An improvement to a result about graph isomorphism networks using the prime factorization theorem

TL;DR

This paper leverages the prime factorization theorem to demonstrate the existence of an injective sum aggregator function for multisets, advancing the theoretical understanding of graph isomorphism networks.

Contribution

It introduces a novel theoretical approach using prime factorization to ensure injectivity in sum aggregation for graph neural networks.

Findings

Existence of an injective sum aggregator function proven

Application of prime factorization to graph neural networks

Theoretical advancement in graph isomorphism network design

Abstract

The unique prime factorization theorem is used to show the existence of a function on a countable set $\mathcal{X}$ so that the sum aggregator function is injective on all multisets of $\mathcal{X}$ of finite size.