research

Written on August 30th, 2023 by Ben Chamberlain

Links and brief descriptions of selected research highlights. For a full list of publications see my Google Scholar.

Graph Neural Networks for Link Prediction with Subgraph Sketching

Scaling graph neural networks for link prediction using data sketches, specifically minhash and hyperloglog. As these sketches have permuatation invariant aggregation functions, this can be achieved within the Message Passing Neural Network framework

Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns

Applying the power of the sheaf to perform diffusion on graphs. In a nutshell, it’s using a small matrix for attention instead of a scalar value on each edge to create a notion of oriented directions.

Graph-Coupled Oscillator Networks

Extending the equivalence between graph neural networks and partial differential equations to incorporate networks of coupled oscillators and showing that with suitable damping, the stable solutions do not suffer from oversmoothing

Understanding over-squashing and bottlenecks on graphs via curvature

Solving the bottleneck problem by endowing graphs with a discrete version of Ricci flow.

Beltrami Flow and Neural Diffusion on Graphs

Extending the idea of diffusion on graphs to a manifold defined be a set of positional encodings and allowing the diffusion process on the positional coordinates to alter the graph topology

GRAND: Graph Neural Diffusion

Making an equivalence between Graph Neural Networks (GNNs) and Partial Differential Equations (PDEs). Using this equivalence to achieve sota results on graph benchmarks by exploiting sophisticated PDE numerical solvers