From 08876d84919b90b194ffdc3bb8c03633504f62da Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Wed, 22 Jul 2026 05:11:34 -0500 Subject: theory: prove estimator and innovation regimes --- RESULTS.md | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) (limited to 'RESULTS.md') diff --git a/RESULTS.md b/RESULTS.md index 0650f04..f7873a1 100644 --- a/RESULTS.md +++ b/RESULTS.md @@ -429,6 +429,23 @@ the frozen 90% d4 threshold; **no prefix is eligible and task seeds 6--8 remain teaching directions are often strongly aligned even in mediocre runs, pointing next to regression gain/tracking over the moving trajectory rather than simply adding vectorizer capacity. +## Theory package and executable predictions + +`THEORY.md` proves the exact linearized variance of simultaneous Rademacher perturbation, +including its cross-layer term; bounds centered finite-sigma bias; gives a smooth-loss descent +condition that separates angle, gain, and curvature; proves the neutral-period innovation/SNR +result and task-fit absorption failure; and tabulates query/work/memory assumptions across the +main comparison set. + +The deterministic numerical verifier covers every frozen C5 axis. Across depth 2/4/8, width 8/32, +and K1/4/16, empirical perturbation MSE is within 1% of the exact prediction in the reported cases. +The finite-difference bias has log-log slope `2.000000` in sigma. A quadratic example changes from +descent to ascent on opposite sides of the predicted learning-rate threshold. Neutral predictor +residual power matches `(1-eta_P)^(2t)` across three rates and four update counts. Finally, +neutral residualization raises the teaching squared cosine from `0.7492` to `0.9656`, whereas +task-period fitting lowers it to `0.5395` by removing soma-correlated teaching. **The frozen C5 +theory package and numerical checks pass.** + ## Paper-faithful non-backprop baselines `PETITE` in the initial request is treated as **PEPITA**. Implementations and hyperparameters were @@ -496,6 +513,7 @@ canonical d2 comparison: `experiments/ep_depth2_sweep.sh`; near-parameter compar `experiments/ep_matched_sweep.sh`. C2 direct causal diagnosis: `experiments/c2_nodepert_validation.sh` followed by `python experiments/analyze_c2_nodepert_validation.py`. +Theory checks: `python experiments/verify_theory.py`. Audited aggregate tables: `experiments/analyze_verified.py`. The claim-locked finalizer is `experiments/finalize_claims.sh`; it rejects missing/dirty inputs, regenerates both main figures, their captions, source-hash manifest, and `results/audited_tables.md`, then runs all smoke checks. -- cgit v1.2.3