An improvement to a result about graph isomorphism networks using the prime factorization theorem
This provides a theoretical improvement for graph isomorphism networks, addressing a known limitation in their aggregation mechanisms, though it appears incremental as it builds on existing mathematical foundations.
The paper tackled the problem of designing injective aggregation functions for graph neural networks by proving the existence of a function on countable sets that makes sum aggregation injective for all finite multisets, using the unique prime factorization theorem.
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.