arXiv:2604.26157v1 Announce Type: cross Abstract: Structural generalization in semantic parsing requires systems to apply learned compositional rules to novel structural combinations. Existing approaches either rely on hand-written algebraic rules (AM-Parser) or fail to generalize structurally (Transformer-based models). We present an alternative requiring no hand-written compositional rules, based on a neural cellular automaton (NCA) with a discrete bottleneck: all compositional rules are learned from data through local iteration. On the SLOG benchmark, the system achieves 100% type-exact match on 11 of 17 structural generalization categories, including three where AM-Parser scores 0 to 74%, with an overall standard deviation of 0.2 across 10 seeds (vs. AM-Parser's 4.3). Analysis reveals that all 5,539 failure instances reduce to exactly two mechanisms: novel combinations of wh-extraction context with reduced verb types, and modifiers appearing on the subject side of verbs.When we decompose results by CCG structural features, each sub-pattern either succeeds on all instances or fails on all. Intermediate scores (e.g., 41.4%) are mixtures of structurally distinct CCG patterns, not partial generalization.All failures correspond to directed operations absent from training; all successes correspond to operations already covered.