicial complexes provide a powerful framework for modeling higher-order interactions in structured data, making them particularly suitable for applications such as trajectory prediction and mesh processing. However, existing simplicial neural networks (SNNs), whether convolutional or attention-based, rely primarily on discrete filtering techniques, which can be restrictive. In contrast, partial differential equations (PDEs) on simplicial complexes offer a principled approach to capture continuous dynamics in such structures. In this work, we introduce continuous simplicial neural network (COSIMO), a novel SNN architecture derived from PDEs on simplicial complexes. We provide theoretical and experimental justifications of COSIMO's stability under simplicial perturbations. Furthermore, we investigate the over-smoothing phenomenon—a common issue in geometric deep learning—demonstrating that COSIMO offers better control over this effect than discrete SNNs. Our experiments on real-world datasets demonstrate that COSIMO achieves competitive performance compared to state-of-the-art SNNs in complex and noisy environments. The implementation codes are available in https://github.com/ArefEinizade2/COSIMO.

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic Gradient Descent (SGD) based solvers have demonstrated strong empirical performance in recent machine learning applications, yet their theoretical guarantee to approximate the OT map is an open question. In this work, we answer it positively by providing both computational and statistical convergence guarantees of SGD. Specifically, we show that SGD methods can estimate the OT map with a minimax convergence rate of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the number of samples drawn from $\mu$. To establish this result, we study the averaged projected SGD algorithm, and identify a suitable projection set that contains a minimizer of the objective, even when the source measure is not compactly supported. Our analysis holds under mild assumptions on the source measure and applies to MTW cost functions,whic include $\|\cdot\|^p$ for $p \in (1, \infty)$. We finally provide numerical evidence for our theoretical results.

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these, $\tau$-leaping samplers have become particularly popular due to their theoretical and empirical success. However, existing theoretical analyses of $\tau$-leaping often rely on somewhat restrictive and difficult-to-verify regularity assumptions, and their convergence bounds contain quadratic dependence on the vocabulary size. In this work, we introduce a new analytical approach for discrete diffusion models that removes the need for such assumptions. For the standard $\tau$-leaping method, we establish convergence guarantees in KL divergence that scale linearly with vocabulary size, improving upon prior results with quadratic dependence. Our approach is also more broadly applicable: it provides the first convergence guarantees for other widely used samplers, including the Euler method and Tweedie $\tau$-leaping. Central to our approach is a novel technique based on differential inequalities, offering a more flexible alternative to the traditional Girsanov change-of-measure methods. This technique may also be of independent interest for the analysis of other stochastic processes.

Seeing hidden structures and objects around corners is critical for robots operating in complex, cluttered environments. Existing methods, however, are limited to detecting and tracking hidden objects rather than reconstructing the occluded full scene. We present HoloRadar, a practical system that reconstructs both line-of-sight (LOS) and non-line-of-sight (NLOS) 3D scenes using a single mmWave radar. HoloRadar uses a two-stage pipeline: the first stage generates high-resolution multi-return range images that capture both LOS and NLOS reflections, and the second stage reconstructs the physical scene by mapping mirrored observations to their true locations using a physics-guided architecture that models ray interactions. We deploy HoloRadar on a mobile robot and evaluate it across diverse real-world environments. Our evaluation results demonstrate accurate and robust reconstruction in both LOS and NLOS regions. Code, dataset and demo videos are available on the project website: https://waves.seas.upenn.edu/projects/holoradar.

Visual localization is a critical component across various domains. The recent emergence of novel scene representations, such as 3D Gaussian Splatting (3D GS), introduces new opportunities for advancing localization pipelines. In this paper, we propose a novel 3D GS-based framework for RGB based, scene-independent camera relocalization, with three main contributions. First, we design a two-stage pipeline with fully exploiting 3D GS. The pipeline consists of an initial stage, which utilizes 2D-3D correspondences between image pixels and 3D Gaussians, followed by pose refinement using the rendered image by 3D GS. Second, we introduce a 3D GS based Relocalization Network, termed GS-RelocNet, to establish correspondences for initial camera pose estimation. Additionally, we present a refinement network that further optimizes the camera pose. Third, we propose a unidirectional 2D-3D feature fusion module and a bidirectional image feature fusion module, integrated into GS-RelocNet and the refinement network, respectively, to enhance feature sharing across the two stages. Experimental results on public 7 Scenes, Cambridge Landmarks, TUM RGB-D and Bonn demonstrate state-of-the-art performance. Furthermore, the beneficial effects of the two feature fusion modules and pose refinement are also highlighted. In summary, we believe that the proposed framework can be a novel universal localization pipeline for further research.

