bibkey: “dorrell2026optimality” authors: “William Dorrell” year: 2026 title: “How Optimality Structures Sparse Dictionaries: A Theory for Understanding SAE Representations” doi: null claim: “A necessary local-optimality condition for l1 plus nonnegativity sparse dictionaries with decoder normalization and bias relates decoder cosines to observed latent values; strictly hierarchical activation patterns violate it except when perfectly aligned.” strata_touched: [] license: “citation-only” triage: “anchor” url: “https://arxiv.org/abs/2606.02385”

How Optimality Structures Sparse Dictionaries: A Theory for Understanding SAE Representations

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arXiv:2606.02385. Cited as the closest general optimality theory; the fiber-law volume does not use its condition in any proof.

Declared identifiers: https://arxiv.org/abs/2606.02385.