# Experiment Notes

## Experiment Phases
- **debug**: Initial implementation, rapid iteration (commits ce24e36)
- **pilot**: Controlled iteration (commits 0b9ebb2, 7baf7ae)
- **frozen**: Code at commit 0b9ebb2 for all reported results

## Status: PHASE 6.5 PROTOCOL AUDIT — PHASE 6A CONCLUSION REVISED

---

## Final Results Summary

### Toy LQ (3 seeds, 8000 steps)
| Method | Costate Cosine | ρ | Nudging |
|--------|---------------|---|---------|
| DFA | 0.001±0.003 | 0.001±0.007 | 0.000±0.001 |
| State Bridge | 0.945±0.002 | 0.931±0.003 | -0.344±0.019 |
| Credit Bridge | 0.944±0.001 | 0.930±0.002 | -0.342±0.019 |

### CIFAR-10 (3 seeds, 100 epochs)
| Method | Test Accuracy |
|--------|:------------:|
| BP | 59.2%±0.4% |
| DFA | 30.0%±0.3% |
| Credit Bridge | 29.6%±1.0% |
| State Bridge | 18.5%±1.8% |

### CIFAR-10 Diagnostics (seed 42)
| Method | BP Cosine | ρ | Nudge |
|--------|-----------|---|-------|
| BP | 0.940 | 0.990 | -0.027 |
| Credit Bridge | 0.056 | ~0 | ~0 |
| DFA | 0.030 | 0.005 | ~0 |
| State Bridge | 0.021 | 0.004 | ~0 |

---

## Key Findings

1. **Terminal gradient matching is essential** for credit bridge.
   Without it, V learns correct values but uninformative gradients (cos → 0.03).
   With it, credit bridge matches state bridge on toy (~0.94 cosine).

2. **State bridge fails on nonlinear systems** despite near-perfect state prediction.
   State prediction error → 0.0000 but test accuracy = 18.5% (worst of all methods).
   This confirms the core hypothesis: bridging state ≠ bridging credit.

3. **Credit bridge modestly outperforms DFA in BP cosine** (0.056 vs 0.030, ~2x)
   but accuracy is comparable (29.6% vs 30.0%).

4. **All non-BP methods struggle** on the deep 12-block MLP architecture.
   The gap to BP (59.2%) is large for all methods.

---

## Changes Log
- `ce24e36`: Initial implementation
- `0b9ebb2`: Sync state bridge to use normalized MSE in both toy and CIFAR
- `7baf7ae`: Add experiment notes and .gitignore

## Experiment IDs
- `toy_lq_frozen/`: Final toy results (3 seeds, synced state bridge)
- `cifar10/`, `cifar10_seed123/`, `cifar10_seed456/`: Final CIFAR results
- `toy_lq/`: Debug-phase toy results (raw state bridge, for ablation)
- `smoke_test/`, `smoke_test2/`: FashionMNIST debug runs

## Design Decisions
1. Terminal gradient matching (term_grad_weight=1.0): output-layer-local, not hidden BP
2. DFA warmup for credit bridge (20% of epochs): prevents value net bootstrap failure
3. Normalized MSE for state bridge: numerical stability
4. Credit normalization: a_norm = a / (RMS(a) + 1e-6)

---

## Phase 2: Explore (commit 2403960+)

### Synthetic Nonlinearity Ladder (Phase 1 of explore)

**Setup**: Teacher-student with phi_alpha(z) = (1-alpha)*z + alpha*tanh(z)
- alpha in {0, 0.25, 0.5, 1.0}, L in {2, 4, 8, 12}
- d=128, C=10, 80 epochs, 3 seeds

**Critical Finding**: Credit bridge advantage scales with nonlinearity.

At alpha=1.0 (full tanh), credit bridge is the BEST method on Gamma and rho at ALL depths:

| L | DFA Gamma | SB Gamma | CB Gamma | DFA rho | SB rho | CB rho |
|---|-----------|----------|----------|---------|--------|--------|
| 2 | 0.03 | 0.52 | **0.53** | 0.03 | 0.47 | **0.57** |
| 4 | 0.05 | 0.34 | **0.45** | 0.06 | 0.32 | **0.51** |
| 8 | 0.06 | 0.25 | **0.36** | 0.07 | 0.23 | **0.42** |
| 12 | 0.07 | 0.22 | **0.24** | 0.07 | 0.21 | **0.32** |

At alpha=0.5 (moderate nonlinearity), SB still wins on Gamma but CB wins on rho at L=4.
At alpha=0 (linear), SB dominates.

