# Teaching Small Language Models to Learn Logic through Meta-Learning

arXiv: https://arxiv.org/abs/2505.14313 · HTML: https://mlsanity.com/paper/2505.14313/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 20 May 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Making Retrieval-Augmented Language Models Robust to Irrelevant Context](https://mlsanity.com/paper/2310.01558/) (2023)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [Leak, Cheat, Repeat: Data Contamination and Evaluation Malpractices in Closed-Source LLMs](https://mlsanity.com/paper/2402.03927/) (2024)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Meta-learning via Language Model In-context Tuning](https://mlsanity.com/paper/2110.07814/) (2021)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Testing the General Deductive Reasoning Capacity of Large Language Models Using OOD Examples](https://mlsanity.com/paper/2305.15269/) (2023)
- [A Closer Look at the Self-Verification Abilities of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2311.07954/) (2023)

## Built on by (most cited first, 1 of 1)

- [Hybrid Models for Natural Language Reasoning: The Case of Syllogistic Logic](https://mlsanity.com/paper/2510.09472/) (2025)

## Abstract (arXiv)

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.