Foundations of Deep Learning
Theory of Learning and Computation in Deep Neural Networks
My work in this area has included theoretical and computation investigation of infinite-width limits, which has provided a backbone for further developments in deep learning theory in my own work and beyond (perturbative and non-perturbative constructions; investigation of other neural network limits; importance of parameterization).
Example topics include:
Theoretical framework and empirical understanding of the role of scale in deep learning ("neural scaling laws"); exactly solvable models
Exact connections between deep neural networks, Gaussian processes (Gaussian field theories), and kernel methods ("NNGP" and "NTK")
Phase transitions and the dynamics of gradient descent in supervised deep learning; connections to dynamical systems and nonconvex optimization
Principled approaches towards information diffusion in ultra-deep neural networks and trainability
Connections between equilibrium and non-equilibrium statistical mechanics and deep learning
Introduction of tools from random matrix theory (free probability theory) to model neural network / glassy landscapes
Empirical Machine Learning & Applications
Correlates of generalization in deep learning; investigation of the pre-training paradigm in distribution shift; emergent capabilities in large neural models; new classes of graph neural networks for molecular physicsÂ
Theoretical Condensed Matter Physics
My doctoral work in quantum many-body theory was focused on identifying and studying new types of quantum and classical behavior and new routes towards the construction of quantum phases.
Example topics include:
Construction of the first topologically protected mechanical systems that is gapless in its bulk.
Simple construction of an experimentally-realizable system that gives rise to a non-Fermi liquid (metal coupled to Goldstone bosons of a Rashba ferromagnet) and calculation of its properties within a combined (N, epsilon) expansion
First proposal that many-body localization and and symmetry-protected topological order can give rise to quantum coherent dynamics in a quantum many-body system
Construction of non-local order parameters for certain classes of low-dimensional symmetry-protected topological phases of fermions