Compositionality is not compression

An influential account of learning treats it as the discovery of a short description: a good model compresses the data by exposing regularity, and model selection balances the length of the model against the length of what remains unexplained.¹1. This viewpoint includes minimum description length [ Rissanen , 1978 , Grünwald , 2007 ] and its foundations in algorithmic information theory [ Li and Vitányi , 2019 ] . ↩ lincs neither rejects this account nor takes it as the definition of learning. Description length is a scalar quantity relative to a coding language. A compositionality obstruction is a typed failure relative to a structural declaration. They answer different questions.

A compact model can encode a systematic violation of an essential composition, while a structurally faithful model may require extra description to preserve sources, qualifiers, uncertainty, or compatibility across contexts. Conversely, reusable compositional structure often makes compression possible. The relationship is therefore productive but not an equivalence. Compression may rank admissible models or repairs, regularize a search, or become one coordinate of an observation profile; it cannot by itself say which structural promise was broken or whether a shorter repair is semantically licensed.

A sharper limitation appears when discovery requires changing the language in which descriptions are compared. Zahavy’s position paper LLMs Can’t Jump uses Einstein’s path to general relativity to argue that compression of observations and deduction from established axioms do not by themselves explain the abductive step that proposes new axioms [ Zahavy , 2026 ] . Whatever one concludes about the paper’s stronger claim concerning present LLMs, it identifies an important boundary: selecting a concise model inside a fixed representational frame is different from inventing and validating a new frame.

lincs makes that boundary expressible. Repair may change a realization inside a declared sketch, or it may propose a conservative change to the declaration itself. The latter can add objects, paths, probes, quotients, or axioms and then ask whether old evidence transports and newly required compositions hold. This does not prove that lincs can generate a creative jump. It supplies a typed language in which such a jump can be proposed, compared with the old frame, and admitted or rejected without confusing novelty with compression.