Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold Network (KAN) with radial basis functions (BEKAN). In BEKAN, we propose three distinct and combinable approaches for incorporating Dirichlet, periodic, and Neumann boundary conditions into the network. For Dirichlet problem, we use smooth and global Gaussian RBFs to construct univariate basis functions for approximating the solution and to encode boundary information at the activation level of the network. To handle periodic problems, we employ a periodic layer constructed from a set of sinusoidal functions to enforce the boundary conditions exactly. For a Neumann problem, we devise a least-squares formulation to guide the parameter evolution toward satisfying the Neumann condition. By virtue of the boundary-embedded RBFs, the periodic layer, and the evolutionary framework, we can perform accurate PDE simulations while rigorously enforcing boundary conditions. For demonstration, we conducted extensive numerical experiments on Dirichlet, Neumann, periodic, and mixed boundary value problems. The results indicate that BEKAN outperforms both multilayer perceptron (MLP) and B-splines KAN in terms of accuracy. In conclusion, the proposed approach enhances the capability of KANs in solving PDE problems while satisfying boundary conditions, thereby facilitating advancements in scientific computing and engineering applications.

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

Open-source data offers a scalable and transparent foundation for estimating vehicle activity and emissions in urban regions. In this study, we propose a data-driven framework that integrates MOVES and open-source GPS trajectory data, OpenStreetMap (OSM) road networks, regional traffic datasets and satellite imagery-derived feature vectors to estimate the link level operating mode distribution and traffic emissions. A neural network model is trained to predict the distribution of MOVES-defined operating modes using only features derived from readily available data. The proposed methodology was applied using open-source data related to 45 municipalities in the Boston Metropolitan area. The "ground truth" operating mode distribution was established using OSM open-source GPS trajectories. Compared to the MOVES baseline, the proposed model reduces RMSE by over 50% for regional scale traffic emissions of key pollutants including CO, NOx, CO2, and PM2.5. This study demonstrates the feasibility of low-cost, replicable, and data-driven emissions estimation using fully open data sources.

We study a class of constrained nonconvex--nonconcave minimax problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax problem satisfies a local Kurdyka-Łojasiewicz (KL) condition, we show that the maximal function of the original problem enjoys a local Hölder smoothness property. We also propose a sequential convex programming (SCP) method for solving constrained optimization problems and establish its convergence rate under a local KL condition. Leveraging these results, we develop an inexact proximal gradient method for the original minimax problem, where the inexact gradient of the maximal function is computed via the SCP method applied to a locally KL-structured subproblem. Finally, we establish complexity guarantees for the proposed method in computing an approximate stationary point of the original minimax problem.

Deep neural networks (DNNs) are increasingly applied to safety-critical tasks in resource-constrained environments, such as video-based driver action and intention recognition. While last layer probabilistic deep learning (LL-PDL) methods can detect out-of-distribution (OOD) instances, their performance varies. As an alternative to last layer approaches, we propose extending pre-trained DNNs with transformation layers to produce multiple latent representations to estimate the uncertainty. W e evaluate our latent uncertainty representation (LUR) and repulsively trained LUR (RLUR) approaches against eight PDL methods across four video-based driver action and intention recognition datasets, comparing classification performance, calibration, and uncertainty-based OOD detection. W e also contribute 28,000 frame-level action labels and 1,194 video-level intention labels for the NuScenes dataset. Our results show that LUR and RLUR achieve comparable in-distribution classification performance to other LL-PDL approaches. F or uncertainty-based OOD detection, LUR matches top-performing PDL methods while being more efficient to train and easier to tune than approaches that require Markov-Chain Monte Carlo sampling or repulsive training procedures.

Concept erasure techniques have been widely deployed in T2I diffusion models to prevent inappropriate content generation for safety and copyright considerations. However, as models evolve to next-generation architectures like Flux, established erasure methods (\textit{e.g.}, ESD, UCE, AC) exhibit degraded effectiveness, raising questions about their true mechanisms. Through systematic analysis, we reveal that concept erasure creates only an illusion of ``amnesia": rather than genuine forgetting, these methods bias sampling trajectories away from target concepts, making the erasure fundamentally reversible. This insight motivates the need to distinguish superficial safety from genuine concept removal. In this work, we propose \textbf{RevAm} (\underline{Rev}oking \underline{Am}nesia), an RL-based trajectory optimization framework that resurrects erased concepts by dynamically steering the denoising process without modifying model weights. By adapting Group Relative Policy Optimization (GRPO) to diffusion models, RevAm explores diverse recovery trajectories through trajectory-level rewards, overcoming local optima that limit existing methods. Extensive experiments demonstrate that RevAm achieves superior concept resurrection fidelity while reducing computational time by 10$\times$, exposing critical vulnerabilities in current safety mechanisms and underscoring the need for more robust erasure techniques beyond trajectory manipulation.

