Source
Bodnar et al. (2022), LIT-1811, §§3.2, 5–6 and Appendix F of arXiv 2202.04579v4; read in full in NOTE-1332. What the experiments showed is THEORY-1139, which this entry extends.
The thesis
The paper’s separation results say that diffusion with the right sheaf separates any labelling: sign flips across the two classes of a bipartite graph, rotations by class for more (Propositions 10–13). It concludes that “solving any node classification task can be reduced to performing diffusion with the right sheaf” (p. 6), and offers its learned model as a way to find that sheaf from features. Its accuracy on heterophilic benchmarks is then credited to the geometry it learns.
Why it is not held
The learned maps were compared with the theory only on a synthetic bipartite graph, where the right sheaf is negative everywhere and the model learned negative transports. No learned map is shown for any benchmark dataset. The model is also a feature-conditioned message function, and such models do well under heterophily for other reasons (p. 10), so benchmark accuracy cannot tell the theory’s mechanism from theirs.