Structural Generalization on SLOG without Hand-Written Rules

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 an overall accuracy of 67.3 \pm 0.2% across 10 seeds (AM-Parser: 70.8 \pm 4.3%), with 11 of 17 structural generalization categories at 100% type-exact match, including three where AM-Parser scores 0--74%. 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. These results suggest that CCG directed types provide higher resolution than SLOG's phenomenon-level categories for characterizing structural generalization, and that the success/failure boundary is determined by the coverage of directed operations in the training data.