Polymorphism Is Rotation: Operational Mechanistic Interpretability from a Two-Layer Transformer to Pythia-70m

ArXi:2605.24577v1 Announce Type: cross 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 re.