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/split_half.json | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) create mode 100644 artifacts/vg_5k/split_half.json (limited to 'artifacts/vg_5k/split_half.json') diff --git a/artifacts/vg_5k/split_half.json b/artifacts/vg_5k/split_half.json new file mode 100644 index 0000000..5140582 --- /dev/null +++ b/artifacts/vg_5k/split_half.json @@ -0,0 +1,18 @@ +{ + "protocol": "Each scene's parts split into disjoint halves within one modality; a relation field is built from each half and the two are matched by the anchor bound. Both halves describe the same scenes, so this upper-bounds any cross-modal result.", + "results": { + "text": { + "scenes": 256, + "mean_parts": 15.9765625, + "split_half_correlation": 0.7933697484313135, + "split_half_anchor_bound": 0.490625 + }, + "vision": { + "scenes": 256, + "mean_parts": 6.0, + "split_half_correlation": 0.9836462733134468, + "split_half_anchor_bound": 0.99375 + } + }, + "cross_modal_bound_for_reference": 0.291 +} \ No newline at end of file -- cgit v1.2.3