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

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

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

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.

The issue names no file, test, or entry point in the MLCommons Algorithmic Efficiency repository. Start by locating the repository's benchmark contribution guidance and determining whether the external ph-training pipeline and ripser-based method fit its scope; done would require a defined integration point, reproducible benchmark evidence, and accepted validation criteria.