Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic $L^2(Ω)$-error bounds for FK-PINNs with $\tanh$ activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of $\tanh$ neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schrödinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.

Generative Path-Finding Method for Wasserstein Gradient Flow

Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the full path from an arbitrary initial distribution to equilibrium is challenging, especially in high dimensions. Eulerian methods suffer from the curse of dimensionality, while existing Lagrangian approaches based on particles or generative maps do not naturally improve efficiency through time step tuning. We propose GenWGP, a generative path finding framework for Wasserstein gradient paths. GenWGP learns a generative flow that transports mass from an initial density to an unknown equilibrium distribution by minimizing a path loss that encodes the full trajectory and its terminal equilibrium condition. The loss is derived from a geometric action functional motivated by Dawson Gartner large deviation theory for empirical distributions of interacting diffusion systems. We formulate both a finite horizon action under physical time parametrization and a reparameterization invariant geometric action based on Wasserstein arclength. Using normalizing flows, GenWGP computes a geometric curve toward equilibrium while enforcing approximately constant intrinsic speed between adjacent network layers, so that discretized distributions remain nearly equidistant in the Wasserstein metric along the path. This avoids delicate time stepping constraints and enables stable training that is largely independent of temporal or geometric discretization. Experiments on Fokker Planck and aggregation type problems show that GenWGP matches or exceeds high fidelity reference solutions with only about a dozen discretization points while capturing complex dynamics.

A Multimodal Foundation Model of Spatial Transcriptomics and Histology for Biological Discovery and Clinical Prediction

Spatial transcriptomics (ST) enables gene expression mapping within anatomical context but remains costly and low-throughput. Hematoxylin and eosin (H\&E) staining offers rich morphology yet lacks molecular resolution. We present \textbf{\ours} (\textbf{S}patial \textbf{T}ranscriptomics and hist\textbf{O}logy \textbf{R}epresentation \textbf{M}odel), a foundation model trained on 1.2 million spatially resolved transcriptomic profiles with matched histology across 18 organs. Using a hierarchical architecture integrating morphological features, gene expression, and spatial context, STORM bridges imaging and omics through robust molecular--morphological representations. STORM enhances spatial domain discovery, producing biologically coherent tissue maps, and outperforms existing methods in predicting spatial gene expression from H\&E images across 11 tumor types. The model is platform-agnostic, performing consistently across Visium, Xenium, Visium HD, and CosMx. Applied to 23 independent cohorts comprising 7,245 patients, STORM significantly improves immunotherapy response prediction and prognostication over established biomarkers, providing a scalable framework for spatially informed discovery and clinical precision medicine.

A Generative Foundation Model for Multimodal Histopathology

Accurate diagnosis and treatment of complex diseases require integrating histological, molecular, and clinical data, yet in practice these modalities are often incomplete owing to tissue scarcity, assay cost, and workflow constraints. Existing computational approaches attempt to impute missing modalities from available data but rely on task-specific models trained on narrow, single source-target pairs, limiting their generalizability. Here we introduce MuPD (Multimodal Pathology Diffusion), a generative foundation model that embeds hematoxylin and eosin (H&E)-stained histology, molecular RNA profiles, and clinical text into a shared latent space through a diffusion transformer with decoupled cross-modal attention. Pretrained on 100 million histology image patches, 1.6 million text-histology pairs, and 10.8 million RNA-histology pairs spanning 34 human organs, MuPD supports diverse cross-modal synthesis tasks with minimal or no task-specific fine-tuning. For text-conditioned and image-to-image generation, MuPD synthesizes histologically faithful tissue architectures, reducing Fréchet inception distance (FID) scores by 50% relative to domain-specific models and improving few-shot classification accuracy by up to 47% through synthetic data augmentation. For RNA-conditioned histology generation, MuPD reduces FID by 23% compared with the next-best method while preserving cell-type distributions across five cancer types. As a virtual stainer, MuPD translates H&E images to immunohistochemistry and multiplex immunofluorescence, improving average marker correlation by 37% over existing approaches. These results demonstrate that a single, unified generative model pretrained across heterogeneous pathology modalities can substantially outperform specialized alternatives, providing a scalable computational framework for multimodal histopathology.

UEPS: Robust and Efficient MRI Reconstruction

Deep unrolled models (DUMs) have become the state of the art for accelerated MRI reconstruction, yet their robustness under domain shift remains a critical barrier to clinical adoption. In this work, we identify coil sensitivity map (CSM) estimation as the primary bottleneck limiting generalization. To address this, we propose UEPS, a novel DUM architecture featuring three key innovations: (i) an Unrolled Expanded (UE) design that eliminates CSM dependency by reconstructing each coil independently; (ii) progressive resolution, which leverages k-space-to-image mapping for efficient coarse-to-fine refinement; and (iii) sparse attention tailored to MRI's 1D undersampling nature. These physics-grounded designs enable simultaneous gains in robustness and computational efficiency. We construct a large-scale zero-shot transfer benchmark comprising 10 out-of-distribution test sets spanning diverse clinical shifts -- anatomy, view, contrast, vendor, field strength, and coil configurations. Extensive experiments demonstrate that UEPS consistently and substantially outperforms existing DUM, end-to-end, diffusion, and untrained methods across all OOD tests, achieving state-of-the-art robustness with low-latency inference suitable for real-time deployment.