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle with extrapolation and may yield physically implausible forecasts. Furthermore, the learned dynamics can exhibit instabilities, making it difficult to apply such models safely and robustly. This article introduces stable port-Hamiltonian neural networks, a machine learning architecture that incorporates physical biases of energy conservation and dissipation while ensuring global Lyapunov stability of the learned dynamics. Through illustrative and real-world examples, we demonstrate that these strong inductive biases facilitate robust learning of stable dynamics from sparse data, while avoiding instability and surpassing purely data-driven approaches in accuracy and physically meaningful generalization. Furthermore, the model's applicability and potential for data-driven surrogate modeling are showcased on multi-physics simulation data.

We present TIDES, a text informed design approach for generating physically sound designs based on a textual description and a set of physical constraints. TIDES jointly optimizes structural (topology) and visual properties. A pre-trained text-image model is used to measure the design's visual alignment with a text prompt and a differentiable physics simulator is used to measure its physical performance. We evaluate TIDES on a series of structural optimization problems operating under different load and support conditions, at different resolutions, and experimentally in the lab by performing the 3-point bending test on 2D beam designs that are extruded and 3D printed. We find that it can jointly optimize the two objectives and return designs that satisfy engineering design requirements (compliance and density) while utilizing features specified by text.

Recent advances in video generation models have sparked interest in world models capable of simulating realistic environments. While navigation has been well-explored, physically meaningful interactions that mimic real-world forces remain largely understudied. In this work, we investigate using physical forces as a control signal for video generation and propose force prompts which enable users to interact with images through both localized point forces, such as poking a plant, and global wind force fields, such as wind blowing on fabric. We demonstrate that these force prompts can enable videos to respond realistically to physical control signals by leveraging the physical prior in the original pretrained model, without using any 3D asset or physics simulator at inference. The primary challenge of force prompting is the difficulty in obtaining high quality paired force-video training data, both in the real world due to the difficulty of obtaining force signals, and in synthetic data due to limitations in the visual quality and domain diversity of physics simulators. Our key finding is that video generation models can *generalize* remarkably well when adapted to follow physical force conditioning from videos synthesized by Blender, even with limited demonstrations of few objects (e.g., flying flags, rolling balls, etc.). Our method can generate videos which simulate forces across diverse geometries, settings, and materials. We also try to understand the source of this generalization and perform ablations on the training data that reveal two key elements: visual diversity and the use of specific text keywords during training. Our approach is trained on only around 15k training examples for a single day on four A100 GPUs, and outperforms existing methods on force adherence and physics realism, bringing world models closer to real-world physics interactions. All datasets, code, and model weights will be open-sourced. Video examples can be found at https://sites.google.com/view/force-prompting-neurips2025

Antimicrobial peptides have emerged as promising molecules to combat antimicrobial resistance. However, fragmented datasets, inconsistent annotations, and the lack of standardized benchmarks hinder computational approaches and slow down the discovery of new candidates. To address these challenges, we present the Expanded Standardized Collection for Antimicrobial Peptide Evaluation (ESCAPE), an experimental framework integrating over 80.000 peptides from 27 validated repositories. Our dataset separates antimicrobial peptides from negative sequences and incorporates their functional annotations into a biologically coherent multilabel hierarchy, capturing activities across antibacterial, antifungal, antiviral, and antiparasitic classes. Building on ESCAPE, we propose a transformer-based model that leverages sequence and structural information to predict multiple functional activities of peptides. Our method achieves up to a 2.56% relative average improvement in mean Average Precision over the second-best method adapted for this task, establishing a new state-of-the-art multilabel peptide classification. ESCAPE provides a comprehensive and reproducible evaluation framework to advance AI-driven antimicrobial peptide research.

We introduce *BecomingLit*, a novel method for reconstructing relightable, high-resolution head avatars that can be rendered from novel viewpoints at interactive rates. Therefore, we propose a new low-cost light stage capture setup, tailored specifically towards capturing faces. Using this setup, we collect a novel dataset consisting of diverse multi-view sequences of numerous subjects under varying illumination conditions and facial expressions. By leveraging our new dataset, we introduce a new relightable avatar representation based on 3D Gaussian primitives that we animate with a parametric head model and an expression-dependent dynamics module. We propose a new hybrid neural shading approach, combining a neural diffuse BRDF with an analytical specular term. Our method reconstructs disentangled materials from our dynamic light stage recordings and enables all-frequency relighting of our avatars with both point lights and environment maps. In addition, our avatars can easily be animated and controlled from monocular videos. We validate our approach in extensive experiments on our dataset, where we consistently outperform existing state-of-the-art methods in relighting and reenactment by a significant margin.

