Professor Jim Smith

by Professor Geoff Nicholls, University of Oxford

by Professor Anastasia Papavasiliou

by Professor Terry Lyons, University of Oxford

Abstract: In this talk, I will discuss the relationship between kernel methods and (two-layer) neural networks for generalization, which aims to theoretically understand the separation from the perspective of function spaces. First, I will start with random features models (a typical two-layer neural network, also a kernel method) from under-parameterized regime to over-parameterized regime, which recovers the double descent and demonstrates the benefits behind over-parameterization. Second, I will compare kernel methods and neural networks via random features from reproducing kernel Hilbert space (RKHS) to Barron space, which leaves an open question: what is the suitable function space of neural networks?

Followed by lunch in the Common Room

Followed by lunch in the Common Room

Followed by lunch in the Common Room

Followed by lunch in the Common Room

Followed by lunch in the Common Room

Followed by lunch in the Common Room