Transferable Physics-Informed Representations via Closed-Form Head Adaptation

Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to learn physical outcomes reasonably well. However, current PINN approaches struggle to predict or solve new PDEs effectively when there is a lack of training examples, indicating they do not generalize well to unseen problem instances. In this paper, we present a transferable learning approach for PINNs premised on a fast Pseudoinverse PINN framework (Pi-PINN). Pi-PINN learns a transferable physics-informed representation in a shared embedding space and enables rapid solving of both known and unknown PDE instances via closed-form head adaptation using a least-squares-optimal pseudoinverse under PDE constraints. We further investigate the synergies between data-driven multi-task learning loss and physics-informed loss, providing insights into the design of more performant PINNs. We demonstrate the effectiveness of Pi-PINN on various PDE problems, including Poisson's equation, Helmholtz equation, and Burgers' equation, achieving fast and accurate physics-informed solutions without requiring any data for unseen instances. Pi-PINN can produce predictions 100-1000 times faster than a typical PINN, while producing predictions with 10-100 times lower relative error than a typical data-driven model even with only two training samples. Overall, our findings highlight the potential of transferable representations with closed-form head adaptation to enhance the efficiency and generalization of PINNs across PDE families and scientific and engineering applications.

Hierarchically Robust Zero-shot Vision-language Models

Vision-Language Models (VLMs) can perform zero-shot classification but are susceptible to adversarial attacks. While robust fine-tuning improves their robustness, existing approaches align fixed text embeddings with an image embedding, sacrificing natural performance and robustness. A robustness degradation also occurs when a model faces adversarial attacks targeting superclasses (parent classes, e.g., mammal) in addition to their base (leaf) classes (e.g., cat). Thus, to enhance adversarial robustness and leverage the inherent hierarchical properties of class space, we propose a novel adversarial fine-tuning framework based on hierarchical embeddings and several levels of adversarially robust alignment of image-text modalities. Additional mechanisms place visual embeddings at the desired depth of hierarchy, and we provide a theoretical connection between the depth of embedding in the hierarchy and the maximum viable margin size. Our model naturally realizes several margin sizes, boosting generalization of adversaries for robustification. As various trees with different parent labels can share the same leaf labels, we also consider aligning over multiple trees to boost semantic variety. Experiments across several datasets are performed.

GRASP: Gradient Realignment via Active Shared Perception for Multi-Agent Collaborative Optimization

Non-stationarity arises from concurrent policy updates and leads to persistent environmental fluctuations. Existing approaches like Centralized Training with Decentralized Execution (CTDE) and sequential update schemes mitigate this issue. However, since the perception of the policies of other agents remains dependent on sampling environmental interaction data, the agent essentially operates in a passive perception state. This inevitably triggers equilibrium oscillations and significantly slows the convergence speed of the system. To address this issue, we propose Gradient Realignment via Active Shared Perception (GRASP), a novel framework that defines generalized Bellman equilibrium as a stable objective for policy evolution. The core mechanism of GRASP involves utilizing the independent gradients of agents to derive a defined consensus gradient, enabling agents to actively perceive policy updates and optimize team collaboration. Theoretically, we leverage the Kakutani Fixed-Point Theorem to prove that the consensus direction $u^*$ guarantees the existence and attainability of this equilibrium. Extensive experiments on StarCraft II Multi-Agent Challenge (SMAC) and Google Research Football (GRF) demonstrate the scalability and promising performance of the framework.

Taming the Instability: A Robust Second-Order Optimizer for Federated Learning over Non-IID Data

In this paper, we present Federated Robust Curvature Optimization (FedRCO), a novel second-order optimization framework designed to improve convergence speed and reduce communication cost in Federated Learning systems under statistical heterogeneity. Existing second-order optimization methods are often computationally expensive and numerically unstable in distributed settings. In contrast, FedRCO addresses these challenges by integrating an efficient approximate curvature optimizer with a provable stability mechanism. Specifically, FedRCO incorporates three key components: (1) a Gradient Anomaly Monitor that detects and mitigates exploding gradients in real-time, (2) a Fail-Safe Resilience protocol that resets optimization states upon numerical instability, and (3) a Curvature-Preserving Adaptive Aggregation strategy that safely integrates global knowledge without erasing the local curvature geometry. Theoretical analysis shows that FedRCO can effectively mitigate instability and prevent unbounded updates while preserving optimization efficiency. Extensive experiments show that FedRCO achieves superior robustness against diverse non-IID scenarios while achieving higher accuracy and faster convergence than both state-of-the-art first-order and second-order methods.

Evolving Jailbreaks: Automated Multi-Objective Long-Tail Attacks on Large Language Models

Large Language Models (LLMs) have been widely deployed, especially through free Web-based applications that expose them to diverse user-generated inputs, including those from long-tail distributions such as low-resource languages and encrypted private data. This open-ended exposure increases the risk of jailbreak attacks that undermine model safety alignment. While recent studies have shown that leveraging long-tail distributions can facilitate such jailbreaks, existing approaches largely rely on handcrafted rules, limiting the systematic evaluation of these security and privacy vulnerabilities. In this work, we present EvoJail, an automated framework for discovering long-tail distribution attacks via multi-objective evolutionary search. EvoJail formulates long-tail attack prompt generation as a multi-objective optimization problem that jointly maximizes attack effectiveness and minimizes output perplexity, and introduces a semantic-algorithmic solution representation to capture both high-level semantic intent and low-level structural transformations of encryption-decryption logic. Building upon this representation, EvoJail integrates LLM-assisted operators into a multi-objective evolutionary framework, enabling adaptive and semantically informed mutation and crossover for efficiently exploring a highly structured and open-ended search space. Extensive experiments demonstrate that EvoJail consistently discovers diverse and effective long-tail jailbreak strategies, achieving competitive performance with existing methods in both individual and ensemble level.

