Partial soft-matching distance: a representational similarity metric that admits ambiguity
Standard RSA collapses partial-correspondence into a single scalar. This proposal keeps the matching uncertainty visible — and surfaces structure that the scalar version was averaging away.
Representational Similarity Analysis is the field’s workhorse for comparing internal representations across models, layers, and brain regions. Its weakness is also its strength: it reduces a representation to a single distance matrix and asks how close two such matrices are. Soft, partial, many-to-many correspondences between units get crushed into the average.
This paper proposes a soft-matching distance that retains the matching itself as part of the metric. Two representations whose units partially overlap return a low distance and a high-rank matching tensor that says where the overlap is. The two come bundled; the practitioner sees both.
In a re-analysis of the Kornblith et al. CKA benchmark, the new metric agrees with CKA on the gross structure (transformers cluster together, ConvNets cluster together) but diverges sharply on the inter-architecture comparisons that have been the most contested. The authors argue, with cautious phrasing, that some prior “models are converging” claims may have been measurement artifacts of metric collapse. The disagreement is worth taking seriously precisely because the new metric was not designed to disagree.