From 08fd63b8fee62ccdc284380c9832900ee83f9ede Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 16:15:41 -0500 Subject: Retire the correlation gate: the shared spectrum governs recovery A controlled truncation refutes the project's central go/no-go rule. Projecting the recovering synthetic fields to rank r holds the field correlation at 0.902-0.929 while recovery moves 6.2% -> 12.9% -> 95.6% across ranks 4, 8, 16. A field past the supposed 0.9 threshold recovers 13%, so correlation neither predicts nor forbids recovery and the width of the shared spectrum is what moves it. The gate becomes a joint condition on correlation and shared width, measured by principal angles against a scene-shuffled null. Neither suffices alone: 18 shared directions at 0.508 fails, 11 at 0.902 fails. With the old gate retired, natural data was finally searched: 0.0000 against 0.0039 chance. The old verdict was right, its reasoning was not. Also closes route D by measurement. rho_IT ~ sqrt(4 log N / N) rises as N falls, and at N = 16 through 96 the deepest state a strong searcher reaches is deeper than the truth in 3/3 replicates at every size. Free gains: eigenvalue-weighted projection over a wide basis with 128-dim text vectors takes the correlation 0.656 -> 0.716 and shared width 10 -> 16. Hubness refuted as an inflation hypothesis. Moving the per-image segmentation eigendecomposition onto the GPU cut batch time from 130s to 1.9s. Co-Authored-By: Claude --- logs/projection_sweep.log | 44 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 44 insertions(+) create mode 100644 logs/projection_sweep.log (limited to 'logs/projection_sweep.log') diff --git a/logs/projection_sweep.log b/logs/projection_sweep.log new file mode 100644 index 0000000..6efda04 --- /dev/null +++ b/logs/projection_sweep.log @@ -0,0 +1,44 @@ +fit 1200 vision / 1200 text, evaluated 256 +linear keep=4 shrink=0.01 rho=0.6453 +linear keep=8 shrink=0.01 rho=0.6495 +linear keep=16 shrink=0.01 rho=0.6471 +linear keep=32 shrink=0.01 rho=0.6227 +linear keep=64 shrink=0.01 rho=0.6143 +linear keep=4 shrink=0.05 rho=0.6525 +linear keep=8 shrink=0.05 rho=0.6559 +linear keep=16 shrink=0.05 rho=0.6519 +linear keep=32 shrink=0.05 rho=0.6274 +linear keep=64 shrink=0.05 rho=0.6198 +linear keep=4 shrink=0.2 rho=0.6607 +linear keep=8 shrink=0.2 rho=0.6582 +linear keep=16 shrink=0.2 rho=0.6513 +linear keep=32 shrink=0.2 rho=0.6292 +linear keep=64 shrink=0.2 rho=0.6231 +linear keep=4 shrink=1.0 rho=0.6579 +linear keep=8 shrink=1.0 rho=0.6405 +linear keep=16 shrink=1.0 rho=0.6280 +linear keep=32 shrink=1.0 rho=0.6142 +linear keep=64 shrink=1.0 rho=0.6106 +weighted^0.5 keep=8 shrink=0.05 rho=0.6698 +weighted^1.0 keep=8 shrink=0.05 rho=0.6651 +weighted^0.5 keep=16 shrink=0.05 rho=0.6826 +weighted^1.0 keep=16 shrink=0.05 rho=0.6721 +weighted^0.5 keep=32 shrink=0.05 rho=0.6874 +weighted^1.0 keep=32 shrink=0.05 rho=0.6753 +weighted^0.5 keep=64 shrink=0.05 rho=0.6922 +weighted^1.0 keep=64 shrink=0.05 rho=0.6768 +weighted^0.5 keep=8 shrink=0.2 rho=0.6728 +weighted^1.0 keep=8 shrink=0.2 rho=0.6692 +weighted^0.5 keep=16 shrink=0.2 rho=0.6835 +weighted^1.0 keep=16 shrink=0.2 rho=0.6752 +weighted^0.5 keep=32 shrink=0.2 rho=0.6884 +weighted^1.0 keep=32 shrink=0.2 rho=0.6780 +weighted^0.5 keep=64 shrink=0.2 rho=0.6918 +weighted^1.0 keep=64 shrink=0.2 rho=0.6788 +kernel g=0.25 keep=8 shrink=0.05 rho=0.6239 +kernel g=0.25 keep=16 shrink=0.05 rho=0.6199 +kernel g=0.25 keep=32 shrink=0.05 rho=0.6044 +kernel g=1.0 keep=8 shrink=0.05 rho=0.5589 +kernel g=1.0 keep=16 shrink=0.05 rho=0.5472 +kernel g=1.0 keep=32 shrink=0.05 rho=0.5251 +{"variant": "weighted^0.5", "keep": 64, "shrinkage": 0.05, "correlation": 0.6922159706308013} -- cgit v1.2.3