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Deep Learning · Generative Models and Autoencoders

Kijung Jeon, Michael Muehlebach, Molei Tao

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $\Sigma$ that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto $\Sigma$, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Applications · Time Series

Ruituo Wu, Hongyu Zhang, Qiang Wang, Jiawei Du, Wei Cui, Ce Zhu, Bing Li

Learning from continuous-time trajectories requires modeling multivariate sensor measurements generated by underlying physical or dynamical processes. Under extreme data compression and heterogeneous sampling, directly optimizing synthetic signals as discrete sample values becomes fundamentally misaligned with the underlining \emph{continuous-time physical processes}, often producing high-frequency, non-physical artifacts that overfit specific models and break reuse across architectures and sampling rates. We propose CHESS, a \emph{function-first} synthesis framework shifts optimization from discrete samples to underlying continuous-time signal trajectories. CHESS injects physics-induced structure by jointly enforcing low-rank spatial coherence and piecewise Chebyshev polynomial temporal parameterization, constraining synthesis to a physically meaningful function manifold. We provide theoretical analysis establishing explicit smoothness and stability guaranties. Experiments on diverse sensor testbeds under the dataset distillation protocol demonstrate CHESS consistently outperform state-of-the-art methods with a compression ratios up to $133\times$ for each synthetic sample. Furthermore, CHESS exhibits strong cross-architecture generalization and enables zero-shot adaptation across different sampling resolutions.

Applications · Health / Medicine

Yinbo Liu, Keyang Ye, Wenshan Sun, Handi Gao, Tian Tian

Reconstructing unified continuous dynamics from sparse, non-contiguous, and unpaired point cloud snapshots remains a fundamental challenge in spatiotemporal analysis for computer vision and developmental biology. Existing methods, including scene flow and Optimal Transport-based approaches, are limited either by explicit reliance on point-wise correspondences or by cumulative errors from frame-to-frame propagation and temporal discontinuity, and limited ability to model multi-attribute dynamics such as gene expression and population changes. We propose FlowCloud, a variational Neural Ordinary Differential Equation (Neural ODE) generative framework. FlowCloud aggregates information from all observed time points into a joint latent representation that initializes a Neural ODE $z(t)$ enabling continuous spatiotemporal evolution modeling while mitigating propagation-induced errors and preserving temporal consistency. Training is performed without predefined correspondences using a multi-faceted objective with complementary roles: Sinkhorn distance for global distribution alignment, Chamfer distance for local geometric consistency, trajectory regularization to encourage smooth and physically plausible dynamics, and supervised losses for multi-attribute prediction. Experiments on human motion and developmental biology datasets demonstrate improved interpolation accuracy and promising short-term extrapolation performance. By unifying geometry, attributes, and population dynamics within a continuous latent framework, FlowCloud offers a novel and robust solution for continuous dynamic reconstruction from unstructured spatiotemporal observations.

Applications · Chemistry, Physics, and Earth Sciences

Weilong Chen, Bojun Zhao, Jan Eckwert, Julija Zavadlav

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but their practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack the reweighting process required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a principled framework that unifies scalable reduced-order modeling with the exactness of importance sampling. CG-BGs act in a coarse-grained coordinate space, using a learned potential of mean force (PMF) to reweight samples generated by a flow-based model. Crucially, we show that this PMF can be efficiently learned from rapidly converged data via force matching. Our results demonstrate that CG-BGs faithfully capture complex interactions mediated by explicit solvent within highly reduced representations, establishing a scalable pathway for the unbiased sampling of larger molecular systems.

Applications · Robotics

Yu Guan, Zekun Qi, Chenghuai Lin, Xuchuan Chen, Wenyao Zhang, Jilong Wang, XinQiang Yu, He Wang, Li Yi

We argue that high-quality motion data can steer tracking policies toward better optimization trajectories early in training. In this work, we introduce LIMMT (Less Is More for Motion Tracking). To our knowledge, this is the first data-centric study for physics-based humanoid motion tracking. We go beyond simply removing erroneous clips. We define motion data quality through three dimensions: physics feasibility, diversity, and complexity. We show that training with under 3% of AMASS yields better tracking performance than training with the full dataset. Extensive experiments and analyses validate the effectiveness of our framework. We will release our code and curated data on GitHub.

