Add Phase 4 diagnostic dissection: frozen credit recovery, online shallow scan, vector field pilot

Key findings:
- Frozen CIFAR: estimators CAN recover credit (SB best, CB 20x > DFA)
- Online shallow: cb_eT wr=0.2 tgw=1.0 achieves S1>0, S2 marginal
- Vector credit field: 0.91-0.96 Gamma/rho on synthetic (vs 0.34 scalar CB)
- Direct vector field avoids scalar V curvature problem entirely

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

1 files changed, 98 insertions, 1 deletions

diff --git a/NOTE.md b/NOTE.md
index 774b72a..006496e 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 2 EXPLORE IN PROGRESS
+## Status: PHASE 4 DIAGNOSTIC DISSECTION COMPLETE
 
 ---
 
@@ -165,3 +165,100 @@ Instead of V_phi -> grad_h V, learn a_phi(h_l, t_l, s) -> R^d directly.
 Train with perturbation-based target: match <a, v> to actual loss change.
 Still satisfies no hidden BP anchor constraint.
 Minimal test: synthetic alpha=1.0, L=4 with M=4 perturbation directions.
+
+---
+
+## Phase 4: Diagnostic Dissection (commit TBD)
+
+### Phase A: Frozen CIFAR Credit Recovery
+
+**Setup**: BP-trained CIFAR-10 network (L=4, d=256, 61.7% test acc), frozen.
+Train credit estimators on fixed representations.
+
+**Key Result**: On frozen BP features, credit estimators CAN recover meaningful credit.
+
+| Method | mean Gamma | mean rho | mean nudge |
+|--------|-----------|---------|-----------|
+| DFA (random) | 0.006 | 0.005 | -0.000022 |
+| State Bridge (eT) | **0.287** | **0.246** | **-0.000957** |
+| Scalar CB (eT) | 0.115 | 0.125 | -0.000370 |
+| Scalar CB (deltaL) | 0.070 | 0.062 | -0.000160 |
+
+**Surprising**: State bridge is BEST on frozen BP features (opposite of synthetic).
+BP-trained features are quasi-linear, so SB's Jacobian approximation works well.
+
+Also tested L=6 d=256 and L=4 d=512: same pattern (SB > CB_eT > CB_deltaL >> DFA).
+
+**Implication**: Estimator is NOT the fundamental bottleneck. The online training
+failure is due to co-adaptation between forward net and credit estimator.
+
+### Phase B: Online Shallow CIFAR Conditioning Scan
+
+**Setup**: L=4, d=256, CIFAR-10, 100 epochs, seed=42 (then 3-seed on best config).
+Sweep: methods={DFA, SB, CB_eT, CB_deltaL}, wr={0,0.05,0.2}, tgw={1.0,4.0}.
+
+**Found 2 positive configs with S1>0 AND S2>0:**
+
+| Config | Acc | Gamma | rho | S1 vs DFA | S2 vs DFA |
+|--------|-----|-------|-----|-----------|-----------|
+| cb_eT wr=0.2 tgw=1.0 | 0.283 | 0.179 | 0.009 | **+0.079** | **+0.014** |
+| cb_eT wr=0.2 tgw=4.0 | 0.285 | 0.187 | 0.002 | **+0.087** | **+0.007** |
+
+**3-seed validation of cb_eT wr=0.2 tgw=1.0:**
+- Seed 42: S1=+0.079, S2=+0.014 (both positive)
+- Seed 123: S1=+0.059, S2=-0.004 (S1 positive, S2 marginal negative)
+- Seed 456: S1=+0.135, S2=+0.003 (both positive, barely)
+
+S1 is consistently positive. S2 is marginal — sometimes positive, sometimes not.
+
+**CB_deltaL failed entirely on online CIFAR** (all configs near chance, Gamma≈0, rho≈0).
+**SB_eT also failed online** (Gamma=0.025, rho=-0.013, despite being best on frozen features).
+
+### Phase C: Direct Vector Credit Field Pilot
+
+**Setup**: Synthetic alpha=1.0, L={4,8}, d=128, 80 epochs, 3 seeds.
+Compare DFA vs Scalar CB vs Vector Field (M=4, M=8).
+
+**BREAKTHROUGH RESULT:**
+
+| Method | L=4 Gamma | L=4 rho | L=8 Gamma | L=8 rho |
+|--------|-----------|---------|-----------|---------|
+| DFA | 0.01±0.01 | 0.01±0.01 | 0.08±0.04 | 0.08±0.04 |
+| Scalar CB | 0.34±0.10 | 0.33±0.11 | 0.26±0.03 | 0.29±0.02 |
+| **Vector M=4** | **0.91±0.05** | **0.96±0.01** | **0.96±0.01** | **0.95±0.01** |
+| **Vector M=8** | **0.84±0.10** | **0.92±0.05** | **0.90±0.10** | **0.93±0.04** |
+
+**Vector field improves over scalar CB by +0.3 to +0.7 on BOTH Gamma and rho.**
+This is consistent across all 6 seed x depth combinations.
+
+The perturbation-based directional target directly trains the credit vector to
+predict local loss sensitivity, avoiding the scalar V curvature problem entirely.
+
+### Experiment IDs (Phase 4)
+- `frozen_cifar/`: Frozen CIFAR credit recovery (L=4 d=256, L=6 d=256, L=4 d=512)
+- `online_shallow/`: Phase B online scan (L=4 d=256, all configs)
+- `online_shallow_3seed/`: 3-seed validation of best config
+- `vector_credit_pilot/`: Phase C vector field vs scalar CB on synthetic
+
+### Answers to Phase 4 Questions
+
+**Q1: On frozen CIFAR, can the current credit estimator recover useful credit?**
+YES. Scalar CB achieves Gamma=0.115, rho=0.125 — 20x better than DFA.
+State bridge is even better (Gamma=0.287, rho=0.246).
+
+**Q2: If yes, why does online training still fail?**
+Co-adaptation. The forward net's features change every epoch, making the value net's
+credit stale. DFA avoids this because its credits don't depend on learning.
+The wr=0.2 warmup helps by letting DFA carry the forward net to a useful feature
+regime before CB takes over, but the S2 signal remains marginal.
+
+**Q3: Can a direct vector credit field improve over scalar CB?**
+YES, dramatically. On synthetic alpha=1.0, vector field (M=4) achieves Gamma=0.91,
+rho=0.96, compared to scalar CB's Gamma=0.34, rho=0.33.
+The scalar V curvature problem is real and avoidable.
+
+### Next Steps
+1. Test vector credit field on CIFAR-10 (the real task)
+2. Key concern: M=4 perturbation directions may not suffice for d=256/512 dimensions
+   (signal/noise ~ sqrt(M/d) ~ sqrt(4/256) ~ 0.12)
+3. May need M=32+ for CIFAR, which is expensive but tractable