Statement

The hypothesis claims that in a trained representation, a purely functional grouping of features (by co-occurrence / co-firing, computed without using position) is significantly more spatially coherent than chance — i.e. functional relatedness carries a spatial signature. Formally: a partition induced from functional statistics alone exceeds a stated permutation null on a spatial-coherence statistic.

This node is the hypothesis (a general, falsifiable claim). The specific observed instance — feature lobes found in one model’s SAE dictionary — is the Feature Lobes (Spatial-Functional Modularity) empirical-pattern. The map keeps the observed pattern and the general claim as different types.

Falsifiability and scope

The claim is scale-dependent (may hold at a coarse partition and weaken at fine granularity) and requires an explicit null model; it is not a shape claim about any single feature, and finding spatial clustering does not by itself establish that the arrangement is causally exploited by downstream computation.

Key evidence

See sae-feature-lobes for the discovered functional-spatial correspondence, and Feature Lobes (Spatial-Functional Modularity) for the discovery-then-verify methodology and the required permutation control.