# Structural Generalization on SLOG without Hand-Written Rules

arXiv: https://arxiv.org/abs/2604.26157 · HTML: https://mlsanity.com/paper/2604.26157/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [Structural generalization is hard for sequence-to-sequence models](https://mlsanity.com/paper/2210.13050/) (2022)
- [ReCOGS: How Incidental Details of a Logical Form Overshadow an Evaluation of Semantic Interpretation](https://mlsanity.com/paper/2303.13716/) (2023)
- [SLOG: A Structural Generalization Benchmark for Semantic Parsing](https://mlsanity.com/paper/2310.15040/) (2023)
- [AMR Dependency Parsing with a Typed Semantic Algebra](https://mlsanity.com/paper/1805.11465/) (2018)
- [Compositional Semantic Parsing Across Graphbanks](https://mlsanity.com/paper/1906.11746/) (2019)
- [Structural generalization in COGS: Supertagging is (almost) all you need](https://mlsanity.com/paper/2310.14124/) (2023)
- [On the Spatiotemporal Dynamics of Generalization in Neural Networks](https://mlsanity.com/paper/2602.01651/) (2026)
- [On the Emergence of Syntax by Means of Local Interaction](https://mlsanity.com/paper/2604.17857/) (2026)

## Abstract (arXiv)

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 ± 0.2% across 10 seeds (AM-Parser: 70.8 ± 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.