I am currently working on developing rigorous theoretical foundations for the generalization performance of machine learning models. Grounded in probability theory, my work aims to characterize the fundamental mechanisms of generalization and design improved training methods based on these insights.

Themes

  • Stochastic recurrence / exit times: rigorous finite-time and rare-event behavior for discrete stochastic dynamics motivated by SGD-like updates.
  • Metastability & Edge of Stability: understanding stability thresholds and large excursions that drive regime switches during training.
  • Anisotropic noise & generalization: linking directional noise, landscape geometry, and algorithmic notions of flatness (e.g., via escape times or stability margins).

Previous Projects

  • Exit-time theory for Kesten’s stochastic recurrence equations: scaling laws for mean exit times and their connection to heavy-tailed stationary behavior.

Current Projects

  • A metastability-based theory for EoS driven by rare events and non-Gaussian effects.
  • Trajectory-aware, data-dependent generalization theory grounded in the regions actually visited by training.
  • CFR+ convergence rates: asymptotic rates for Counterfactual Regret Minimization+ in imperfect-information games (Poker), with provable exponents in simple benchmark games.