Beyond Erdos-Renyi: Generalization in Algorithmic Reasoning on Graphs

Neural algorithmic reasoning excels in many graph algorithms, but assessment mainly focuses on the Erdős-Rényi (ER) graph family. This study delves into graph algorithmic models' generalization across diverse distributions. Testing a leading model exposes overreliance on ER graphs for generalization assessment. We further investigate two scenarios: generalisation to every target distribution and single target distributions. Our results suggest that achieving the former is not as trivial and achieving the latter can be aided selecting source distribution via novel Tree Mover's Distance interpretation.