Theory · Everything Else

Siyi Lyu, Quan Liu, Feng Yan

Vision Transformers (ViTs) excel in semantic recognition but exhibit systematic failures in spatial reasoning tasks such as mental rotation. While often attributed to data scale, this work argues that the limitation arises from the intrinsic circuit complexity of the architecture. By formalizing spatial understanding as a **Group Homomorphism Problem**—requiring that latent embeddings preserve the algebraic composition of physical transformations acting on images—a fundamental computational bottleneck is identified. Specifically, for non-solvable groups (e.g., $\mathrm{SO}(3)$), maintaining such structure-preserving embeddings is lower-bounded by the Word Problem, which is $\mathsf{NC^1}$-complete. In contrast, constant-depth ViTs with polynomial precision are strictly bounded by the complexity class $\mathsf{TC^0}$. Under the standard conjecture $\mathsf{TC^0} \subsetneq \mathsf{NC^1}$, a **complexity boundary** emerges: constant-depth architectures lack the logical depth required to capture non-solvable spatial structures. This theoretical gap is empirically validated via the **Latent Space Algebra (LSA)** benchmark, which reveals a structural collapse in ViT representations as the compositional depth of non-solvable tasks increases.

Applications · Chemistry, Physics, and Earth Sciences

Xin Ju, Hadrian Fung, Yuyan Zhang, Carl Jacquemyn, Matthew Jackson, Randolph Settgast, Sally Benson, Gege Wen

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical simulations of these systems are notoriously computationally expensive due to geological heterogeneity, high resolution requirements, and the tight coupling of physical processes with distinct propagation time scales. Here we propose the Adaptive Physics Transformer (APT), a geometry-, mesh-, and physics-agnostic neural operator that explicitly addresses these challenges. APT fuses a graph-based encoder to extract high-resolution local heterogeneous features with a global attention mechanism to resolve long-range physical impacts. Our results demonstrate that APT outperforms state-of-the-art architectures in subsurface tasks across both regular and irregular grids with robust super-resolution capabilities. Notably, APT is the first architecture that directly learns from adaptive mesh refinement simulations. We also demonstrate APT's capability for cross-dataset learning, positioning it as a robust and scalable backbone for large-scale subsurface foundation model development.

Applications · Computer Vision

Jihyun Lee, Changmin Lee, Donghwan Kim, Tae-Kyun Kim

While existing methods for reconstructing hand–object interactions have made impressive progress, they either focus on rigid or part-wise rigid objects—limiting their ability to model real-world objects (e.g., cloth, stuffed animals) that exhibit highly non-rigid deformations—or model deformable objects without full 3D hand reconstruction. To bridge this gap, we present PhysHandi (Physics-based Reconstruction of Hand and Deformable Object Interactions), a framework that enables full 3D reconstruction of both interacting hands and non-rigid objects. Our key idea is to physically simulate object deformations driven by forces induced from densely reconstructed 3D hand motions, ensuring that the reconstructed object dynamics are both physically plausible and coherent with the interacting hand movements. Furthermore, we demonstrate that such simulation of object deformations can, in turn, refine and improve hand reconstruction via inverse physics. In experiments, PhysHandi outperforms the state-of-the-art baseline across reconstruction and future prediction.

