Learning from graphs: a spectral perspective

The architecture of a neural network constrains the space of functions it can implement. Equivariance is one such constraint—enabling weight sharing and guaranteeing generalization. But symmetries alone might not be enough: for example, social networks, finite grids, and sampled spheres have few automorphisms. I will discuss how spectral graph theory yields vertex representations and a generalized convolution that shares weights beyond symmetries.