Teaching Small Language Models to Learn Logic through Meta-Learning

TL;DR

This paper explores using meta-learning to improve small language models' ability to learn and generalize logical reasoning, specifically syllogistic reasoning, outperforming larger models in low-data scenarios.

Contribution

It introduces a novel application of meta-learning to logic learning in small language models, enhancing their reasoning generalization capabilities.

Findings

Meta-learning improves logical reasoning in small models.

Meta-trained models outperform GPT-4o and o3-mini on syllogistic tasks.

Significant benefits observed in low-data regimes.

Abstract

Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the problem as premise selection and construct controlled datasets to isolate logical competence. Beyond evaluation, an open challenge is enabling LLMs to acquire abstract inference patterns that generalize to novel structures. We propose to apply few-shot meta-learning to this domain, thereby encouraging models to extract rules across tasks rather than memorize patterns within tasks. Although meta-learning has been little explored in the context of logic learnability, our experiments show that it is effective: small models (1.5B-7B) fine-tuned with meta-learning demonstrate strong gains in generalization, with especially pronounced benefits in low-data regimes. These meta-learned models outperform GPT-4o and o3-mini on our syllogistic reasoning task.