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/synth_v1/degeneracy_gate.json | 45 +++++++++++++++++++++++++++++++++ 1 file changed, 45 insertions(+) create mode 100644 artifacts/synth_v1/degeneracy_gate.json (limited to 'artifacts/synth_v1') diff --git a/artifacts/synth_v1/degeneracy_gate.json b/artifacts/synth_v1/degeneracy_gate.json new file mode 100644 index 0000000..6a910d0 --- /dev/null +++ b/artifacts/synth_v1/degeneracy_gate.json @@ -0,0 +1,45 @@ +{ + "protocol": "One spectral-start descent per trial, plus one descent started at the truth. A positive gap means the searcher stopped above the truth; zero means it found something the energy cannot distinguish from the truth; negative means the truth is beaten.", + "rows": [ + { + "label": "omit-size", + "size": 256, + "energy_gap_found_minus_truth": 0.43996140951295937, + "truth_descends_further_by": 0.0, + "blind_accuracy": 0.049479166666666664, + "verdict": "truth is DEEPER than what is found -- optimiser failure" + }, + { + "label": "noise035", + "size": 256, + "energy_gap_found_minus_truth": 0.04761915721057547, + "truth_descends_further_by": 0.0020415746981433114, + "blind_accuracy": 0.88671875, + "verdict": "truth is DEEPER than what is found -- optimiser failure" + }, + { + "label": "rank8", + "size": 256, + "energy_gap_found_minus_truth": 0.364986204015837, + "truth_descends_further_by": 0.006232799331109179, + "blind_accuracy": 0.06510416666666667, + "verdict": "truth is DEEPER than what is found -- optimiser failure" + }, + { + "label": "synth-full", + "size": 256, + "energy_gap_found_minus_truth": 0.07695912511043244, + "truth_descends_further_by": 0.0005474964148536876, + "blind_accuracy": 0.8828125, + "verdict": "truth is DEEPER than what is found -- optimiser failure" + }, + { + "label": "natural-best", + "size": 256, + "energy_gap_found_minus_truth": 0.08529010447794294, + "truth_descends_further_by": 0.16736025860425965, + "blind_accuracy": 0.02734375, + "verdict": "truth is DEEPER than what is found -- optimiser failure" + } + ] +} \ No newline at end of file -- cgit v1.2.3