Cross-Model SAE Coactivation Survives Length, Topic, and Lexical Controls

Cross-model matches of sparse-autoencoder (SAE) features have been judged against random pairings or neuron baselines, neither of which re-runs the pairing rule. Gemma-2-9B and Mistral-7B, from different families with different tokenizers, each have a released-SAE obituary feature, and the two share their top five documents: is it the same feature? Our controls support a more specific answer: matched features of these two models respond to the same inputs beyond chance and pair selection, and that shared response survives the topic and vocabulary controls we ran; this is coactivation, not feature identity. Such matches are cheap: two sets of 1,500 features reciprocally match about half of each other under idealized chance, and any document property both models encode (length, topic, vocabulary) can make features coactivate. We run the pairing rule inside a document-permutation null, score frozen pairs on documents the rule never saw, and add controls that each fix one named nuisance. In a non-pre-registered follow-up, all nine cross-family cells (Gemma-2, Mistral, Qwen3, Llama-3) hold on disjoint C4 text (p = 1/2001 each, Bonferroni over the 17-cell roster). The sharing survives length- and coarse topic-matched nulls (one cell); on three representative cells, every control leaves at least 0.88 of the excess its reference arm leaves. Regressing out a unigram TF-IDF lexical model, which a pre-registered gate shows is not inert, leaves 92–94% of the excess: the shared-vocabulary explanation is narrowed, not closed. A registered token-aligned test shows the sharing is not reducible to document means (it beats a within-document word-order shuffle; mean pair correlation 0.522/0.398/0.335) and, in a leakage-clean design, keeps R_tok^clean = 0.92–0.99 of its token-level excess after conditioning on the document and the current word. The claim does not extend to compositional or syntactic sharing, a capability trend (swapping only one model’s SAE width moves its cell from z = 22.1 to 14.1), or shared computation (both cross-model ablation probes were inconclusive). The controls can say no: they rejected three decisive-looking secondary results, all reported (a cross-lingual metric that tracks network depth rather than language, its depth-corrected residual, and a 70M-to-7B match null on natural text). Cross-model matches should be scored against a null that re-runs the matching, on documents the matching never saw, one nuisance per control; code, nulls, receipts and registrations are in the anonymous supplement, to be released upon publication.