Polymorphism Is Rotation: Operational Mechanistic Interpretability from a Two-Layer Transformer to Pythia-70m
Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually unintelligible interior coordinates. One matrix multiplication per model pair removes it: an orthogonal Procrustes fit on a single batch of activations transfers sparse-autoencoder feature dictionaries and steering vectors between independently trained models, with no retraining. The phenomenon is invisible to the standard SAE universality metric. Decoder-column cosine similarity matches across seeds at 98%, the SAE-universality headline number, while an SAE trained...
| Authors | Jordan F. McCann |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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