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 6 Memo: Snapshot Exploitability + Local Update Rule Swap
+
+**Date**: 2026-03-24
+
+## Phase 6A: Snapshot Exploitability
+
+**Setup**: BP-trained CIFAR-10 snapshot (L=4, d=256, 61.9% acc). Train estimators on frozen features, then do k-step local updates and measure real loss change.
+
+### Results (5-step DeltaLoss, inner-product surrogate)
+
+| Credit | Gamma | rho | dL_5step |
+|--------|-------|-----|----------|
+| DFA | 0.009 | -0.023 | **-0.0001** |
+| ScalarCB | 0.122 | 0.090 | +0.042 |
+| Vec_M4 | 0.378 | 0.411 | +0.057 |
+| Oracle BP | 1.000 | 0.998 | +0.011 |
+
+**Finding**: Better credit quality is ANTI-CORRELATED with loss decrease. DFA (worst credit) produces the only method that doesn't increase loss. Vec (best credit) increases loss the most. Even Oracle BP increases loss at 5 steps.
+
+**Verdict**: This is **Case B** — the local update rule is the bottleneck.
+
+## Phase 6C: Local Update Rule Swap
+
+Tested target-shift rule (h_{l+1}^target = h_{l+1} - eta * a_norm) at eta in {0.01, 0.1, 0.3, 1.0}.
+
+### Results (5-step DeltaLoss)
+
+| Credit | inner_prod | shift_0.1 | shift_0.3 | shift_1.0 |
+|--------|:---:|:---:|:---:|:---:|
+| DFA | -0.0001 | **-0.0003** | +0.0004 | +0.001 |
+| Vec_M4 | +0.057 | +0.002 | +0.009 | +0.048 |
+| Oracle BP | +0.011 | +0.0002 | +0.001 | +0.005 |
+
+Target-shift reduces the damage but never achieves negative DeltaLoss for non-DFA credits. The cosine rule produces near-zero effects at all settings.
+
+## Root Cause Analysis
+
+The issue is deeper than the update rule. A BP-trained snapshot sits at a minimum of the full-backprop loss surface. Any local update that doesn't have access to the full gradient chain will push parameters in a direction that may locally align with the credit but globally increases loss. This is because:
+
+1. The inner-product surrogate `<F_l(h), a_l>` assumes a_l is the desired direction for the residual output. But even perfect credit (Oracle BP) doesn't produce good updates via this mechanism — the gradient of the surrogate w.r.t. block parameters is NOT the same as the gradient of the global loss.
+
+2. Target-shift reduces the magnitude of harmful updates but doesn't fix the direction. At small eta, updates are negligible. At large eta, the target shifts too far and becomes harmful.
+
+3. DFA "works" precisely because its random credits produce near-zero effective updates — it's approximately doing nothing, which is better than doing the wrong thing.
+
+## Implications
+
+**The project's fundamental limitation is NOT in the credit estimator.** It's in the local surrogate update paradigm itself. The inner-product surrogate `<F(h), a>` is not a valid proxy for global loss minimization, regardless of credit quality.
+
+**Potential directions:**
+1. Use credit to set per-block learning targets rather than gradients (e.g., knowledge distillation-style objectives)
+2. Use credit to modulate a more expressive local loss (e.g., local CE with projected targets)
+3. Abandon block-local updates entirely and use credit to define a global but differentiable auxiliary loss