Multi-Objective Evolutionary Optimization of Chance-Constrained Multiple-Choice Knapsack Problems with Implicit Probability Distributions

The multiple-choice knapsack problem (MCKP) is a classic combinatorial optimization with wide practical applications. This paper investigates a significant yet underexplored extension of MCKP: the multi-objective chance-constrained MCKP (MO-CCMCKP) under implicit probability distributions. The goal of the problem is to simultaneously minimize the total cost and maximize the confidence level of satisfying the capacity constraint, capturing essential trade-offs in domains like 5G network configuration. To address the computational challenge of evaluating chance constraints under implicit distributions, we first propose an order-preserving efficient resource allocation Monte Carlo (OPERA-MC) method. This approach adaptively allocates sampling resources to preserve dominance relationships while reducing evaluation time significantly. Further, we develop NHILS, a hybrid evolutionary algorithm that integrates specialized initialization and local search into NSGA-II to navigate sparse feasible regions. Experiments on synthetic benchmarks and real-world 5G network configuration benchmarks demonstrate that NHILS consistently outperforms several state-of-the-art multi-objective optimizers in convergence, diversity, and feasibility. The benchmark instances and source code will be made publicly available to facilitate research in this area.

Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern numerical solvers. We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms. Scale-PINN incorporates the iterative residual-correction principle, a cornerstone of numerical solvers, directly into the loss formulation, marking a paradigm shift in how PINN losses can be conceived and constructed. This integration enables Scale-PINN to achieve unprecedented convergence speed across PDE problems from different physics domain, including reducing training time on a challenging fluid-dynamics problem for state-of-the-art PINN from hours to sub-2 minutes while maintaining superior accuracy, and enabling application to representative problems in aerodynamics and urban science. By uniting the rigor of numerical methods with the flexibility of deep learning, Scale-PINN marks a significant leap toward the practical adoption of PINNs in science and engineering through scalable, physics-informed learning. Codes are available at https://github.com/chiuph/SCALE-PINN.

Information Fidelity in Tool-Using LLM Agents: A Martingale Analysis of the Model Context Protocol

As AI agents powered by large language models (LLMs) increasingly use external tools for high-stakes decisions, a critical reliability question arises: how do errors propagate across sequential tool calls? We introduce the first theoretical framework for analyzing error accumulation in Model Context Protocol (MCP) agents, proving that cumulative distortion exhibits linear growth and high-probability deviations bounded by $O(\sqrt{T})$. This concentration property ensures predictable system behavior and rules out exponential failure modes. We develop a hybrid distortion metric combining discrete fact matching with continuous semantic similarity, then establish martingale concentration bounds on error propagation through sequential tool interactions. Experiments across Qwen2-7B, Llama-3-8B, and Mistral-7B validate our theoretical predictions, showing empirical distortion tracks the linear trend with deviations consistently within $O(\sqrt{T})$ envelopes. Key findings include: semantic weighting reduces distortion by 80\%, and periodic re-grounding approximately every 9 steps suffices for error control. We translate these concentration guarantees into actionable deployment principles for trustworthy agent systems.

Agentic Spatio-Temporal Grounding via Collaborative Reasoning

Spatio-Temporal Video Grounding (STVG) aims to retrieve the spatio-temporal tube of a target object or person in a video given a text query. Most existing approaches perform frame-wise spatial localization within a predicted temporal span, resulting in redundant computation, heavy supervision requirements, and limited generalization. Weakly-supervised variants mitigate annotation costs but remain constrained by the dataset-level train-and-fit paradigm with an inferior performance. To address these challenges, we propose the Agentic Spatio-Temporal Grounder (ASTG) framework for the task of STVG towards an open-world and training-free scenario. Specifically, two specialized agents SRA (Spatial Reasoning Agent) and TRA (Temporal Reasoning Agent) constructed leveraging on modern Multimoal Large Language Models (MLLMs) work collaboratively to retrieve the target tube in an autonomous and self-guided manner. Following a propose-and-evaluation paradigm, ASTG duly decouples spatio-temporal reasoning and automates the tube extraction, verification and temporal localization processes. With a dedicate visual memory and dialogue context, the retrieval efficiency is significantly enhanced. Experiments on popular benchmarks demonstrate the superiority of the proposed approach where it outperforms existing weakly-supervised and zero-shot approaches by a margin and is comparable to some of the fully-supervised methods.

Landscape-aware Automated Algorithm Design: An Efficient Framework for Real-world Optimization

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the target problem to guide the search process, making them impractical for real-world optimization tasks, where each evaluation consumes substantial computational resources. This research proposes an innovative and efficient framework that decouples algorithm discovery from high-cost evaluation. Our core innovation lies in combining a Genetic Programming (GP) function generator with an LLM-driven evolutionary algorithm designer. The evolutionary direction of the GP-based function generator is guided by the similarity between the landscape characteristics of generated proxy functions and those of real-world problems, ensuring that algorithms discovered via proxy functions exhibit comparable performance on real-world problems. Our method enables deep exploration of the algorithmic space before final validation while avoiding costly real-world evaluations. We validated the framework's efficacy across multiple real-world problems, demonstrating its ability to discover high-performance algorithms while substantially reducing expensive evaluations. This approach shows a path to apply LLM-based automated algorithm design to computationally intensive real-world optimization challenges.