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A longstanding question in cognitive science concerns the learning mechanismsunderlying compositionality in human cognition. Humans can infer the structuredrelationships (e.g., grammatical rules) implicit in their sensory observations(e.g., auditory speech), and use this knowledge to guide the composition ofsimpler meanings into complex wholes. Recent progress in artificial neuralnetworks has shown that when large models are trained on enough linguisticdata, grammatical structure emerges in their representations. We extend thiswork to the domain of mathematical reasoning, where it is possible to formulateprecise hypotheses about how meanings (e.g., the quantities corresponding tonumerals) should be composed according to structured rules (e.g., order ofoperations). Our work shows that neural networks are not only able to infersomething about the structured relationships implicit in their training data,but can also deploy this knowledge to guide the composition of individualmeanings into composite wholes.

Compositional Processing Emerges in Neural Networks Solving Math Problems