**Interpretation**: State bridge fails via Jacobian mismatch, not value prediction error.
Credit bridge avoids this by learning value field gradients directly.
The crossover happens around alpha=0.7-1.0.

### CIFAR-10 Depth Scan (Phase 2 of explore, in progress)

Sweep L={2,4,6,8,12}, d=512, 100 epochs on CIFAR-10.
Preliminary results (L=2,4, seed=42):

| L | Method | Acc | Gamma | rho |
|---|--------|-----|-------|-----|
| 2 | DFA | 0.312 | 0.196 | 0.001 |
| 2 | CB | 0.311 | 0.175 | **0.031** |
| 4 | DFA | 0.314 | 0.100 | 0.003 |
| 4 | CB | 0.298 | 0.123 | -0.002 |

CIFAR is much harder -- rho signal is very weak for all non-BP methods.

### Changes Log (explore phase)
- `2403960`: Add synthetic ladder and CIFAR depth scan experiments
- Student blocks now use pre-LayerNorm for stability (fixes L>=8 blowup)
- Added gradient clipping to block updates

### Experiment IDs (explore phase)
- `synth_ladder_smoke/`: Initial 3-alpha x 2-depth smoke test
- `synth_ladder_v2_lo/`: Full alpha=0,0.25 x L=2,4,8,12 x 3 seeds
- `synth_ladder_v2_hi/`: Full alpha=0.5,1.0 x L=2,4,8,12 x 3 seeds
- `cifar_depth_scan_s42/`: CIFAR L=2,4,6,8,12 x d=512 x seed=42 (COMPLETE)
- `boundary_ablation_s_sweep/`: s_type in {eT, deltaL, eT_hL, deltaL_hL}
- `boundary_ablation_tgw_sweep/`: tgw in {0, 0.25, 1.0, 4.0}
- `boundary_ablation_wr_sweep/`: warmup ratio in {0, 0.05, 0.2, 0.5}
- `boundary_ablation_s123/`, `boundary_ablation_s456/`: s_type sweep with seeds 123, 456
- `boundary_ablation_deltaL_wr/`: deltaL with warmup ratio sweep

### Phase 3 Results: Boundary-Condition Ablation

At alpha=1.0, L=4 (best synthetic regime), 3 seeds:

**s_type (conditioning code):**
| Code | Gamma | rho | Acc |
|------|-------|-----|-----|
| eT (dim=10) | 0.452+/-0.042 | 0.509+/-0.033 | 0.523 |
| deltaL (dim=d) | **0.562+/-0.007** | **0.510+/-0.014** | 0.448 |
| eT+proj(h_L) | 0.002 | 0.016 | 0.559 |
| deltaL+proj(h_L) | 0.018 | 0.026 | 0.564 |

**deltaL gives best Gamma. Concatenating h_L destroys credit quality (value net cheats).**

**Terminal gradient matching weight:**
tgw=0 -> Gamma=0.12; tgw=1 -> Gamma=0.46; tgw=4 -> Gamma=0.57 (but acc drops).
Terminal gradient matching is monotonically beneficial for credit quality.

**Warmup ratio:**
wr=0 -> best Gamma (0.68) but worst acc (0.46).
wr=0.5 -> worst Gamma (0.23) but best acc (0.66).
Clear tradeoff between credit quality and accuracy.

Best single config: deltaL + tgw=1.0 + wr=0.05 -> **Gamma=0.768, rho=0.691**

### CIFAR deltaL Test
deltaL conditioning (s=grad_{h_L} CE, dim=512) on CIFAR L=4: FAILED.
Acc=17.2%, Gamma≈0, rho≈0. The 512-dim conditioning is too high-dimensional
for the value net. Confirms the scalar V approach has a dimensionality bottleneck.

### Pivot Recommendation: Direct Vector Credit Field
See `report_explore/MEMO_pivot_vector_field.md`.
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

---

## Phase 5: Vector Field Audit + Real-Task Transfer

### Phase 5A: Synthetic Audit (4 sanity checks)

**Setup**: alpha=1.0, L={4,8}, d=128, 3 seeds, 80 epochs

**Smoke test result (L=4, seed=42):**

| Method | Gamma | rho | nudge |
|--------|-------|-----|-------|
| scalar_cb | 0.224 | 0.210 | -0.007 |
| vec_eT_M4 | **0.847** | **0.951** | -0.026 |
| vec_shuffleCtrl | 0.051 | 0.068 | -0.001 |
| vec_noTerm | 0.955 | 0.971 | -0.027 |
| vec_onesided | 0.832 | 0.943 | -0.024 |

