PILD: Physics-Informed Learning via Diffusion

Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and first-principles physical constraints by introducing a virtual residual observation sampled from a Laplace distribution to supervise generation during training. To further integrate physical laws, a conditional embedding module is incorporated to inject physical information into the denoising network at multiple layers, ensuring consistent guidance throughout the diffusion process. The proposed PILD framework is concise, modular, and broadly applicable to problems governed by ordinary differential equations, partial differential equations, as well as algebraic equations or inequality constraints. Extensive experiments across engineering and scientific tasks including estimating vehicle trajectories, tire forces, Darcy flow and plasma dynamics, demonstrate that our PILD substantially improves accuracy, stability, and generalization over existing physics-informed and diffusion-based baselines.

One Tool Is Enough: Reinforcement Learning for Repository-Level LLM Agents

Locating the files and functions requiring modification in large open-source software (OSS) repositories is challenging due to their scale and structural complexity. Existing large language model (LLM)-based methods typically treat this as a repository-level retrieval task and rely on multiple auxiliary tools, which overlook code execution logic and complicate model control. We propose RepoNavigator, an LLM agent equipped with a single execution-aware tool-jumping to the definition of an invoked symbol. This unified design reflects the actual flow of code execution while simplifying tool manipulation. RepoNavigator is trained end-to-end via Reinforcement Learning (RL) directly from a pretrained model, without any closed-source distillation. Experiments demonstrate that RL-trained RepoNavigator achieves state-of-the-art performance, with the 7B model outperforming 14B baselines, the 14B model surpassing 32B competitors, and even the 32B model exceeding closed-source models such as Claude-3.7. These results confirm that integrating a single, structurally grounded tool with RL training provides an efficient and scalable solution for repository-level issue localization.

Joint Radiation Power, Antenna Position, and Beamforming Optimization for Pinching-Antenna Systems with Motion Power Consumption

Pinching-antenna systems (PASS) have been recently proposed to improve the performance of wireless networks by reconfiguring both the large-scale and small-scale channel conditions. However, existing studies ignore the physical constraints of antenna placement and assume fixed antenna radiation power. To fill this research gap, this paper investigates the design of PASS taking into account the motion power consumption of pinching-antennas (PAs) and the impact of adjustable antenna radiation power. To that end, we minimize the average power consumption for a given quality-of-service (QoS) requirement, by jointly optimizing the antenna positions, antenna radiation power ratios, and transmit beamforming. To the best of the authors' knowledge, this is the first work to consider radiation power optimization in PASS, which provides an additional degree of freedom (DoF) for system design. The cases with both continuous and discrete antenna placement are considered, where the main challenge lies in the fact that the antenna positions affect both the magnitude and phase of the channel coefficients of PASS, making system optimization very challenging. To tackle the resulting unique obstacles, an alternating direction method of multipliers (ADMM)-based framework is proposed to solve the problem for continuous antenna movement, while its discrete counterpart is formulated as a mixed integer nonlinear programming (MINLP) problem and solved by the block coordinate descent (BCD) method. Simulation results validate the performance enhancement achieved by incorporating PA movement power assumption and adjustable radiation power into PASS design, while also demonstrating the efficiency of the proposed optimization framework. The benefits of PASS over conventional multiple-input multiple-output (MIMO) systems in mitigating the large-scale path loss and inter-user interference is also revealed.

Hybrid least squares for learning functions from highly noisy data

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are powerful in the small noise regime are suboptimal when large noise is present. We propose a hybrid approach that combines Christoffel sampling with certain types of optimal experimental design to address this issue. We show that the proposed algorithm enjoys appropriate optimality properties for both sample point generation and noise mollification, leading to improved computational efficiency and sample complexity compared to existing methods. We also extend the algorithm to convex-constrained settings with similar theoretical guarantees. When the target function is defined as the expectation of a random field, we extend our approach to leverage adaptive random subspaces and establish results on the approximation capacity of the adaptive procedure. Our theoretical findings are supported by numerical studies on both synthetic data and on a more challenging stochastic simulation problem in computational finance.

Joint stochastic localization and applications

Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic localization schemes and discuss their localization rates and regularization. We then introduce a joint stochastic localization framework for constructing couplings between probability distributions. As an initial application, we extend the optimal couplings between normal distributions under the 2-Wasserstein distance to log-concave distributions and derive a normal approximation result. As a further application, we introduce a family of distributional distances based on the couplings induced by joint stochastic localization. Under a specific choice of the localization process, the induced distance is topologically equivalent to the 2-Wasserstein distance for probability measures supported on a common compact set. Moreover, weighted versions of this distance are related to several statistical divergences commonly used in practice. The proposed distances also motivate new methods for distribution estimation that are of independent interest.

