Measuring Systematic Generalization in Neural Proof Generation with Transformers

TL;DR

This paper investigates the systematic reasoning abilities of Transformer language models in natural language logical proofs, revealing strengths in backward-chaining and challenges with longer sequences, highlighting their internal reasoning strategies.

Contribution

It provides new insights into how TLMs generalize in logical reasoning tasks, especially comparing forward and backward chaining, and shows how training on longer proofs improves performance.

Findings

TLMs improve generalization after exposure to longer proofs

Backward-chaining proofs lead to better generalization than forward-chaining

Models not trained to generate proofs generalize better to longer problems

Abstract

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a logical reasoning task in natural language, which involves reasoning over relationships between entities grounded in first-order logical proofs. Specifically, we perform soft theorem-proving by leveraging TLMs to generate natural language proofs. We test the generated proofs for logical consistency, along with the accuracy of the final inference. We observe length-generalization issues when evaluated on longer-than-trained sequences. However, we observe TLMs improve their generalization performance after being exposed to longer, exhaustive proofs. In addition, we discover that TLMs are able to generalize better using backward-chaining proofs compared to their forward-chaining counterparts, while they find it easier to generate forward chaining proofs. We observe that models that are not trained to generate proofs are better at generalizing to problems based on longer proofs. This suggests that Transformers have efficient internal reasoning strategies that are harder to interpret. These results highlight the systematic generalization behavior of TLMs in the context of logical reasoning, and we believe this work motivates deeper inspection of their underlying reasoning strategies.