item 21: GSM carry-cot 57.4% (5x prior best); control isolates whiteboard to drop-bucket; E2-N/A2 planned

PLAN_SELFPACED.md

@@ -51,6 +51,56 @@ protection); (c) easy-bucket damage < carry-always's (83→45 was the
 unprotected number). Hard-bucket *gain* over carry-always is hoped for,
 not predicted.
 
+### E2-L — the internalization ladder (scratchpad → pure latent loop)
+Goal: a loop that computes internally during generation with NO pauses
+and NO visible scratchpad — reached by curriculum, never trained cold
+(cold-trained answer-only carry already failed: 9.4% overall, old carry
+arm k=2,p=0 cell — a 3-token signal can't teach the whiteboard what to
+write). Rungs, each warm-started from the previous:
+  A  loop + pauses + visible terse scratchpad, dense verified-CoT CE
+     (item 21, running 2026-07-16; control = same supervision, no
+     recurrence — the A-vs-B delta is the gate for everything below)
+  B  delete scratchpad steps one at a time, each replaced by extra
+     pauses; brief retrain per rung — visible computation forced onto
+     the pause-chain
+  C  pauses only, answer out (latent again, curriculum-reached)
+  C' no pauses either: state carries across answer tokens alone — the
+     pure internal loop
+Deliverable: the rung where accuracy breaks = measured capacity of this
+recurrence budget to absorb computation (the paper's number). Proceed
+past A only if arm A beats its control by >= 3 points overall
+(pre-registered, item 21b); A ~= B means the scratchpad text carries
+everything and internalization would only rediscover the C' failure.
+
+### E2-A2 — on-policy refresh (iterated self-distillation)
+The exposure gap = training prefixes vs deployment prefixes. Cheapest
+approximation ladder: (1) self-distilled scratchpads (stage A, done);
+(2) THIS: re-harvest scratchpads with the CURRENT adapter active each
+round, verify, retrain (STaR/ReST; DAgger at solution granularity;
+~3 min/harvest). Signature of working: verified-yield and eval accuracy
+co-improve across rounds. Gated on the A-vs-B verdict.
+
+### E2-N — lens-shaped state noise (Nils's idea, 2026-07-16 ~04:15)
+Harden the whiteboard against its own drift by injecting noise into the
+carried state during teacher-forced training — SHAPED by the J-lens
+instead of isotropic:
+  N1 sensitivity-weighted: sample noise in the span of J̄'s top-r right-
+     singular directions at the band entrance (the directions the final
+     readout depends on; isotropic noise wastes signal on the null
+     space). Cheap: jbar.pt exists; --lensnoise rank,scale flag.
+  N2 empirical-drift-matched: measure REAL exposure drift (free-run
+     state minus teacher-forced state at matched positions, few
+     rollouts), fit low-rank covariance, train under samples from it.
+     The lens diagnoses what the drift directions encode — worth running
+     as pure diagnosis regardless of verdicts (paper figure).
+  N3 concept-jitter: lens-read the carried concept (e.g. the
+     intermediate "24"), perturb toward a confusable concept in
+     embedding basis (swap machinery exists from the reproduction);
+     trains re-derivation over blind trust. Most ambitious.
+Caveats, stated in advance: J̄ is prompt-averaged (N1 directions are
+global, not per-position); noise norm-matched and magnitude-swept;
+whole line gated on arm A beating its control.
+
 ### E3 — power knob (only if E1 or E2 shows clean gating)
 Warm-start rung-2 band-LoRA under the gate; joint fine-tune. Question: do
 gate-bought iterations do MORE per iteration with a trainable band?