Assembly Theory and the Smallest Grammar Problem

What the math gives to ML

The paper identifies the assembly index exactly with the minimum number of productions in a straight-line grammar, turning repeated-substring structure into an explicit optimization target rather than an informal compression heuristic. This suggests a neural sequence representation based on a corpus-level or document-level acyclic grammar whose nonterminals are reusable learned spans. The most practical transfer is grammar-aware tokenization or context compression: process each repeated span once, retain a compact expansion DAG, and reconstruct token-level outputs only where needed. The key falsifiable benefit is reduced effective sequence length and quadratic attention cost on highly repetitive inputs, while the grammar size provides a direct diagnostic of compression quality.