irreducibility-requires-both-tests
IN premise — summaries/2026/08/24/engels-2024-not-all-features-linear-sR-references-chunk-1.md
Created 2026-08-25T02:58:02+00:00
A feature is classified as irreducible only if both S(f) is high (high mutual information across projections) and M_ε(f) is low (low geometric concentration in a strip); either condition alone is insufficient.
Summary
A feature counts as truly irreducible only when it passes two independent checks at the same time: it must carry substantial information across many different views of the data, and it must not be crammed into a thin geometric slice of the space. Requiring both prevents a shortcut where a feature that is merely information-heavy but narrowly concentrated, or broadly spread but essentially empty of signal, gets mislabeled as irreducible.