Co-occurring SAE features cluster into spatial functional lobes

- Using the Gemma-2-2B Gemma Scope SAE (layer 12, 16k features, average L0=41), functional co-occurrence of features (co-firing within 256-token blocks over 50,000 Pile documents) is spectrally clustered via five affinity measures, without using decoder-vector positions. [li-etal-2024-geometry] - The purely functional partition matches the features' actual spatial positions: a 2-lobe split separates code/math from natural-language features, and a 3-lobe split further separates short-message/dialogue from long-form scientific text. [li-etal-2024-geometry] - The phi coefficient gives the strongest functional-spatial correspondence, significant at 954 standard deviations (vs a permuted-label null) and 74 (vs a random-decoder null). [li-etal-2024-geometry] - "Lobes" is a naming metaphor to functional brain lobes (functionally related plus spatially clustered), not a claim of anatomical correspondence. [li-etal-2024-geometry]