Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in the training phase, which often are not available, and thus rely on synthetic data. Here, we present a reconstruction method that generates dense fields from sparse measurements, without assuming availability of the spatial statistics, nor of examples of the dense fields. This is made possible through the introduction of an automatically differentiable numerical simulator into the training phase of the method. The method is shown to have superior results over statistical and neural network based methods on a set of three standard problems from fluid mechanics.

We introduce OSVBench, a new benchmark for evaluating Large Language Models (LLMs) on the task of generating complete formal specifications for verifying the functional correctness of operating system kernels. This benchmark is built upon a real-world operating system kernel, Hyperkernel, and consists of 245 complex specification generation tasks in total, each of which is a long-context task of about 20k-30k tokens. The benchmark formulates the specification generation task as a program synthesis problem confined to a domain for specifying states and transitions. This formulation is provided to LLMs through a programming model. The LLMs must be able to understand the programming model and verification assumptions before delineating the correct search space for syntax and semantics and generating formal specifications. Guided by the operating system's high-level functional description, the LLMs are asked to generate a specification that fully describes all correct states and transitions for a potentially buggy code implementation of the operating system. Experimental results with 12 state-of-the-art LLMs indicate limited performance of existing LLMs on the specification generation task for operating system verification. Significant disparities in their performance highlight differences in their ability to handle long-context code generation tasks. The code are available at https://github.com/lishangyu-hkust/OSVBench

High-resolution highway traffic state information is essential for Intelligent Transportation Systems, but typical traffic data acquired from loop detectors and probe vehicles are often too sparse and noisy to capture the detailed dynamics of traffic flow. We propose PMA-Diffusion, a physics-guided mask-aware diffusion framework that reconstructs unobserved highway speed fields from sparse, incomplete observations. Our approach trains a diffusion prior directly on sparsely observed speed fields using two mask-aware training strategies: Single-Mask and Double-Mask. At the inference phase, the physics-guided posterior sampler alternates reverse-diffusion updates, observation projection, and physics-guided projection based on adaptive anisotropic smoothing to reconstruct the missing speed fields. The proposed framework is tested on the I-24 MOTION dataset with varying visibility ratios. Even under severe sparsity, with only 5% visibility, PMA-Diffusion outperforms other baselines across three reconstruction error metrics. Furthermore, PMA-diffusion trained with sparse observation nearly matches the performance of the baseline model trained on fully observed speed fields. The results indicate that combining mask-aware diffusion priors with a physics-guided posterior sampler provides a reliable and flexible solution for traffic state estimation under realistic sensing sparsity.

We introduce FieldSeer I, a geometry-aware world model that forecasts electromagnetic field dynamics from partial observations in 2-D TE waveguides. The model assimilates a short prefix of observed fields, conditions on a scalar source action and structure/material map, and generates closed-loop rollouts in the physical domain. Training in a symmetric-log domain ensures numerical stability. Evaluated on a reproducible FDTD benchmark (200 unique simulations, structure-wise split), FieldSeer I achieves higher suffix fidelity than GRU and deterministic baselines across three practical settings: (i) software-in-the-loop filtering (64x64, P=80->Q=80), (ii) offline single-file rollouts (80x140, P=240->Q=40), and (iii) offline multi-structure rollouts (80x140, P=180->Q=100). Crucially, it enables edit-after-prefix geometry modifications without re-assimilation. Results demonstrate that geometry-conditioned world models provide a practical path toward interactive digital twins for photonic design.

We introduce fermionic neural Gibbs states (fNGS), a variational framework for modeling finite-temperature properties of strongly interacting fermions. fNGS starts from a reference mean-field thermofield-double state and uses neural-network transformations together with imaginary-time evolution to systematically build strong correlations. Applied to the doped Fermi-Hubbard model, a minimal lattice model capturing essential features of strong electronic correlations, fNGS accurately reproduces thermal energies over a broad range of temperatures, interaction strengths, even at large dopings, for system sizes beyond the reach of exact methods. These results demonstrate a scalable route to studying finite-temperature properties of strongly correlated fermionic systems beyond one dimension with neural-network representations of quantum states.

