Compositional Processing Emerges in Neural Networks Solving Math Problems

• URL: http://arxiv.org/abs/2105.08961v1
• Date: Wed, 19 May 2021 07:24:42 GMT
• Title: Compositional Processing Emerges in Neural Networks Solving Math Problems
• Authors: Jacob Russin, Roland Fernandez, Hamid Palangi, Eric Rosen, Nebojsa Jojic, Paul Smolensky, Jianfeng Gao
• Abstract summary: Recent progress in artificial neural networks has shown that when large models are trained on enough linguistic data, grammatical structure emerges in their representations. We extend this work to the domain of mathematical reasoning, where it is possible to formulate precise hypotheses about how meanings should be composed. Our work shows that neural networks are not only able to infer something about the structured relationships implicit in their training data, but can also deploy this knowledge to guide the composition of individual meanings into composite wholes.
• Score: 100.80518350845668
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations (e.g., auditory speech), and use this knowledge to guide the composition of simpler meanings into complex wholes. Recent progress in artificial neural networks has shown that when large models are trained on enough linguistic data, grammatical structure emerges in their representations. We extend this work to the domain of mathematical reasoning, where it is possible to formulate precise hypotheses about how meanings (e.g., the quantities corresponding to numerals) should be composed according to structured rules (e.g., order of operations). Our work shows that neural networks are not only able to infer something about the structured relationships implicit in their training data, but can also deploy this knowledge to guide the composition of individual meanings into composite wholes.

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