work Explainable AI for Nashville Water System AI-powered anomaly detection for urban water distribution — combining graph neural networks, physics-informed hydraulics, and explainable real-time diagnostics. DAE-CBF Safety on the constraint manifold — verification and control for differential-algebraic systems. Safe AI-Embedded Robots End-to-end safety verification and synthesis for robotic systems whose controllers — or whose safety certificates themselves — are neural networks. Resilient CPS Safety and stability under sensor faults, actuator failures, and adversarial attacks — from CDC 2020 fault-tolerant CBFs to GM-award LiDAR defense. fun Grokking and the Fourier Manifold A 39x training speedup by naming the manifold that grokking lives on, and the limits of manifold-agnostic tricks. LLM Internals for Math Reasoning Does the Fourier structure that explains grokking in toy models show up inside pre-trained LLMs — and if so, why don't they generalize? Concept Probing in Large LLMs Do 2.7–14B transformers represent the concepts in a math word problem, and where do wrong answers actually come from? A matched-pair probing rig settles both questions across six cells. Representation Engineering of LLM Reasoning What lives in the residual stream when an LLM solves a math word problem — relation type, value binding, and schema correctness — read off via RepE on 8 model × problem cells.