SafeMate: A Modular RAG-Based Agent for Context-Aware Emergency Guidance

Despite the abundance of public safety documents and emergency protocols, most individuals remain ill-equipped to interpret and act on such information during crises. Traditional emergency decision support systems (EDSS) are designed for professionals and rely heavily on static documents like PDFs or SOPs, which are difficult for non-experts to navigate under stress. This gap between institutional knowledge and public accessibility poses a critical barrier to effective emergency preparedness and response. We introduce SafeMate, a retrieval-augmented AI assistant that delivers accurate, context-aware guidance to general users in both preparedness and active emergency scenarios. Built on the Model Context Protocol (MCP), SafeMate dynamically routes user queries to tools for document retrieval, checklist generation, and structured summarization. It uses FAISS with cosine similarity to identify relevant content from trusted sources.

Investigating Robotaxi Crash Severity Using Geographical Random Forest

This paper quantitatively investigates the crash severity of Autonomous Vehicles (AVs) with spatially localized machine learning and macroscopic measures of the urban built environment. We address spatial heterogeneity and spatial autocorrelation, while focusing on land use patterns and human behavior. Our Geographical Random Forest (GRF) model, accompanied with a crash severity risk map of San Francisco, presents three findings that are useful for commercial operations of AVs and robotaxis. First, spatially localized machine learning performed better than regular machine learning, when predicting AV crash severity. Bias-variance tradeoff was evident as we adjust the localization weight hyperparameter. Second, land use was the most important built environment measure, compared to intersections, building footprints, public transit stops, and Points Of Interests (POIs). Third, it was predicted that city center areas with greater diversity and commercial activities were more likely to result in low-severity AV crashes, than residential neighborhoods. Residential land use may be associated with higher severity due to human behavior and less restrictive environment. This paper recommends to explicitly consider geographic locations, and to design safety measures specific to residential neighborhoods, when robotaxi operators train their AV systems.

SafeMate: A Model Context Protocol-Based Multimodal Agent for Emergency Preparedness

Despite the abundance of public safety documents and emergency protocols, most individuals remain ill-equipped to interpret and act on such information during crises. Traditional emergency decision support systems (EDSS) are designed for professionals and rely heavily on static documents like PDFs or SOPs, which are difficult for non-experts to navigate under stress. This gap between institutional knowledge and public accessibility poses a critical barrier to effective emergency preparedness and response. We introduce SafeMate, a retrieval-augmented AI assistant that delivers accurate, context-aware guidance to general users in both preparedness and active emergency scenarios. Built on the Model Context Protocol (MCP), SafeMate dynamically routes user queries to tools for document retrieval, checklist generation, and structured summarization. It uses FAISS with cosine similarity to identify relevant content from trusted sources.

CLDG: Contrastive Learning on Dynamic Graphs

The graph with complex annotations is the most potent data type, whose constantly evolving motivates further exploration of the unsupervised dynamic graph representation. One of the representative paradigms is graph contrastive learning. It constructs self-supervised signals by maximizing the mutual information between the statistic graph's augmentation views. However, the semantics and labels may change within the augmentation process, causing a significant performance drop in downstream tasks. This drawback becomes greatly magnified on dynamic graphs. To address this problem, we designed a simple yet effective framework named CLDG. Firstly, we elaborate that dynamic graphs have temporal translation invariance at different levels. Then, we proposed a sampling layer to extract the temporally-persistent signals. It will encourage the node to maintain consistent local and global representations, i.e., temporal translation invariance under the timespan views. The extensive experiments demonstrate the effectiveness and efficiency of the method on seven datasets by outperforming eight unsupervised state-of-the-art baselines and showing competitiveness against four semi-supervised methods. Compared with the existing dynamic graph method, the number of model parameters and training time is reduced by an average of 2,001.86 times and 130.31 times on seven datasets, respectively.

Toward Efficient Kernel-Based Solvers for Nonlinear PDEs

This paper introduces a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing challenges with a large number of collocation points, our approach eliminates these operators from the kernel. We model the solution using a standard kernel interpolation form and differentiate the interpolant to compute the derivatives. Our framework obviates the need for complex Gram matrix construction between solutions and their derivatives, allowing for a straightforward implementation and scalable computation. As an instance, we allocate the collocation points on a grid and adopt a product kernel, which yields a Kronecker product structure in the interpolation. This structure enables us to avoid computing the full Gram matrix, reducing costs and scaling efficiently to a large number of collocation points. We provide a proof of the convergence and rate analysis of our method under appropriate regularity assumptions. In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.