Large deviations of one-hidden-layer neural networks

In this talk, I will present large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. I will explain how to derive quenched and annealed large deviation principle for the empirical weight evolution during training when letting the number of neurons and the number of training iterations simultaneously tend to infinity. The weight evolution is treated as an interacting dynamic particle system. The distinctive aspect compared to prior work on interacting particle systems lies in the discrete particle updates, simultaneously with a growing number of particles. This talk is based on joint work with Daniel Willhalm.