We present UniFoil, the largest publicly available universal airfoil database based on Reynolds-Averaged Navier–Stokes (RANS) simulations. It contains over 500,000 samples spanning a wide range of Reynolds and Mach numbers, capturing both transitional and fully turbulent flows across incompressible to compressible regimes. UniFoil is designed to support machine learning research in fluid dynamics, particularly for modeling complex aerodynamic phenomena. Most existing datasets are limited to incompressible, fully turbulent flows with smooth field characteristics, thus overlooking the critical physics of laminar–turbulent transition and shock-wave interactions—features that exhibit strong nonlinearity and sharp gradients. UniFoil fills this gap by offering a broad spectrum of realistic flow conditions. In the database, turbulent simulations utilize the Spalart–Allmaras (SA) model, while transitional flows are modeled using an $e^N$-based transition prediction method coupled with the SA model. The database includes a comprehensive geometry set comprising over 4,800 natural laminar flow (NLF) airfoils and 30,000 fully turbulent (FT) airfoils, effectively covering the diversity of airfoil designs relevant to aerospace, wind energy, and marine applications. This database is also highly valuable for scientific machine learning (SciML), enabling the development of data-driven models that more accurately capture the transport processes associated with laminar–turbulent transition. UniFoil is freely available under a permissive CC-BY-SA license.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 × 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

Super-resolution (SR) advances astronomical imaging by enabling cost-effective high-resolution capture, crucial for detecting faraway celestial objects and precise structural analysis. However, existing datasets for astronomical SR (ASR) exhibit three critical limitations: flux inconsistency, object-crop setting, and insufficient data diversity, significantly impeding ASR development. We propose STAR, a large-scale astronomical SR dataset containing 54,738 flux-consistent star field image pairs covering wide celestial regions. These pairs combine Hubble Space Telescope high-resolution observations with physically faithful low-resolution counterparts generated through a flux-preserving data generation pipeline, enabling systematic development of field-level ASR models. To further empower the ASR community, STAR provides a novel Flux Error (FE) to evaluate SR models in physical view. Leveraging this benchmark, we propose a Flux-Invariant Super Resolution (FISR) model that could accurately infer the flux-consistent high-resolution images from input photometry, suppressing several SR state-of-the-art methods by 24.84% on a novel designed flux consistency metric, showing the priority of our method for astrophysics. Extensive experiments demonstrate the effectiveness of our proposed method and the value of our dataset. Code and models are available at https://github.com/GuoCheng12/STAR.

Tree ensembles have demonstrated state-of-the-art predictive performance across a wide range of problems involving tabular data. Nevertheless, the black-box nature of tree ensembles is a strong limitation, especially for applications with critical decisions at stake. The Hoeffding or ANOVA functional decomposition is a powerful explainability method, as it breaks down black-box models into a unique sum of lower-dimensional functions, provided that input variables are independent. In standard learning settings, input variables are often dependent, and the Hoeffding decomposition is generalized through hierarchical orthogonality constraints. Such generalization leads to unique and sparse decompositions with well-defined main effects and interactions. However, the practical estimation of this decomposition from a data sample is still an open problem. Therefore, we introduce the TreeHFD algorithm to estimate the Hoeffding decomposition of a tree ensemble from a data sample. We show the convergence of TreeHFD, along with the main properties of orthogonality, sparsity, and causal variable selection. The high performance of TreeHFD is demonstrated through experiments on both simulated and real data, using our treehfd Python package (https://github.com/ThalesGroup/treehfd). Besides, we empirically show that the widely used TreeSHAP method, based on Shapley values, is strongly connected to the Hoeffding decomposition.

360-degree monocular depth estimation plays a crucial role in scene understanding owing to its 180-degree by 360-degree field-of-view (FoV). To mitigate the distortions brought by equirectangular projection, existing methods typically divide 360-degree images into distortion-less perspective patches. However, since these patches are processed independently, depth inconsistencies are often introduced due to scale drift among patches. Recently, video depth estimation (VDE) models have leveraged temporal consistency for stable depth predictions across frames. Inspired by this, we propose to represent a 360-degree image as a sequence of perspective frames, mimicking the viewpoint adjustments users make when exploring a 360-degree scenario in virtual reality. Thus, the spatial consistency among perspective depth patches can be enhanced by exploiting the temporal consistency inherent in VDE models. To this end, we introduce a training-free pipeline for 360-degree monocular depth estimation, called ST²360D. Specifically, ST²360D transforms a 360-degree image into perspective video frames, predicts video depth maps using VDE models, and seamlessly merges these predictions into a complete 360-degree depth map. To generate sequenced perspective frames that align with VDE models, we propose two tailored strategies. First, a spherical-uniform sampling (SUS) strategy is proposed to facilitate uniform sampling of perspective views across the sphere, avoiding oversampling in polar regions typically with limited structural details. Second, a latitude-guided scanning (LGS) strategy is introduced to organize the frames into a coherent sequence, starting from the equator, prioritizing low-latitude slices, and progressively moving toward higher latitudes. Extensive experiments demonstrate that ST²360D achieves strong zero-shot capability on several datasets, supporting resolutions up to 4K.

