Zoom Seminar: Neural network symmetrisation in Markov categories, with application to equivariant diffusion by Dr Rob Cornish

Abstract: For data that exhibit symmetries, it is often of interest to parameterise a neural network that is invariant or equivariant with respect to some group actions. Recently there has been interest in doing so via symmetrisation techniques. In contrast to intrinsic methods, which enforce equivariance at each layer of the architecture, these approaches start with a model that is unconstrained and then modify it in some way to become equivariant.

In this talk, I will present a recent paper (https://arxiv.org/abs/2406.11814) that provides a general theory of neural network symmetrisation using the framework of Markov categories. Its central result characterises all possible symmetrisation procedures with considerable generality, requiring essentially no assumptions on the groups, actions, and neural network architectures involved. This recovers all existing symmetrisation methods as special cases, and also extends to provide a novel methodology for stochastic models, a problem that had not previously been considered. Moreover, by using Markov categories, the resulting theory becomes highly conceptual: low-level technical details are abstracted away, and significant parts may be expressed visually via string diagrams in a way that more closely resembles a computer implementation. I will also describe some recent follow-on work that applies stochastic symmetrisation at scale for equivariant diffusion modelling, obtaining significant empirical benefits over previous baselines on molecular generation tasks.