HyperGraphX: Graph Transductive Learning with Hyperdimensional Computing and Message Passing

TL;DR

The paper addresses transductive graph learning under label scarcity by introducing HyperGraphX, which fuses hyperdimensional computing with weightless, message-passing-like propagation. It encodes nodes as high-dimensional binary vectors in the original input dimension and uses binding and bundling operations, with key updates $H^{(l+1)} = (\hat{D}^{-1/2}\hat{A}\hat{D}^{-1/2}H^{(l)})$, $h_v^{(l+1)} = \bigvee_{(u,v)\in E} h_u^{(l)}$, and a residual-like bundling $H = \alpha H^{(0)} + (1-\alpha) H^{(L)}$. Across seven graphs, HyperGraphX outperforms major GNNs (GCN, GAT, GeomGCN, GCNII) and state-of-the-art HD methods (HDGL) in accuracy, while delivering orders-of-magnitude faster training times, highlighting strong potential for energy-efficient hardware such as process-in-memory and neuromorphic devices. This approach offers a practical path to scalable, robust graph learning on energy-constrained platforms without sacrificing predictive performance.

Abstract

We present a novel algorithm, \hdgc, that marries graph convolution with binding and bundling operations in hyperdimensional computing for transductive graph learning. For prediction accuracy \hdgc outperforms major and popular graph neural network implementations as well as state-of-the-art hyperdimensional computing implementations for a collection of homophilic graphs and heterophilic graphs. Compared with the most accurate learning methodologies we have tested, on the same target GPU platform, \hdgc is on average 9561.0 and 144.5 times faster than \gcnii, a graph neural network implementation and HDGL, a hyperdimensional computing implementation, respectively. As the majority of the learning operates on binary vectors, we expect outstanding energy performance of \hdgc on neuromorphic and emerging process-in-memory devices.