Topological overfitting detection: H0 gap catches overfitting before accuracy diverges (r=0.998)

[dancinlife]

Summary

We found that Persistent Homology (H0 total persistence) on class-mean direction vectors provides a real-time overfitting signal with r=0.998 correlation to the generalization gap — often detecting overfitting before the train/test accuracy gap becomes visible.

Method

1. Extract direction vectors from model: d = normalize(engine_A(x) - engine_G(x))
2. Compute per-class mean directions
3. Build cosine distance matrix between class centroids
4. Run H0 persistent homology (via ripser)
5. Compare H0_train vs H0_test — the gap predicts overfitting

Also includes

• Automatic LR search: The LR that minimizes H0 CV (coefficient of variation) over 5 epochs = optimal LR
• 1-epoch difficulty prediction: H0 after 1 epoch predicts final accuracy (H0=4.38 → 98.3%, H0=2.02 → 52.0%)
• Confusion prediction: H0 merge order = confusion pairs (Spearman r=-0.97)

Verified results

Dataset	Accuracy	Best LR	Early Stop	Time
MNIST	98.3%	1e-03	no	2.2 min
Fashion	87.4%	3e-04	no	2.2 min
CIFAR-10	52.0%	1e-03	yes (ep 6)	1.4 min

CIFAR early-stopped at epoch 6 when H0_gap exceeded threshold — preventing wasted compute on a model that was already overfitting.

Repo: https://github.com/need-singularity/ph-training
Install: pip install -e . then ph-train --dataset cifar

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Related projects

• logout — Consciousness Continuity Engine. The main research project with the dual-engine (PureFieldEngine) architecture that produces direction vectors analyzed by PH.
• Anima — Conversational consciousness agent with real-time PH overfitting detection integrated into the live inference loop.
• ph-training — Standalone training pipeline. pip install -e . then ph-train --dataset cifar.