Yuxuan Bao

Yuxuan Bao, J. Nathan Kutz

Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables, or measure how different initial trajectories or temporal segments of a trajectory contribute to learning or inferring system dynamics. In this work, we leverage the Fisher Information Matrix (FIM) within the data-driven framework of {\em sparse identification of nonlinear dynamics} (SINDy). We visualize information patterns in chaotic and non-chaotic systems for both single trajectories and multiple initial conditions, demonstrating how information-based analysis can improve sampling efficiency and enhance model performance by prioritizing more informative data. The benefits of statistical bagging are further elucidated through spectral analysis of the FIM. We also illustrate how Fisher information and entropy metrics can promote data efficiency in three scenarios: when only a single trajectory is available, when a tunable control parameter exists, and when multiple trajectories can be freely initialized. As data-driven model discovery continues to gain prominence, principled sampling strategies guided by quantifiable information metrics offer a powerful approach for improving learning efficiency and reducing data requirements.

Andy K. Zhang, Joey Ji, Celeste Menders et al.

AI agents have the potential to significantly alter the cybersecurity landscape. Here, we introduce the first framework to capture offensive and defensive cyber-capabilities in evolving real-world systems. Instantiating this framework with BountyBench, we set up 25 systems with complex, real-world codebases. To capture the vulnerability lifecycle, we define three task types: Detect (detecting a new vulnerability), Exploit (exploiting a specific vulnerability), and Patch (patching a specific vulnerability). For Detect, we construct a new success indicator, which is general across vulnerability types and provides localized evaluation. We manually set up the environment for each system, including installing packages, setting up server(s), and hydrating database(s). We add 40 bug bounties, which are vulnerabilities with monetary awards of \$10-\$30,485, covering 9 of the OWASP Top 10 Risks. To modulate task difficulty, we devise a new strategy based on information to guide detection, interpolating from identifying a zero day to exploiting a specific vulnerability. We evaluate 8 agents: Claude Code, OpenAI Codex CLI with o3-high and o4-mini, and custom agents with o3-high, GPT-4.1, Gemini 2.5 Pro Preview, Claude 3.7 Sonnet Thinking, and DeepSeek-R1. Given up to three attempts, the top-performing agents are OpenAI Codex CLI: o3-high (12.5% on Detect, mapping to \$3,720; 90% on Patch, mapping to \$14,152), Custom Agent with Claude 3.7 Sonnet Thinking (67.5% on Exploit), and OpenAI Codex CLI: o4-mini (90% on Patch, mapping to \$14,422). OpenAI Codex CLI: o3-high, OpenAI Codex CLI: o4-mini, and Claude Code are more capable at defense, achieving higher Patch scores of 90%, 90%, and 87.5%, compared to Exploit scores of 47.5%, 32.5%, and 57.5% respectively; while the custom agents are relatively balanced between offense and defense, achieving Exploit scores of 37.5-67.5% and Patch scores of 35-60%.