Benjamin Chamberlain: A Continuous Perspective on Graph Neural Networks


In this talk I will discuss several recent papers that develop new graph neural networks by considering their relation to continuous processes. I will discuss how graph neural networks can be arrived at as numerical schemes to solve differential equations, what they have to do with Perelman’s famous solution to the Poincare conjecture and how they are related to string theory.

Graphs are fundamentally discrete structures and at first glance, treating them continuously does not appear to be a promising research direction. However, there are many examples where handling discrete objects as if they were continuous has been a catalyst to progress. Photons are now known to be discrete, but modelling quantum physical processes with continuous differential equations such as heat diffusion produced many great breakthroughs in classical physics and chemistry. In computer science, digital images are also discrete, but continuous tools such as diffusion based denoising are still widely used and the question of whether digital images are best modelled continuously or discretely remains a source of great philosophical debate. Even in ML, the most common approach to handling discrete objects is to embed them into a continuous space. I will show that for graph ML too, there is much to be gained from unlocking the magnificent toolbox of continuous mathematics.


Ben Chamberlain is a staff ML researcher at Twitter where he works on graph ML. He was previously the Head of Machine Learning at and was named one of Corinium’s Top 50 Innovators in data and analytics in the UK in 2019. He did his PhD with Marc Deisenroth at Imperial College London in large scale graph ML and his first degree is from the University of Oxford in physics. He has published on subjects that include graph neural networks, social network analysis, recommender systems, natural language processing and the design of online controlled experiments. Ben has over ten years of industry experience and has previously worked with the British intelligence services (GCHQ and MI6), British military (the SAS, Ministry of Defence and the Defence Science and Technology Lab) and the former investment bank, Lehman Brothers . Outside of ML, Ben enjoys playing and watching rugby and tennis.