Stepping VLMs onto the Court: Benchmarking Spatial Intelligence in Sports

Sports have long attracted broad attention as they push the limits of human physical and cognitive capabilities. Amid growing interest in spatial intelligence for vision-language models (VLMs), sports provide a natural testbed for understanding high-intensity human motion and dynamic object interactions. To this end, we present CourtSI, the first large-scale spatial intelligence dataset tailored to sports scenarios. CourtSI contains over 1M QA pairs, organized under a holistic taxonomy that systematically covers spatial counting, distance measurement, localization, and relational reasoning, across representative net sports including badminton, tennis, and table tennis. Leveraging well-defined court geometry as metric anchors, we develop a semi-automatic data engine to reconstruct sports scenes, enabling scalable curation of CourtSI. In addition, we introduce CourtSI-Bench, a high-quality evaluation benchmark comprising 3,686 QA pairs with rigorous human verification. We evaluate 25 proprietary and open-source VLMs on CourtSI-Bench, revealing a remaining human-AI performance gap and limited generalization from existing spatial intelligence benchmarks. These findings indicate that sports scenarios expose limitations in spatial intelligence capabilities captured by existing benchmarks. Further, fine-tuning Qwen3-VL-8B on CourtSI improves accuracy on CourtSI-Bench by 23.5 percentage points. The adapted model also generalizes effectively to CourtSI-Ext, an evaluation set built on a similar but unseen sport, and demonstrates enhanced spatial-aware commentary generation. Together, these findings demonstrate that CourtSI provides a scalable pathway toward advancing spatial intelligence of VLMs in sports.

Early warning prediction: Onsager-Machlup vs Schrödinger

Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate early-warning tasks. This study proposes a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling. Through systematic comparison, six methods including diffusion maps (DM) are selected to construct low-dimensional representations. Based on these, a data-driven stochastic differential equation model is established to robustly estimate the probability evolution scoring function of the system. Building on this, a new Score Function (SF) indicator is defined by incorporating Schrödinger bridge theory to quantify the likelihood of significant state transitions in the system. Experiments demonstrate that this indicator exhibits higher sensitivity and robustness in epilepsy prediction, enables earlier identification of critical points, and clearly captures dynamic features across various stages before and after seizure onset. This work provides a systematic theoretical framework and practical methodology for extracting early-warning signals from high-dimensional data.

Vibe Checker: Aligning Code Evaluation with Human Preference

Large Language Models (LLMs) have catalyzed vibe coding, where users leverage LLMs to generate and iteratively refine code through natural language interactions until it passes their vibe check. Vibe check is tied to real-world human preference and goes beyond functionality: the solution should feel right, read cleanly, preserve intent, and remain correct. However, current code evaluation remains anchored to pass@k and captures only functional correctness, overlooking the non-functional instructions that users routinely apply. In this paper, we hypothesize that instruction following is the missing piece underlying vibe check that represents human preference in coding besides functional correctness. To quantify models' code instruction following capabilities with measurable signals, we present VeriCode, a taxonomy of 30 verifiable code instructions together with corresponding deterministic verifiers. We use the taxonomy to augment established evaluation suites, resulting in Vibe Checker, a testbed to assess both code instruction following and functional correctness. Upon evaluating 31 leading LLMs, we show that even the strongest models struggle to comply with multiple instructions and exhibit clear functional regression. Most importantly, a composite score of functional correctness and instruction following correlates the best with human preference, with the latter emerging as the primary differentiator on real-world programming tasks. Our work identifies core factors of the vibe check, providing a concrete path for benchmarking and developing models that better align with user preferences in coding.

HAC-LOCO: Learning Hierarchical Active Compliance Control for Quadruped Locomotion under Continuous External Disturbances

Despite recent remarkable achievements in quadruped control, it remains challenging to ensure robust and compliant locomotion in the presence of unforeseen external disturbances. Existing methods prioritize locomotion robustness over compliance, often leading to stiff, high-frequency motions, and energy inefficiency. This paper, therefore, presents a two-stage hierarchical learning framework that can learn to take active reactions to external force disturbances based on force estimation. In the first stage, a velocity-tracking policy is trained alongside an auto-encoder to distill historical proprioceptive features. A neural network-based estimator is learned through supervised learning, which estimates body velocity and external forces based on proprioceptive measurements. In the second stage, a compliance action module, inspired by impedance control, is learned based on the pre-trained encoder and policy. This module is employed to actively adjust velocity commands in response to external forces based on real-time force estimates. With the compliance action module, a quadruped robot can robustly handle minor disturbances while appropriately yielding to significant forces, thus striking a balance between robustness and compliance. Simulations and real-world experiments have demonstrated that our method has superior performance in terms of robustness, energy efficiency, and safety. Experiment comparison shows that our method outperforms the state-of-the-art RL-based locomotion controllers. Ablation studies are given to show the critical roles of the compliance action module.

Cooperative Circumnavigation for Multi-Quadrotor Systems via Onboard Sensing

A cooperative circumnavigation framework is proposed for multi-quadrotor systems to enclose and track a moving target without reliance on external localization systems. The distinct relationships between quadrotor-quadrotor and quadrotor-target interactions are evaluated using a heterogeneous perception strategy and corresponding state estimation algorithms. A modified Kalman filter is developed to fuse visual-inertial odometry with range measurements to enhance the accuracy of inter-quadrotor relative localization. An event-triggered distributed Kalman filter is designed to achieve robust target state estimation under visual occlusion by incorporating neighbor measurements and estimated inter-quadrotor relative positions. Using the estimation results, a cooperative circumnavigation controller is constructed, leveraging an oscillator-based autonomous formation flight strategy. We conduct extensive indoor and outdoor experiments to validate the efficiency of the proposed circumnavigation framework in occluded environments. Furthermore, a quadrotor failure experiment highlights the inherent fault tolerance property of the proposed framework, underscoring its potential for deployment in search-and-rescue operations.