Deep Learning · Generative Models and Autoencoders

Yuanbin Man, Ying Huang, Zhile Ren, Miao Yin

4D generation, or dynamic 3D content generation, integrates spatial, temporal, and view dimensions to model realistic dynamic scenes, playing a foundational role in advancing world models and physical AI. However, maintaining long-chain consistency across both frames and viewpoints through the unique spatio-camera-motion (SCM) attention mechanism introduces substantial computational and memory overhead, often leading to out-of-memory (OOM) failures and prohibitive generation times. To address these challenges, we propose Turbo4DGen, an ultra-fast acceleration framework for diffusion-based multi-view 4D content generation. Turbo4DGen introduces a spatiotemporal cache mechanism that persistently reuses intermediate attention across denoising steps, combined with dynamically semantic-aware attention pruning and an adaptive SCM chain bypass scheduler, to drastically reduce redundant SCM attention computation. Our experimental results show that Turbo4DGen achieves an average 9.7$\times$ speedup without quality degradation on the ObjaverseDy and Consistent4D datasets. To the best of our knowledge, Turbo4DGen is the first dedicated acceleration framework for 4D generation.

Social Aspects · Everything Else

Yucen Gao, Zhemeng Yu, Zhuoran Li, Jianxiong Guo, Xiaofeng Gao

Social recruitment offers a solution to worker scarcity in Spatial Crowdsourcing (SC) but faces challenges that are often ignored in traditional Influence Maximization. First, task heterogeneity arising from offline execution constraints breaks the ``interest-implies-participation'' assumption, as social influence often fails to translate into physical presence. Second, finite task demand creates a ``saturation trap'', a non-submodular setting in which utility drops sharply to zero once demand is met. To bridge these gaps, we propose GKD-Recruiter, a Task-Aware framework designed to maximize Effective Task Satisfaction (ETS). We explicitly model the complex worker-task affinity via a heterogeneous graph and capture directional social influence using a novel Influential GAT. To robustly fuse these distinct signals, we introduce a Graph Knowledge Distillation mechanism. Furthermore, we employ Rainbow DQN to navigate the non-submodular combinatorial search space, avoiding the local optima that trap greedy heuristics. Extensive experiments on real-world datasets demonstrate that GKD-Recruiter significantly outperforms state-of-the-art baselines in both solution quality and inference efficiency. The code is available at \url{https://anonymous.4open.science/r/GKD-Recruiter-3A4B}.

Optimization · Large Scale, Parallel and Distributed

Demyan Yarmoshik, Nhat Trung Nguyen, Alexander Rogozin, Alexander Gasnikov

This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while local variables are subject to coupled and node-specific constraints. Such problem formulations arise in machine learning applications, including federated learning and multi-task learning, as well as in resource allocation and distributed control. We analyze this problem under smooth and non-smooth assumptions, considering both strongly convex and general convex objective functions. Our main contribution is an optimal algorithm for the smooth, strongly convex regime, whose convergence rate matches established lower complexity bounds. We further provide near-optimal methods for the remaining cases.

Applications · Neuroscience, Cognitive Science

Haowei Xu, Yixin Chen, Wanyi Fu, Hongbin Han, Zhaoheng Xie

Neuromodulation can be viewed as closed-loop control of high-dimensional spatiotemporal fields on irregular 3D morphologies, coupling membrane electrophysiology with ionic reaction–diffusion. This view supports high-rate feedback and systematic in-silico evaluation, yet is difficult in practice. Unlike classical PDE control with known equations on regular domains, neuronal microenvironments exhibit complex, often unknown biophysics on irregular shapes. High-fidelity simulators are too costly for real-time control with repeated planning. The discretized field is sparsely observed and must satisfy hard full-field safety constraints. We introduce **NeuronCtrl**, a modular operator-level framework for safe, closed-loop generative control of neuronal microenvironment dynamics. Given measurements, actions, and morphology, a history-conditioned observer infers the latent field, a morphology-aware neural operator predicts one-step dynamics, and a flow-matching conditional flow proposes actions conditioned on user preferences. Safety is enforced via complementary barrier-based mechanisms at both the action and field levels, ensuring constraint satisfaction with minimal intervention. When latency is critical, the multi-step generator is distilled into a single-step policy while retaining the same safety filter. Experiments across three high-fidelity 3D neuromodulation benchmarks spanning deep brain stimulation, extracellular reaction--diffusion control, and astrocytic potassium regulation, demonstrate superior trade-offs among cost, safety, and latency. Code is available at https://anonymous.4open.science/r/NeuronControl-D900.

