IS17: Applications of Stochastic Analysis to Deep Learning

Organizer: Eulalia Nualart (Pompeu Fabra University)

The Proportional Scaling Limit of Neural Networks

Mufan Li

Recent advances in deep learning performance have all relied on scaling up the number of parameters within neural networks, consequently making asymptotic scaling limits a compelling approach to theoretical analysis. In this talk, we explore the proportional infinite-depth-and-width limit, where the role of depth can be adequately studied, and the limit remains a great model of finite size networks. At initialization, we characterize the limiting distribution of the network via a stochastic differential equation (SDE) for the feature covariance matrix. Furthermore, in the linear network setting, we can also characterize the spectrum of the covariance matrix in the large data limit via a geometric variant of Dyson Brownian motions. Finally, we will briefly discuss ongoing work towards analyzing training dynamics.