The widespread adoption of large language models (LLMs) across industries has increased the demand for high-quality and customizable outputs. However, traditional alignment methods often require retraining large pretrained models, making it difficult to quickly adapt and optimize LLMs for diverse applications. To address this limitation, we propose a novel \textit{Residual Alignment Model} (\textit{RAM}) that formalizes the alignment process as a type of importance sampling. In this framework, the unaligned upstream model serves as the proposal distribution, while the alignment process is framed as secondary sampling based on an autoregressive alignment module that acts as an estimator of the importance weights. This design enables a natural detachment of the alignment module from the target aligned model, improving flexibility and scalability. Based on this model, we derive an efficient sequence-level training strategy for the alignment module, which operates independently of the proposal module. Additionally, we develop a resampling algorithm with iterative token-level decoding to address the common first-token latency issue in comparable methods. Experimental evaluations on two leading open-source LLMs across diverse tasks, including instruction following, domain adaptation, and preference optimization, demonstrate that our approach consistently outperforms baseline models.

Retrieval-augmented generation (RAG) has become a widely adopted paradigm for enabling knowledge-grounded large language models (LLMs). However, standard RAG pipelines often fail to ensure that model reasoning remains consistent with the evidence retrieved, leading to factual inconsistencies or unsupported conclusions. In this work, we reinterpret RAG as \textit{Retrieval-Augmented Reasoning} and identify a central but underexplored problem: \textit{Reasoning Misalignment}—the divergence between an LLM's internal reasoning trajectory and the evidential constraints provided by retrieval. To address this issue, we propose \textsc{AlignRAG}, a novel iterative framework grounded in \textit{Critique-Driven Alignment (CDA)}. We further introduce \textsc{AlignRAG-auto}, an autonomous variant that dynamically terminates refinement, removing the need to pre-specify the number of critique iterations. At the heart of \textsc{AlignRAG} lies a \textit{contrastive critique synthesis} mechanism that generates retrieval-sensitive critiques while mitigating self-bias. This mechanism trains a dedicated retrieval-augmented \textit{Critic Language Model (CLM)} using labeled critiques that distinguish between evidence-aligned and misaligned reasoning. Empirical evaluations show that our approach significantly improves reasoning fidelity. Our 8B-parameter CLM improves performance over the Self-Refine baseline by \textbf{12.1\%} on out-of-domain tasks and outperforms a standard 72B-parameter CLM by \textbf{2.2\%}. Furthermore, \textsc{AlignRAG-auto} achieves this state-of-the-art performance while dynamically determining the optimal number of refinement steps, enhancing efficiency and usability. \textsc{AlignRAG} remains compatible with existing RAG architectures as a \textit{plug-and-play} module and demonstrates strong robustness under both informative and noisy retrieval scenarios. Overall, \textsc{AlignRAG} offers a principled solution for aligning model reasoning with retrieved evidence, substantially improving the factual reliability and robustness of RAG systems. Our source code is provided at \href{https://github.com/upup-wei/RAG-ReasonAlignment}{link}.

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a flexible framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

A fundamental challenge in organic chemistry is identifying and predicting the sequence of reactions that synthesize a desired target molecule. Due to the combinatorial nature of the chemical search space, single-step reactant prediction—i.e., single-step retrosynthesis—remains difficult, even for state-of-the-art template-free generative methods. These models often struggle to produce an accurate yet diverse set of feasible reactions in a chemically rational manner. In this paper, we propose RETRO SYNFLOW (RSF), a discrete flow-matching framework that formulates single-step retrosynthesis as a Markov bridge between a given product molecule and its corresponding reactants. Unlike prior approaches, RSF introduces a reaction center identification step to extract intermediate structures, or synthons, which serve as a more informative and structured source distribution for the discrete flow model. To further improve the diversity and chemical feasibility of generated samples, RSF incorporates Feynman-Kac (FK) steering with Sequential Monte Carlo (SMC) resampling at inference time. This approach leverages a learned forward-synthesis reward oracle to guide the generation process toward more promising reactant candidates. Empirically, RSF substantially outperforms the previous state-of-the-art methods in top-1 accuracy. In addition, FK-steering significantly improves round-trip accuracy, demonstrating stronger chemical validity and synthetic feasibility, all while maintaining competitive top-k performance. These results establish RSF as a new leading approach for single-step retrosynthesis prediction.