From 42a9a7f9cd5da392194c5ae4e5b68a3966ad427b Mon Sep 17 00:00:00 2001 From: Yuren Hao Date: Tue, 14 Jul 2026 07:40:21 -0500 Subject: RESULT 19: wall-2 loop-gain theory, beta window formalism, probe mid-verdicts, three new controllers Co-Authored-By: Claude Fable 5 Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn --- docs/campaign/CASCADE_ABLATION_PLAN.md | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) (limited to 'docs/campaign/CASCADE_ABLATION_PLAN.md') diff --git a/docs/campaign/CASCADE_ABLATION_PLAN.md b/docs/campaign/CASCADE_ABLATION_PLAN.md index 173cc77..3d72386 100644 --- a/docs/campaign/CASCADE_ABLATION_PLAN.md +++ b/docs/campaign/CASCADE_ABLATION_PLAN.md @@ -565,6 +565,37 @@ direction), not training-under-fault; wave-2 = co-training with faults injected + +### RESULT 19 (2026-07-14): WALL-2 THEORY SESSION — loop-gain decomposition, the beta WINDOW, and three new controllers. +**Mechanism formalized.** The nudged solve is a fixed-point iteration whose per-sweep error gain +factorizes as **rho ~ beta x ||output curvature|| x ||down J^T chain|| x ||up J chain||** (follow the +error once around the clamp-closed loop: top-force Hessian ~ sigma(W_out)^2, force chain down, +rebuild chain up). Feedforwardness does NOT protect the iteration — the beta-clamp + force chain +CLOSE a loop through the stack. The continuous flow stays unconditionally stable (solver wall, not +physics wall; analog has no ceiling). Confirmations: f3e3 (3x beta -> earlier crossing), w2_blow +(beta down -> drift 0.062->0.027), sig telemetry (sigma 430 vs stage1b ~90 => curvature factor ~20x). +**The beta operating WINDOW**: beta_min (wall-1 SNR floor, rises as true grad shrinks) < beta < +beta_max (wall-2 loop-gain ceiling ~ margin/(sigma^2 ||J||^2), falls as training sharpens). fw72m +died because the fixed floor 1e-3 ended up ABOVE the falling ceiling. Window at 195k was still OPEN +below 1e-3 (blow healthy AND beating ctl on val) — the crash was constant-transplanting, not a +closed window. +**Probe mid-flight verdicts (s195000 -> 201k):** ctl replicating the crossing trajectory; blow +(3e-4) healthiest (drift 0.027, val 3.909 < ctl 4.073); geta07 FAILING (drift pinned 0.498, val +4.236) => monotone/positive-spectrum divergence suspected — damping structurally ineffective there; +geta05_k5 = second damping dose (clean refutation if it also fails); w2_bcap + w2_adapt chained. +**New machinery (committed):** (1) adaptive relax (--relax_tol: sweep-to-tolerance + rho-triggered +geta backtrack + FINAL FULL-STEP graphed round — the E-read identity (z-o)=d REQUIRES undamped +last substitution; mixing there leaks iteration residual into E (gn 1e5 bug, caught by smoke)); +(2) rho^ meter (per-sweep residual ratio = free live loop-gain gauge, GOV['rho']); (3) +**beta-cap-by-loop-gain (--beta_cap_rho): rho^>thresh -> cap *= 0.8, cap OVERRIDES the floor** +(the ceiling can sit below the floor near the wall; survival first). Paired smokes at the wall +ckpt: adaptive 0.771 vs legacy 0.754 cos (no regression). +**Control-map placement (aep-dynamics toolbox, second in-vivo transfer):** old drift>0.5 guard = +lagging column (silent through all precursors); rho^ servo = leading/online column; candidate +construction-column addition = **sigma-cap on W_out** (one clamp hits BOTH walls' drivers: the +wall-2 curvature factor AND the wall-1 governor collapse). K exonerated again at 72M (K3 vs K8 +cos 0.910 vs 0.899, probe at s140000). + ### RESULT 18 (2026-07-14): WALL-2 RETURNS AT SCALE — fw72m diverged at ~195k steps; f3e3 confirms beta-stress. Timeline (fw72m, 72M/FineWeb/32k): healthy to 168k (drift 0.013-0.017, skips 0, best val 3.7117 @~184k ~= 1.13B tokens); precursor drift SPIKE 0.044 @172k (transient); boundary contact 192-196k -- cgit v1.2.3