Compositional Processing Emerges in Neural Networks Solving Math Problems

TL;DR

This paper demonstrates that neural networks trained on math problems can learn and apply compositional rules, similar to human cognition, to infer structured relationships and compose meanings into complex solutions.

Contribution

It extends understanding of compositionality in neural networks from language to mathematical reasoning, showing networks can infer and utilize structured relationships.

Findings

Neural networks infer structured relationships in math data.

Networks can compose meanings based on learned rules.

Results suggest emergent compositional processing in neural models.

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.