Universal Function Approximation on Graphs

TL;DR

This paper introduces a universal function approximation framework for graphs that achieves state-of-the-art classification performance and has desirable theoretical properties, inspired by topological and linguistic methods.

Contribution

It presents a novel framework for universal graph function approximation with strong theoretical guarantees and practical effectiveness on multiple datasets.

Findings

Achieves state-of-the-art results on four graph classification datasets.

Provides a framework with desirable theoretical properties.

Algorithm complexity is O(number of edges times number of nodes).

Abstract

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We show how this allows us to achieve state-of-the-art performance on four different well-known datasets in graph classification and separate classes of graphs that other graph-learning methods cannot. Our approach is inspired by persistent homology, dependency parsing for NLP, and multivalued functions. The complexity of the underlying algorithm is O(#edges x #nodes) and code is publicly available (https://github.com/bruel-gabrielsson/universal-function-approximation-on-graphs).