**Check B (shuffle)**: PASS — shuffled control collapses (5/6 near zero across full audit)
**Check C (noTerm)**: Terminal NOT needed — perturbation target alone gives 0.95+ Gamma
**Check D (onesided)**: PASS — one-sided ≈ central difference

**Full 3-seed audit**: All 6 configs pass (delta_Gamma >= 0.49, delta_rho >= 0.55)

### Phase 5B: Frozen CIFAR Vector Transfer

**Setup**: CIFAR-10, frozen BP ref (L=4, d=256, 61.7%), 100 epochs estimators

| Method | Gamma | rho | nudge |
|--------|-------|-----|-------|
| DFA | 0.005 | 0.005 | -0.000006 |
| ScalarCB_eT | 0.115 | 0.120 | -0.000370 |
| StateBridge_eT | 0.287 | 0.264 | -0.000957 |
| **Vec_eT_M4** | **0.364** | **0.426** | **-0.001406** |

**TRANSFER SUCCESS**: Vec beats scalar CB by +0.25 Gamma, +0.31 rho.
Vec also beats state bridge on rho (0.43 vs 0.26).
M=4 is sufficient (M=8, M=16 give same results).

### Phase 5C: Online CIFAR Vector Pilot

**Setup**: CIFAR-10, L=4, d=256, 100 epochs, seed=42

| Config | Acc | Gamma | rho | S1 | S2 |
|--------|-----|-------|-----|----|----|
| DFA | 0.312 | 0.101 | -0.005 | 0 | 0 |
| vec wr=0.2 tw=1.0 | 0.243 | 0.001 | 0.000 | -0.100 | +0.005 |
| (for comparison: scalar CB wr=0.2 tgw=1.0 from Phase 4) | 0.283 | 0.179 | 0.009 | +0.079 | +0.014 |

**ONLINE FAILURE**: Vector field does WORSE than scalar CB online, despite being
much better on frozen features. No config achieves S1>0.

### Core Finding of Phases 4-5

**The bottleneck is NOT the credit estimator.** Improving credit quality from
scalar CB (Gamma=0.12) to vector field (Gamma=0.36) on frozen features does NOT
help online training. The bottleneck is in the **local surrogate update**:
<F_l(h_l), a_l> cannot effectively exploit directional credit information,
and co-adaptation between forward net and credit estimator rapidly degrades
the signal.

### Experiment IDs (Phase 5)
- `vector_audit/`: Phase 5A smoke test
- `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

---

## Phase 6.5: Protocol Audit (REVISES Phase 6A conclusion)

### Phase 6.5A: Same-Batch Linesearch

**CRITICAL REVISION**: Phase 6A's "better credit → worse loss" was a protocol artifact.

Phase 6A used: normalized credit + held-out evaluation + gradient clamping.
Phase 6.5A uses: raw + norm credit, same-batch + held-out eval, no clamping, eta sweep.

**With same-batch evaluation, better credit DOES produce more loss decrease:**

| Method | Gamma | dL_same (norm, all, best eta) | dL_held |
|--------|-------|-------------------------------|---------|
| DFA | 0.01 | -0.003 | +0.004 |
| ScalarCB | 0.12 | -0.025 | +0.027 |
| Vec_M4 | 0.38 | **-0.135** | +0.045 |
| Oracle BP | 1.00 | **-0.406** | +0.094 |

Same-batch loss decrease is MONOTONIC with credit quality.
But held-out loss INCREASES for all non-DFA methods.

**This is Case D: the local surrogate exploits credit correctly on training data,
but the update overfits to the batch. Better credit = more effective overfitting.**

### Key confounds identified in Phase 6A:
1. **Normalization** inflated DFA's weak credits to same magnitude as Vec's
2. **Held-out evaluation** showed generalization failure, not exploitability failure
3. **Gradient clamping** distorted the natural credit quality ordering

### Raw vs Norm:
- Raw credit: tiny updates (BP grad RMS ≈ 0.00004). Vec raw best dL_same=-0.005
- Norm credit: amplifies to useful magnitude but also amplifies overfitting

### Revised diagnosis:
The bottleneck is NOT "surrogate can't exploit credit" (Phase 6A was wrong).
It IS "local surrogate with good credit overfits to mini-batch."
This suggests: regularization of local updates (larger batches, weight decay,
gradient noise) could make better credit usable.

### Experiment IDs (Phase 6.5)
- `exploit_linesearch/`: Phase 6.5A smoke test (Oracle + Vec, last1, raw)
- `exploit_linesearch_full/`: Phase 6.5A full sweep (all methods, ranges, norm modes)