Persistent Homology Automates Detection of Circular Feature Manifolds in GPT-2
burny_tech · x · 2026-11-10
Siddharth Setlur proposes using persistent homology from algebraic topology to automatically detect multidimensional feature manifolds in language models.
- Prior work (Engels et al. 2024, Modell et al. 2025) found features like days of the week, months, and 20th-century years in GPT-2 small layer 7 lie on circles, but discovery relied on SAE ablation plus manual inspection of low-d PCA projections.
- Two limitations: manual inspection doesn't scale, and low-d PCA can miss nontrivial geometry in high-d space (d=768) — possibly explaining why so few multidimensional features were found.
- Method: compute the n-th persistence diagram of the ablated point cloud; points far from the diagonal indicate significant n-dimensional "circles", automating manifold detection.
- The author previously worked on topological deep learning, using algebraic topology invariants in ML loss functions.
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