From b246cc878c3db48e6d993a6a293176ee9be97e77 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Tue, 9 Jun 2026 15:28:30 -0500 Subject: Add MNIST real-data validation of e0 theorem and estimator New script validates both no-fit claims on MNIST-subset MLPs. e0 theorem: 16 configs, hidden share 0.39-0.82, measured E_B[e0] within 0.0001-0.0089 of prediction (512 real-backward draws each). Estimator: 96 trajectories, velocity MAE 0.00196 (3.9% of mean gap), bias -0.0006, beating fixed K(0) everywhere; kernels computed via a layerwise gram identity self-tested against autograd at machine precision. Co-Authored-By: Claude Fable 5 --- notes/36_evidence_ledger.md | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) (limited to 'notes/36_evidence_ledger.md') diff --git a/notes/36_evidence_ledger.md b/notes/36_evidence_ledger.md index 63e797d..14af7df 100644 --- a/notes/36_evidence_ledger.md +++ b/notes/36_evidence_ledger.md @@ -100,8 +100,13 @@ standard lazy approximation whose breakdown is *measured* (item 3c below). overprediction (+0.0026), FA near-unbiased (+0.0005); cause: drift velocity decays after s (alpha_t < t/s; e.g. true alpha_50 = 1.46 (BP) / 1.17 (FA) vs linear 2.5). Honest error story, no fitted correction. -5. **MNIST replication (note 38)**: same protocol, width 256, depth 2, - N in {128,256,512}, 48 traj: see `real_data_validation_mnist/`. +5. **MNIST replication (note 38)**: same protocol, widths {128,256} x + N {128,256,512} x 2 inits x 8 feedbacks = 96 traj, lazy step + (`eta lam_max/N = 0.05`): velocity MAE **0.00196** (= 3.9% of mean gap), + bias -0.0006, corr 0.911 (gap range only 0.040-0.063, so MAE/bias are the + operative stats); fixed K(0) MAE 0.0061 biased high — same bracket as + synthetic. At eta lam_max/N = 0.3 the lazy chain breaks as expected + (scope boundary, recorded in note 38). ### (d) The soft ramp + closed form (T7) -- cgit v1.2.3