Preregistered hypotheses (H001–H011b)

Each hypothesis below was written with falsifiable sub-predictions and a pre-specified outcome decision tree, then committed to git before its experiment ran — the commit history is the preregistration timestamp. Results were appended afterwards, with the original predictions preserved for audit.

The honest headline of this series is a negative one: across all 14 hypotheses, the Hodge Laplacian never confers a unique advantage once an external residual is present (H008c). Outcomes below are reported exactly as they resolved — including the many nulls and refutations.

Outcomes at a glance

# Question (abbreviated) Resolved outcome
H001 Why does minimal Hodge MP lose on MUTAG; what closes the gap? Symmetric normalisation closes it (matches MLP); residual hurts here
H002 Does the winning architecture beat MLP on PROTEINS? Equality; strong “topology beats MLP” claim refuted
H003 Does scale (NCI1) lift the Hodge = MLP ceiling? Narrow positive (+8.6 pp), regime-bound
H004 Is sample size the mechanism? Mechanism ruled out
H005 Is feature density the mechanism? Mechanism ruled out (+ a feature-degradation robustness result)
H006 Can Hodge classify from graph structure alone? Signal present on all 3 datasets, but rank-inverted vs the full-feature gain
H007 Which structural proxy explains the gain? None — no single proxy is predictive
H008 Does the NCI1 result hold vs GIN / GAT? Regime-bound: GIN/GAT collapse to class prior at matched capacity
H008b Does degree normalisation close the GIN–Hodge gap? Refuted — normalisation alone does not recover
H008c Is the external residual the operative factor? Confirmed — the primary finding. Operator (Hodge vs adjacency) is secondary
H009 Does a learned sheaf Laplacian beat fixed operators? No — adds no value
H010 Does high-pass (Hodge) beat low-pass cross-dataset? No — high-pass is equal or worse
H011 Does L₁ edge propagation capture signal L₀ cannot? Degenerate on NCI1 (≈ no triangles); inconclusive
H011b L₁ on triangle-rich COLLAB Pending — directional smoke result only; full run compute-constrained

Individual preregistrations and their full resolved outcomes are listed in the sidebar.

Table of contents

Santiago Maniches (ORCID 0009-0005-6480-1987). MIT licence. All accuracy figures are obtained under a constrained matched-capacity protocol and are not benchmark-performance claims — see Limitations.

Edit this page on GitHub

This site uses Just the Docs, a documentation theme for Jekyll.