# Phase 5C Memo: Online Shallow CIFAR Vector Pilot

**Date**: 2026-03-24
**Config**: CIFAR-10, L=4, d=256, 100 epochs, seed=42

## Question
Does the vector field's frozen credit advantage translate to online training?

## Results

| Config | Acc | Gamma | rho | S1 vs DFA | S2 vs DFA |
|--------|-----|-------|-----|-----------|-----------|
| DFA | 0.312 | 0.101 | -0.005 | 0 | 0 |
| vec wr=0.0 tw=1.0 | 0.159 | 0.007 | 0.005 | -0.094 | +0.010 |
| vec wr=0.0 tw=4.0 | 0.155 | -0.004 | 0.007 | -0.105 | +0.012 |
| vec wr=0.2 tw=1.0 | 0.243 | 0.001 | 0.000 | -0.100 | +0.005 |
| vec wr=0.2 tw=4.0 | 0.199 | 0.004 | 0.001 | -0.097 | +0.006 |

**No positive configs (S1 > 0 AND S2 > 0) found.**

Recall from Phase 4: scalar CB (wr=0.2 tgw=1.0) achieved S1=+0.079 online. The vector field does *worse* (S1=-0.100) despite being *much better* on frozen features (Gamma: 0.364 vs 0.115).

## Diagnosis

The vector field's online failure is NOT an estimator problem — it excels at credit recovery on fixed representations. The failure is in **co-adaptation**: when the forward net changes, the perturbation-based directional targets become stale. The vector field is actually MORE sensitive to representation drift than scalar CB because:

1. The perturbation target requires accurate tail-forward loss evaluation, which changes every epoch
2. The vector net directly outputs d-dimensional credit, giving it more capacity to overfit to current representations
3. Scalar CB's bridge consistency + EMA target provides implicit regularization against distribution shift

## Conclusion

The vector credit field is a **better estimator** (Phase 5B confirmed this clearly) but a **worse online learner** under the current local surrogate training framework. The bottleneck is definitively in **local exploitability / co-adaptation**, not in credit estimation quality.

This is the core finding of Phases 4-5: **improving the credit estimator beyond scalar CB does not help online training because the forward net's local surrogate update cannot exploit even moderately good credit signals.**

## Recommended Next Steps

The path forward is NOT to keep improving the credit estimator. Instead:
1. **Fix the local surrogate**: The inner product <F_l(h), a_l> may be too crude to exploit directional credit information
2. **Investigate representation stabilization**: Techniques like periodic re-training, replay buffers for the credit estimator, or slower forward net updates
3. **Consider hybrid approaches**: Use vector field credit for the first few layers only (where co-adaptation is less severe), DFA for deeper layers