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# 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 2 EXPLORE IN PROGRESS
---
## 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**
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