Traffic state estimation (TSE) becomes challenging when probe-vehicle penetration is low and observations are spatially sparse. Pure data-driven methods lack physical explanations and have poor generalization when observed data is sparse. In contrast, physical models have difficulty integrating uncertainties and capturing the real complexity of traffic. To bridge this gap, recent studies have explored combining them by embedding physical structure into Gaussian process. These approaches typically introduce the governing equations as soft constraints through pseudo-observations, enabling the integration of model structure within a variational framework. However, these methods rely heavily on penalty tuning and lack principled uncertainty calibration, which makes them sensitive to model mis-specification. In this work, we address these limitations by presenting a novel Physics-Embedded Gaussian Process (PEGP), designed to integrate domain knowledge with data-driven methods in traffic state estimation. Specifically, we design two multi-output kernels informed by classic traffic flow models, constructed via the explicit application of the linearized differential operator. Experiments on HighD, NGSIM show consistent improvements over non-physics baselines. PEGP-ARZ proves more reliable under sparse observation, while PEGP-LWR achieves lower errors with denser observation. Ablation study further reveals that PEGP-ARZ residuals align closely with physics and yield calibrated, interpretable uncertainty, whereas PEGP-LWR residuals are more orthogonal and produce nearly constant variance fields. This PEGP framework combines physical priors, uncertainty quantification, which can provide reliable support for TSE.

Large Language Model (LLM) agent systems have advanced rapidly, driven by their strong generalization in zero-shot settings. To further enhance reasoning and accuracy on complex tasks, Multi-Agent Debate (MAD) has emerged as a promising framework that engages multiple LLM agents in structured debates to encourage diverse reasoning. However, triggering MAD for every query is inefficient, as it incurs substantial computational (token) cost and may even degrade accuracy by overturning correct single-agent answers. To address these limitations, we propose intelligent Multi-Agent Debate (iMAD), a token-efficient framework that selectively triggers MAD only when it is likely to be beneficial (i.e., correcting an initially wrong answer). To achieve this goal, iMAD learns generalizable model behaviors to make accurate debate decisions. Specifically, iMAD first prompts a single agent to produce a structured self-critique response, from which we extract 41 interpretable linguistic and semantic features capturing hesitation cues. Then, iMAD uses a lightweight debate-decision classifier, trained using our proposed FocusCal loss, to determine whether to trigger MAD, enabling robust debate decisions without test dataset-specific tuning. Through extensive experiments using six (visual) question answering datasets against five competitive baselines, we have shown that iMAD significantly reduces token usage (by up to 92%) while also improving final answer accuracy (by up to 13.5%).

The Agentic Paradigm faces a significant Software Engineering Absence, yielding Agentic systems commonly lacking robustness, observability, and evolvability. To address these deficiencies, we propose a principled engineering framework comprising Runtime Goal Refinement (RGR), Observable Cognitive Architecture (OCA), and Evolutionary Memory Architecture (EMA). In this framework, RGR ensures robustness and intent alignment via knowledge-constrained refinement and human-in-the-loop clarification; OCA builds an observable and maintainable white-box architecture using component decoupling, logic layering, and state-control separation; and EMA employs an execution-evolution dual-loop for evolvability. We implemented and empirically validated Fairy, a mobile GUI agent based on this framework. On RealMobile-Eval, our novel benchmark for ambiguous and complex tasks, Fairy outperformed the best SoTA baseline in user requirement completion by 33.7%. Subsequent controlled experiments, human-subject studies, and ablation studies further confirmed that the RGR enhances refinement accuracy and prevents intent deviation; the OCA improves maintainability; and the EMA is crucial for long-term performance. This research provides empirically validated specifications and a practical blueprint for building reliable, observable, and evolvable Agentic AI systems.

The massive growth in the utilization of edge AI has made the applications of machine learning models ubiquitous in different domains. Despite the computation and communication efficiency of these systems, due to limited computation resources on edge devices, relying on more computationally rich systems on the cloud side is inevitable in most cases. Cloud inference systems can achieve the best performance while the computation and communication cost is dramatically increasing by the expansion of a number of edge devices relying on these systems. Hence, there is a trade-off between the computation, communication, and performance of these systems. In this paper, we propose a novel framework, dubbed as Eccentric that learns models with different levels of trade-offs between these conflicting objectives. This framework, based on an adaptation of knowledge from the edge model to the cloud one, reduces the computation and communication costs of the system during inference while achieving the best performance possible. The Eccentric framework can be considered as a new form of compression method suited for edge-cloud inference systems to reduce both computation and communication costs. Empirical studies on classification and object detection tasks corroborate the efficacy of this framework.