Add Phase 6: snapshot exploitability reveals local update rule is the bottleneck

Phase 6A: Better credit is ANTI-CORRELATED with loss decrease on fixed snapshot.
  DFA (Gamma=0.01) → dL=-0.0001 (only method that decreases loss)
  Vec_M4 (Gamma=0.38) → dL=+0.057 (increases loss most)
  Oracle BP (Gamma=1.0) → dL=+0.011 (still increases loss)

Phase 6C: Target-shift rule reduces damage but cannot make non-DFA credits productive.
  The inner-product surrogate <F_l(h), a_l> is fundamentally mismatched with directional credit.

Conclusion: Case B — the primary bottleneck is the local update paradigm itself,
not the credit estimator quality or tracking/co-adaptation.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

1 files changed, 45 insertions, 1 deletions

diff --git a/NOTE.md b/NOTE.md
index 36e0be9..6242a41 100644
--- a/NOTE.md
+++ b/NOTE.md
@@ -5,7 +5,7 @@
 - **pilot**: Controlled iteration (commits 0b9ebb2, 7baf7ae)
 - **frozen**: Code at commit 0b9ebb2 for all reported results
 
-## Status: PHASE 5 VECTOR FIELD AUDIT + TRANSFER COMPLETE
+## Status: PHASE 6 EXPLOITABILITY DISSECTION COMPLETE
 
 ---
 
@@ -329,3 +329,47 @@ the signal.
 - `vector_audit_full/`: Phase 5A full 3-seed audit
 - `frozen_cifar_vec/`: Phase 5B frozen CIFAR vector transfer
 - `online_vec_pilot/`: Phase 5C online CIFAR vector pilot
+
+---
+
+## Phase 6: Exploitability Dissection
+
+### Phase 6A: Snapshot Exploitability
+
+**Setup**: BP-trained CIFAR snapshot (L=4, d=256, 61.9% acc).
+Offline-trained estimators. k-step local updates with real loss measurement.
+
+**CRITICAL FINDING: Better credit → worse loss decrease.**
+
+| Credit | Gamma | rho | dL_5step (inner_product) |
+|--------|-------|-----|-------------------------|
+| DFA | 0.009 | -0.023 | **-0.0001** (only negative!) |
+| ScalarCB | 0.122 | 0.090 | +0.042 |
+| Vec_M4 | 0.378 | 0.411 | +0.057 |
+| Oracle BP | 1.000 | 0.998 | +0.011 |
+
+Credit quality is ANTI-CORRELATED with loss decrease.
+DFA (worst credit) is the only method not increasing loss.
+
+### Phase 6C: Local Update Rule Swap
+
+Tested target-shift (`h_target = h_{l+1} - eta * a_norm`) at eta in {0.01, 0.1, 0.3, 1.0}.
+
+Target-shift reduces damage (Vec dL: +0.057 → +0.002 at eta=0.1) but never achieves
+negative DeltaLoss for any non-DFA credit. Cosine rule produces near-zero effects.
+
+### Root Cause
+
+The inner-product surrogate `<F_l(h), a>` is not a valid proxy for global loss minimization.
+The gradient of this surrogate w.r.t. block parameters ≠ gradient of global loss w.r.t. same parameters.
+A BP-trained snapshot is at a minimum reachable only by full BP; local updates systematically push uphill.
+
+DFA works because its credits are weak enough to produce near-zero updates, effectively doing nothing.
+
+### This is Case B from the diagnostic logic tree:
+Better credit does NOT lead to better snapshot loss decrease.
+**The primary bottleneck is the local update rule itself, not the estimator or tracking.**
+
+### Experiment IDs (Phase 6)
+- `snapshot_exploit/`: Phase 6A snapshot exploitability
+- `update_swap/`: Phase 6C local update rule comparison