From 1e4fbaf8e773509798387d19b806f6daf38f8b5c Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Wed, 22 Jul 2026 13:47:35 -0500 Subject: baseline: add residual response mirroring --- THEORY.md | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) (limited to 'THEORY.md') diff --git a/THEORY.md b/THEORY.md index 7038969..c64eb46 100644 --- a/THEORY.md +++ b/THEORY.md @@ -291,6 +291,28 @@ mean/minimum feedback-forward cosine `0.9887/0.9661`, norm ratios `[0.9537,1.0444]`, and zero forward-parameter access error in the update. These are mechanics, not task evidence. A frozen comparator gate is required. +The frozen WM short task gate later exposed a finite-sample defect of the +estimate-then-average rule: each new `What` remains noisy even when `Q=W`, so +an exponential tracker has a nonzero stationary error. Residual response +mirroring (RRM) makes a substantive rule change. Given the same local probe +and observed child response, it predicts the child response through Q and uses +only the residual: + +```text +u = conv(z, W), +uhat = conv(z, Q), +Delta Q = eta_M corr(z, u-uhat) / (count sigma^2). +``` + +In expectation this is the same contraction toward W, but when Q exactly +matches W the update is zero for every individual probe rather than only in +expectation. The readout uses the identical signed response residual. An +executable audit measures fixed-point update RMS `2.75e-18`, response-residual +fraction `3.08e-17`, and zero update dependence on forward parameters after +the observations are fixed. RRM needs one extra local Q prediction convolution +per mirror event, which is charged separately. It remains inherited local +weight estimation, not SDIL novelty. + ## 2. What is sufficient for a descent step Flatten all forward parameters into `theta`, let `p = grad L(theta)`, and let -- cgit v1.2.3