From 4f7ee05cc3b072478062e53645af016861c4b529 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 17:59:32 -0500 Subject: The failure is the optimiser, not the information: a 257x faster descent and a benchmark The gate settles which failure mode each field is in, and refutes the symmetry hypothesis I proposed. On the caption-omitted field the truth is a STRICT local minimum -- descent started at the truth does not move at all -- the anchor bound says the information is 99.7% intact, and our solver stops 0.44 above it at 4.9% accuracy. That is a pure optimiser failure. Natural data is the opposite: descent from the truth falls a further 0.167, so the truth is not even locally optimal, which is the information-deficit signature the 0.291 bound predicted. Steepest descent was brute-forcing all 32,640 candidate permutations through the full energy every step, including a batched cube trace with the triangle term active -- 203 seconds per descent, which is why the gates were hopeless. The pairwise term needs one matrix product for the whole table: swapping p,q changes the alignment sum by 2(C_pq + C_qp - C_pp - C_qq + 2 A_pq B_pq) with C = A @ B. Verified against brute force to 1e-9 before use, and the fast descent reaches the same optimum. 203s -> 0.79s. Adds a matching benchmark with known-reachable answers and the solver families never tried on these fields: Gromov-Wasserstein, entropic GW with an annealed regulariser, BAPG. Co-Authored-By: Claude --- artifacts/vg_5k/field_geometry.json | 54 +++++++++++++++++++++++++++++++++++++ 1 file changed, 54 insertions(+) create mode 100644 artifacts/vg_5k/field_geometry.json (limited to 'artifacts/vg_5k/field_geometry.json') diff --git a/artifacts/vg_5k/field_geometry.json b/artifacts/vg_5k/field_geometry.json new file mode 100644 index 0000000..7d36682 --- /dev/null +++ b/artifacts/vg_5k/field_geometry.json @@ -0,0 +1,54 @@ +{ + "protocol": "Each geometry is applied to each modality independently, so no transform crosses the gauge or uses the pairing. The bound is the anchor upper bound; the last column re-computes it with a rank comparison operator instead of a linear one.", + "label": "natural-best", + "rows": [ + { + "geometry": "euclidean (current)", + "correlation": 0.7157944505313568, + "anchor_bound": 0.3359375, + "anchor_bound_rank_operator": 0.1453125 + }, + { + "geometry": "global rank (copula)", + "correlation": 0.6453667782045476, + "anchor_bound": 0.171875, + "anchor_bound_rank_operator": 0.1453125 + }, + { + "geometry": "row rank", + "correlation": 0.6374571651517471, + "anchor_bound": 0.165625, + "anchor_bound_rank_operator": 0.1484375 + }, + { + "geometry": "local scaling", + "correlation": 0.7162509779848556, + "anchor_bound": 0.3625, + "anchor_bound_rank_operator": 0.1703125 + }, + { + "geometry": "diffusion t=3", + "correlation": 0.5659469014331384, + "anchor_bound": 0.0546875, + "anchor_bound_rank_operator": 0.0453125 + }, + { + "geometry": "heat kernel", + "correlation": 0.7381033036202107, + "anchor_bound": 0.31875, + "anchor_bound_rank_operator": 0.1546875 + }, + { + "geometry": "hyperbolic d=16", + "correlation": 0.7135662664726405, + "anchor_bound": 0.246875, + "anchor_bound_rank_operator": 0.1703125 + } + ], + "best": { + "geometry": "local scaling", + "correlation": 0.7162509779848556, + "anchor_bound": 0.3625, + "anchor_bound_rank_operator": 0.1703125 + } +} \ No newline at end of file -- cgit v1.2.3