Hypergraph Signal Processing and Neural Networks

Overview

We build signal processing and learning tools for hypergraphs, whose edges link many nodes at once and capture group interactions that pairwise graphs break apart. We represent a hypergraph by an adjacency tensor and process signals with the t-product. On that basis, our t-HGSP framework defines shifts, Fourier transforms, filtering, and sampling on hypergraphs. These operators underpin tensor hypergraph neural networks, which we connect to signal denoising and extend with hypergraph U-Nets and HyperNATE, an attention model that trains 10–100× faster.

A central focus is directed hypergraphs, where a set of nodes jointly drives another, as in chemical reactions, causal mechanisms, and traffic flows. Our t-DHGSP framework stores each directed hyperedge in a head-first adjacency tensor. Its t-product shift responds only when the whole tail set is active, and a directed Fourier transform follows from the t-SVD. We have used it for traffic denoising and brain connectome analysis. Most recently, we learn directed acyclic hypergraphs from observational data for causal discovery: the Fourier decomposition of the t-product turns acyclicity into a differentiable constraint.