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>

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+# Phase 6A Memo: Snapshot Exploitability
+
+**Date**: 2026-03-24
+**Config**: BP snapshot, CIFAR-10, L=4, d=256 (61.9% acc), seed=42
+
+## Question
+On a fixed snapshot, does better credit lead to better real loss decrease via the current local surrogate?
+
+## Results
+
+| Method | Gamma | rho | dL_1step | dL_5step | dL_20step |
+|--------|-------|-----|----------|----------|-----------|
+| DFA | 0.009 | -0.023 | **-0.0004** | **+0.0002** | **-0.0007** |
+| ScalarCB | 0.122 | 0.090 | +0.003 | +0.042 | +0.405 |
+| Vec_M4 | 0.378 | 0.411 | +0.003 | +0.050 | +0.272 |
+| Oracle BP | 1.000 | 0.998 | **-0.001** | +0.007 | +0.026 |
+
+## Key Finding: The Local Surrogate is Anti-Correlated with Credit Quality
+
+**Better credit produces WORSE loss change.** DFA (Gamma≈0) is the only method that decreases loss. ScalarCB (Gamma=0.12) and Vec (Gamma=0.38) both increase loss, with Vec slightly worse. Even Oracle BP increases loss at 5+ steps.
+
+The inner-product surrogate `L_local = <F_l(h_l), a_l>` is fundamentally broken as a local update rule for directional credit:
+- It treats a_l as a "desired direction for the residual output" rather than a gradient
+- The gradient of this surrogate w.r.t. block parameters pushes F_l(h) to align with a_l, but this is NOT the same as making h_{l+1} = h_l + F_l(h_l) move in the direction that decreases global loss
+- DFA "works" precisely because its random credits are small and roughly isotropic — the updates are near-random perturbations that don't systematically damage the representation
+
+## Verdict
+
+**This is Case B: the local update rule is the bottleneck, not the estimator or tracking.**
+
+Improving credit quality from DFA (Gamma=0.01) through ScalarCB (0.12) to Vec (0.38) to Oracle BP (1.0) does NOT improve — and actually worsens — real parameter update quality.
+
+## Implication
+
+The project should pivot from "better credit estimator" to "better local update coupling." The target-shift local regression rule (Phase 6C) is the natural next experiment:
+
+`L_shift = 0.5 * || h_l + F_l(h_l) - sg(h_{l+1} - eta * a_{l+1}^norm) ||^2`
+
+This directly tells each block: "adjust your output so the next hidden state moves toward the credit-indicated direction."