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Compositional generalization is a key ability of humans that enables us tolearn new concepts from only a handful examples. Neural machine learningmodels, including the now ubiquitous Transformers, struggle to generalize inthis way, and typically require thousands of examples of a concept duringtraining in order to generalize meaningfully. This difference in abilitybetween humans and artificial neural architectures, motivates this study on aneuro-symbolic architecture called the Compositional Program Generator (CPG).CPG has three key features: \textit{modularity}, \textit{composition}, and\textit{abstraction}, in the form of grammar rules, that enable it togeneralize both systematically to new concepts in a few-shot manner, as well asproductively by length on various sequence-to-sequence language tasks. For eachinput, CPG uses a grammar of the input language and a parser to generate aparse in which each grammar rule is assigned its own unique semantic module, aprobabilistic copy or substitution program. Instances with the same parse arealways processed with the same composed modules, while those with differentparses may be processed with different modules. CPG learns parameters for themodules and is able to learn the semantics for new rules and typesincrementally, without forgetting or retraining on rules it's already seen. Itachieves perfect generalization on both the SCAN and COGS benchmarks using just14 examples for SCAN and 22 examples for COGS -- state-of-the-art accuracy witha 1000x improvement in sample efficiency.

Compositional Program Generation for Few-Shot Systematic Generalization