From 8b28522305612d6300f485e14046ae38d49af426 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Wed, 22 Jul 2026 17:02:45 -0500 Subject: protocol: freeze dynamic projection training gate --- THEORY.md | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) (limited to 'THEORY.md') diff --git a/THEORY.md b/THEORY.md index f659d0f..b8416a3 100644 --- a/THEORY.md +++ b/THEORY.md @@ -571,6 +571,32 @@ transient loss and parameter growth. This is consistent with the two-sided condition above: sign control is necessary but does not bound the evolving gain `d c` or nonnormal deep-network transients. +The post-S0 dynamic controller instead separates a slow neutral predictor from +a fast instruction-off projection. On the current minibatch, let its neutral +residual be `e0=a0-P h-b`. Each cell forms + +```text +q_t = Cov_t(e0, h) / Var_t(h), +e_perp = (e0 - mean_t(e0)) - q_t (h - mean_t(h)). +``` + +Only `s+e_perp` enters plasticity. The fit for `q_t` never observes `s`, so it +cannot regress away a task instruction merely because that instruction is +correlated with soma. For the diagonal affine traffic intervention, +`e0=D h+c` and hence `e_perp=0` in exact arithmetic at every task state. The +effective homogeneous coefficient is then `k=-lambda`, which satisfies both +Jury bounds for the frozen positive learning rate, momentum below one, and +small positive decay. Unlike a fixed negative margin, nulling `D` is invariant +to changes in the nonnegative input-covariance eigenvalue `c`. + +This is an empirical local certificate for the intervention being tested, not +a global stability theorem for a nonlinear ResNet. Finite-batch regression, +roundoff, cross-layer nonnormality, and traffic outside the diagonal affine +family remain possible failure modes. The separately frozen D1 training-prefix +gate in `DYNAMIC_INNOVATION.md` therefore requires both the measured local +certificate and bounded loss, parameter, optimizer, and BatchNorm trajectories +before any validation endpoint can open. + ### Intermittent feedback tracking can hide behind a final cosine An idealized mirror event every `k` task updates uses -- cgit v1.2.3