Deep Learning · Generative Models and Autoencoders

Phil Sidney Ostheimer, Mayank Kumar Nagda, Andriy Balinskyy, Gabriel Rodrigues, Jean Radig, Carl Herrmann, Stephan Mandt, Marius Kloft, Sophie Fellenz

Diffusion models (DMs) excel on dense continuous data, but are not designed for sparse continuous data. They do not model exact zeros that represent the deliberate absence of a signal. As a result, they erase sparsity patterns and perform unnecessary computation on mostly zero entries. With Sparsity-Exploiting Diffusion (SED), we model only non-zero values, preserving sparsity. SED delivers computational savings while maintaining or improving generation quality by skipping zeros during training and inference. Across physics and biology benchmarks, SED matches or surpasses conventional DMs and domain-specific baselines, while vision experiments provide intuitive insights into the limitations of dense DMs and the benefits of SED.

Applications · Chemistry, Physics, and Earth Sciences

Yaotian Yang, Yiwen Tang, Yizhe Chen, Xiao Chen, Jiangjie Qiu, Hao Xiong, Haoyu Yin, Zhiyao Luo, Yifei Zhang, Sijia Tao 等

Reconstructing atomistic crystal structures from a single noisy STEM projection is an ill-posed inverse problem: multiple lattices can explain similar contrast, and purely feed-forward models cannot verify physical validity. We present **AutoMat**, a failure-aware agentic *controller* that performs inference-time hypothesis search with *closed-loop verification* to convert Scanning Transmission Electron Microscopy (STEM) images into simulation-ready crystal structures and downstream properties. AutoMat composes perception and physics modules—pattern-adaptive denoising, physics-guided template retrieval (as a fallback), symmetry-constrained atomic reconstruction, and MLIP-based relaxation/validation—and triggers rollback-and-retry when verification fails. For systematic evaluation, we introduce **STEM2Mat-Bench**, a benchmark dataset containing 450+ annotated samples. Performance is assessed using lattice root-mean-square deviation (RMSD), formation energy mean absolute error (MAE), and structure matching accuracy. Results demonstrate that AutoMat outperforms existing approaches including SOTA models, specialized domain tools, and closed-source multimodal large models. This work establishes a direct pathway from microscopic characterization to atomic-scale modeling, addressing a fundamental challenge in materials science.

Applications · Chemistry, Physics, and Earth Sciences

Jephte Abijuru, Mayank Kumar Nagda, Phil Sidney Ostheimer, Jan Tauberschmidt, Sebastian Vollmer, Stephan Mandt, Marius Kloft, Sophie Fellenz

Physics-informed neural networks (PINNs) enforce physical laws by minimizing partial differential equation (PDE) residuals and auxiliary constraints. Standard training relies on a mean-squared error (MSE) objective, which implicitly assumes independent Gaussian residuals with a fixed global variance. We show theoretically and empirically that residuals encountered during PINN training are heterogeneous and heavy-tailed, revealing a systematic mismatch with this assumption. As a consequence, a small number of large residuals can disproportionately dominate both the loss and gradient, leading to poorly balanced optimization dynamics. Motivated by this mismatch, we adopt a Student-$t$ residual model to explicitly capture heavy-tailed behavior. An equivalent hierarchical representation yields an expectation–maximization (EM) algorithm that alternates between estimating residual-dependent weights and optimizing network parameters via a weighted MSE objective, allowing existing PINN solvers to be reused in the M-step. The resulting training dynamics bound the influence of extreme residuals and admit almost sure convergence guarantees under standard stochastic optimization assumptions. Experiments across a diverse suite of challenging PDE benchmarks demonstrate consistently improved solution accuracy and robustness compared to standard PINN training.

