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 +++++++++++--- LAB_NOTES.md | 22 ++++++++++++++++++++++ 2 files changed, 33 insertions(+), 3 deletions(-) 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. diff --git a/LAB_NOTES.md b/LAB_NOTES.md index 8c0e9d5..e6aa208 100644 --- a/LAB_NOTES.md +++ b/LAB_NOTES.md @@ -562,6 +562,28 @@ orbit lever is unavailable on this corpus. See `NATURAL_RESULTS.md`. +## 2026-08-01: landscape reshaping does not substitute for correlation + +At the natural-data field quality of 0.656, every solver returns chance. +Full-rank spectral initialisation gives 0.0039 against 0.0039 chance, +refinement 0.0078, and a rank-truncation ladder from four to full rank +stays at or below chance throughout. Coarse-to-sharp smoothing is the +standard way to widen basins and thin decoys, and it recovers nothing +here. + +The reading is categorical rather than about this one method. Below the +polynomial threshold the deficit is information the algorithm class +cannot exploit, not a basin it fails to locate, so reshaping has nothing +to work with. Solver-side candidates should therefore wait on the +correlation rather than compete with it, and the only non-correlation +lever still open is population size, since the phase boundary is joint +in the two. + +Compute note: NCSA Delta A40 was brought in for the correlation-raising +battery -- larger backbones and finer segmentation over the same corpus +-- with three array tasks starting immediately against a queue of 810, +9,624 GPU-hours remaining on the account. + ## Current experimental gate The node-level ordering-and-basin gate is passed on VG by content-projected -- cgit v1.2.3