Relational reasoning and generalization using non-symbolic neural networks

TL;DR

This paper demonstrates that neural networks can learn and generalize various forms of equality and relational reasoning, challenging the idea that symbolic reasoning is exclusive to humans.

Contribution

It shows neural networks can perform out-of-sample generalization of equality, including complex hierarchical cases, using only positive training data.

Findings

Neural networks can learn basic equality from data.

They generalize to sequential equality problems with only positive examples.

They achieve zero-shot generalization on hierarchical equality tasks.

Abstract

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We find neural networks are able to learn (1) basic equality (mathematical identity), (2) sequential equality problems (learning ABA-patterned sequences) with only positive training instances, and (3) a complex, hierarchical equality problem with only basic equality training instances ("zero-shot'" generalization). In the two latter cases, our models perform tasks proposed in previous work to demarcate human-unique symbolic abilities. These results suggest that essential aspects of symbolic reasoning can emerge from data-driven, non-symbolic learning processes.