Incident response (IR) requires fast, coordinated, and well-informed decision-making to contain and mitigate cyber threats. While large language models (LLMs) have shown promise as autonomous agents in simulated IR settings, their reasoning is often limited by a lack of access to external knowledge. In this work, we present AutoBnB-RAG, an extension of the AutoBnB framework that incorporates retrieval-augmented generation (RAG) into multi-agent incident response simulations. Built on the Backdoors & Breaches (B&B) tabletop game environment, AutoBnB-RAG enables agents to issue retrieval queries and incorporate external evidence during collaborative investigations. We introduce two retrieval settings: one grounded in curated technical documentation (RAG-Wiki), and another using narrative-style incident reports (RAG-News). We evaluate performance across eight team structures, including newly introduced argumentative configurations designed to promote critical reasoning. To validate practical utility, we also simulate real-world cyber incidents based on public breach reports, demonstrating AutoBnB-RAG's ability to reconstruct complex multi-stage attacks. Our results show that retrieval augmentation improves decision quality and success rates across diverse organizational models. This work demonstrates the value of integrating retrieval mechanisms into LLM-based multi-agent systems for cybersecurity decision-making.

Recent advancements in multimodal large language models (MLLMs) have driven researchers to explore how well these models read data visualizations, e.g., bar charts, scatter plots. More recently, attention has shifted to visual question answering with maps (Map-VQA). However, Map-VQA research has primarily focused on choropleth maps, which cover only a limited range of thematic categories and visual analytical tasks. To address these gaps, we introduce MapIQ, a benchmark dataset comprising 14,706 question-answer pairs across three map types: choropleth maps, cartograms, and proportional symbol maps spanning topics from six distinct themes (e.g., housing, crime). We evaluate multiple MLLMs using six visual analytical tasks, comparing their performance against one another and a human baseline. An additional experiment examining the impact of map design changes (e.g., altered color schemes, modified legend designs, and removal of map elements) provides insights into the robustness and sensitivity of MLLMs, their reliance on internal geographic knowledge, and potential avenues for improving Map-VQA performance.

To guarantee safe and robust deployment of large language models (LLMs) at scale, it is critical to accurately assess their adversarial robustness. Existing adversarial attacks typically target harmful responses in single-point greedy generations, overlooking the inherently stochastic nature of LLMs and overestimating robustness. We show that for the goal of eliciting harmful responses, repeated sampling of model outputs during the attack complements prompt optimization and serves as a strong and efficient attack vector. By casting attacks as a resource allocation problem between optimization and sampling, we determine compute-optimal trade-offs and show that integrating sampling into existing attacks boosts success rates by up to 37\% and improves efficiency by up to two orders of magnitude. We further analyze how distributions of output harmfulness evolve during an adversarial attack, discovering that many common optimization strategies have little effect on output harmfulness. Finally, we introduce a label-free proof-of-concept objective based on entropy maximization, demonstrating how our sampling-aware perspective enables new optimization targets. Overall, our findings establish the importance of sampling in attacks to accurately assess and strengthen LLM safety at scale.

Conventional language model (LM) safety alignment relies on a reactive, disjoint procedure: attackers exploit a static model, followed by defensive fine-tuning to patch exposed vulnerabilities. This sequential approach creates a mismatch -- attackers overfit to obsolete defenses, while defenders perpetually lag behind emerging threats. To address this, we propose Self-RedTeam, an online self-play reinforcement learning algorithm where an attacker and defender agent co-evolve through continuous interaction. We cast safety alignment as a two-player zero-sum game, where a single model alternates between attacker and defender roles -- generating adversarial prompts and safeguarding against them -- while a reward LM adjudicates outcomes. This enables dynamic co-adaptation. Grounded in the game-theoretic framework of zero-sum games, we establish a theoretical safety guarantee which motivates the design of our method: if self-play converges to a Nash Equilibrium, the defender will reliably produce safe responses to any adversarial input. Empirically, Self-RedTeam uncovers more diverse attacks (+21.8% SBERT) compared to attackers trained against static defenders and achieves higher robustness on safety benchmarks (e.g., +65.5% on WildJailBreak) than defenders trained against static attackers. We further propose hidden Chain-of-Thought, allowing agents to plan privately, which boosts adversarial diversity and reduces over-refusals. Our results motivate a shift from reactive patching to proactive co-evolution in LM safety training, enabling scalable, autonomous, and robust self-improvement of LMs via multi-agent reinforcement learning (MARL).