Rigorous numerics · Conformal inference · Foundations of machine learning
I am a fourth-year joint B.S.–M.S. student at Florida Atlantic University studying applied mathematics, where I work with Jason Mireles-James and Yu Xiang.
My research is focused on the mathematical foundations of machine learning, and on using those foundations to build better algorithms.
Modern neural networks are typically trained with adaptive optimizers like RMSProp and Adam, which often operate in a chaotic regime called the Edge of Stability. My work uses computer-assisted proofs to rigorously validate quasiperiodic and chaotic structures, and their corresponding routes to chaos, in these optimizers. Eventually I hope to develop a comprehensive theory explaining which mechanisms in an adaptive optimizer drive chaotic behavior. If you are curious, here are interactive visualizers for RMSProp and Adam.
Conformal inference offers a distribution-free way to flag anomalous data with rigorous, finite-sample statistical guarantees. I am developing conformal inference frameworks that bound the false discovery rate under practical constraints — decentralization, limited communication bandwidth, and non-exchangeability.