Applications · Chemistry, Physics, and Earth Sciences

Jephte Abijuru, Mayank Kumar Nagda, Phil Sidney Ostheimer, Sebastian Vollmer, Marius Kloft, Sophie Fellenz

Physics-Informed Neural Networks (PINNs) embed physical laws into deep learning models. However, conventional PINNs often suffer from failure modes leading to inaccurate solutions. We trace these failure modes to two structural pathologies: gradient shattering, where gradients degrade with depth and provide little training signal, and flow mismatch, where training pushes predictions along trajectories that diverge from the PDE solution path. We introduce ResPINNs, which reformulate PINNs as residual flows, networks that iteratively refine their own predictions through explicit corrective steps, in the spirit of classical iterative solvers. Our analysis shows that this design mitigates both pathologies by keeping updates aligned with descent and by preserving informative gradients across depth. Extensive experiments on PDE benchmarks confirm that ResPINNs achieve higher accuracy with substantially fewer parameters than conventional architectures.

Sherry Yang

Large language model (LLM) agents trained using reinforcement learning has achieved superhuman performance in low-cost environments like games, mathematics, and coding. However, these successes have not translated to complex domains where the cost of interaction is high, such as the physical cost of running robots, the time cost of ML engineering, and the resource cost of scientific experiments. The true bottleneck for achieving the next level of agent performance for these complex and high-cost domains lies in the expense of executing actions to acquire reward signals. To address this gap, this paper argues that we should use world models as an intermediary between agents and the real world. We discuss how world models, viewed as models of dynamics, rewards, and task distributions, can overcome fundamental barriers of high-cost actions such as extreme off-policy learning and sample inefficiency in long-horizon tasks. Moreover, we demonstrate how world models can provide critical and rich learning signals to agents across a broad set of domains, including machine learning engineering, computer use, robotics, and AI for science. Lastly, we identify the challenges of building these world models and propose actionable items along dataset curation, architecture design, scaling, and evaluation of world models.

Applications · Computer Vision

Jue Gong, Zihan Zhou, Jingkai Wang, Xiaohong Liu, Yulun Zhang, Xiaokang Yang

Face fill-light enhancement (FFE) brightens underexposed faces by adding virtual fill light while keeping the original scene illumination and background unchanged. Most face relighting methods aim to reshape overall lighting, which can suppress the input illumination or modify the entire scene, leading to foreground–background inconsistency and mismatching practical FFE needs. To support scalable learning, we introduce LightYourFace-160K (LYF-160K), a large-scale paired dataset built with a physically consistent renderer that injects a disk-shaped area fill light controlled by six disentangled factors, producing 160K before-and-after pairs. We first pretrain a physics-aware lighting prompt (PALP) that embeds the 6D parameters into diffusion-compatible conditioning tokens, using an auxiliary planar-light reconstruction objective. Building on a pretrained diffusion backbone, we then train FiLitDiff, an efficient one-step model conditioned on these physically grounded lighting codes, enabling fast, controllable, and high-fidelity fill lighting at low computational cost. Experiments on held-out paired sets demonstrate strong perceptual quality and competitive full-reference metrics, while better preserving background illumination. The dataset and model will be released.

Applications · Chemistry, Physics, and Earth Sciences

Martin Andrae, Erik Larsson, So Takao, Tomas Landelius, Fredrik Lindsten

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble Kalman filter, rely on Gaussian approximations that are violated for complex dynamics or observation operators. To address this limitation, we introduce DAISI, a scalable filtering algorithm built on flow-based generative models that enables flexible probabilistic inference using data-driven priors. The core idea is to use a stationary, pre-trained generative prior that first incorporates forecast information through a novel *inverse-sampling step*, before assimilating observations via guidance-based conditional sampling. This allows us to leverage any forecasting model as part of the DA pipeline without having to retrain or fine-tune the generative prior at each assimilation step. Experiments on challenging nonlinear systems show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations where traditional methods struggle.

Deep Learning · Graph Neural Networks

Edward Berman, Luisa Li, Jung Yeon Park, Robin Walters

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks. Our code is available at https://anonymous.4open.science/r/rayleigh_analysis-BD52/README.md .