From 58b9c84dae293359f498fdf6afd533df5c9d3c25 Mon Sep 17 00:00:00 2001 From: Yuren Hao Date: Sat, 1 Aug 2026 14:45:16 -0500 Subject: Landscape reshaping does not substitute for field correlation A rank-truncation ladder from four to full rank returns chance accuracy at the natural-data correlation of 0.656, as does full-rank spectral initialisation with refinement. Coarse-to-sharp smoothing widens basins and thins decoys, and recovers nothing, so below the polynomial threshold the deficit is information the algorithm class cannot use rather than a basin it cannot find. Solver-side candidates should wait on the correlation instead of competing with it. Co-Authored-By: Claude --- CANDIDATE_REGISTER.md | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) (limited to 'CANDIDATE_REGISTER.md') diff --git a/CANDIDATE_REGISTER.md b/CANDIDATE_REGISTER.md index 31906ff..efed50e 100644 --- a/CANDIDATE_REGISTER.md +++ b/CANDIDATE_REGISTER.md @@ -40,7 +40,7 @@ them or widen the true basin. | Candidate | Cost | Status | |---|---|---| | Third-order terms, tr(M^3) | low | done: deepens truth and decoys alike | -| Rank-truncation ladder, coarse to sharp | low | running | +| Rank-truncation ladder, coarse to sharp | low | done: at chance, all ranks | | Convex-concave path following (PATH, FAQ family) | medium | queued | | Entropic doubly-stochastic relaxation | low | done: stalls far above truth | | Degree normalisation of the fields | low | queued | @@ -48,8 +48,16 @@ them or widen the true basin. | Sparsified fields, top-k neighbours only | low | queued | | Functional term: held-out generalisation of the induced map | medium | running | -Path following is the canonical landscape-deformation method for -quadratic assignment and has never been tried here. The functional term +The rank ladder settles the category. At the natural-data field quality +every rank from four to full returns chance accuracy, as does full-rank +spectral initialisation with refinement -- 0.0039 against 0.0039 chance. +**Landscape reshaping does not substitute for field correlation:** below +the polynomial threshold the deficit is information the algorithm class +cannot use, not basins it cannot find, so smoothing has nothing to +recover. Path following is the canonical landscape-deformation method for +quadratic assignment and remains untried, but this result lowers its +expected value at the current correlation and it should wait until the +correlation moves. The functional term is landscape reshaping by orthogonal information: a decoy that copies relational statistics still has to induce a map that generalises. -- cgit v1.2.3