Research

My research studies the mathematical foundations of machine learning through learning theory, optimization, and applied probability.

Learning and generalization

I study how neural network architecture and optimization affect learning. Recent work considers convergence guarantees for recurrent neural networks and shallow Transformers, together with optimization and generalization bounds for stochastic Gauss–Newton methods.

• Finite-Time Analysis of Gradient Descent for Shallow Transformers
• Convergence of Gradient Descent for Recurrent Neural Networks

Reinforcement learning

I work on the theory of policy optimization and value estimation, including natural actor–critic methods and learning under partial observability. A recurring question is how memory and function approximation influence the efficiency of learning algorithms.

• Recurrent Natural Policy Gradient for POMDPs
• Code for recurrent natural policy gradient

Geometry and optimization

I study the geometry of optimization methods used in machine learning, including Gauss–Newton methods, natural policy gradients, and Fisher–Rao gradient flows.

• Geometric Convergence of Gauss–Newton for Neural Networks
• Stochastic Gauss–Newton in Deep Neural Networks
• Fisher–Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients

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