Teaching Small Language Models to Learn Logic through Meta-Learning

• URL: http://arxiv.org/abs/2505.14313v2
• Date: Tue, 07 Oct 2025 12:44:37 GMT
• Title: Teaching Small Language Models to Learn Logic through Meta-Learning
• Authors: Leonardo Bertolazzi, Manuel Vargas Guzmán, Raffaella Bernardi, Maciej Malicki, Jakub Szymanik,
• Abstract summary: Small models (1.5B-7B) fine-tuned with meta-learning demonstrate strong gains in generalization.<n>These meta-learned models outperform GPT-4o and o3-mini on our syllogistic reasoning task.
• Score: 4.923078123348596
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• A Syllogistic Probe: Tracing the Evolution of Logic Reasoning in Large Language Models [17.118221176971982]
  We explore whether large language models (LLMs) exhibit a similar evolution in the underlying logical framework.<n>Using existential import as a probe, we evaluate syllogism under traditional and modern logic.
  arXiv  Detail & Related papers  (2026-01-24T11:51:52Z)
• Learning to Reason via Mixture-of-Thought for Logical Reasoning [56.24256916896427]
  Mixture-of-Thought (MoT) is a framework that enables LLMs to reason across three complementary modalities: natural language, code, and truth-table.<n>MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions.
  arXiv  Detail & Related papers  (2025-05-21T17:59:54Z)
• InductionBench: LLMs Fail in the Simplest Complexity Class [53.70978746199222]
  Large language models (LLMs) have shown remarkable improvements in reasoning.<n>Inductive reasoning, where one infers the underlying rules from observed data, remains less explored.<n>We introduce InductionBench, a new benchmark designed to evaluate the inductive reasoning ability of LLMs.
  arXiv  Detail & Related papers  (2025-02-20T03:48:00Z)
• The Inherent Limits of Pretrained LLMs: The Unexpected Convergence of Instruction Tuning and In-Context Learning Capabilities [51.594836904623534]
  We investigate whether instruction-tuned models possess fundamentally different capabilities from base models that are prompted using in-context examples.<n>We show that the performance of instruction-tuned models is significantly correlated with the in-context performance of their base counterparts.<n>Specifically, we extend this understanding to instruction-tuned models, suggesting that their pretraining data similarly sets a limiting boundary on the tasks they can solve.
  arXiv  Detail & Related papers  (2025-01-15T10:57:55Z)
• GIVE: Structured Reasoning of Large Language Models with Knowledge Graph Inspired Veracity Extrapolation [108.2008975785364]
  Graph Inspired Veracity Extrapolation (GIVE) is a novel reasoning method that merges parametric and non-parametric memories to improve accurate reasoning with minimal external input.<n>GIVE guides the LLM agent to select the most pertinent expert data (observe), engage in query-specific divergent thinking (reflect), and then synthesize this information to produce the final output (speak)
  arXiv  Detail & Related papers  (2024-10-11T03:05:06Z)
• Deconfounded Causality-aware Parameter-Efficient Fine-Tuning for Problem-Solving Improvement of LLMs [12.48241058167222]
  Large Language Models (LLMs) have demonstrated remarkable efficiency in tackling various tasks based on human instructions. But studies reveal that they often struggle with tasks requiring reasoning, such as math or physics limitation. This raises questions about whether LLMs truly comprehend embedded knowledge or merely learn to replicate the token distribution without a true understanding of the content. We propose Decon Causal Adaptation (DCA), a novel parameter-efficient fine-tuning (PEFT) method to enhance the model's reasoning capabilities.
  arXiv  Detail & Related papers  (2024-09-04T13:17:09Z)
• IDEA: Enhancing the Rule Learning Ability of Large Language Model Agent through Induction, Deduction, and Abduction [3.961279440272764]
  We introduce RULEARN to assess the rule-learning abilities of large language models in interactive settings.<n>We propose IDEA, a novel reasoning framework that integrates the process of Induction, Deduction, and Abduction.<n>Our evaluation of the IDEA framework, which involves five representative LLMs, demonstrates significant improvements over the baseline.
  arXiv  Detail & Related papers  (2024-08-19T23:37:07Z)
• LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models [52.03659714625452]
  Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied.
  arXiv  Detail & Related papers  (2024-04-23T21:08:49Z)
• From Understanding to Utilization: A Survey on Explainability for Large Language Models [27.295767173801426]
  This survey underscores the imperative for increased explainability in Large Language Models (LLMs) Our focus is primarily on pre-trained Transformer-based LLMs, which pose distinctive interpretability challenges due to their scale and complexity. When considering the utilization of explainability, we explore several compelling methods that concentrate on model editing, control generation, and model enhancement.
  arXiv  Detail & Related papers  (2024-01-23T16:09:53Z)
• LogicAsker: Evaluating and Improving the Logical Reasoning Ability of Large Language Models [63.14196038655506]
  We introduce LogicAsker, a novel approach for evaluating and enhancing the logical reasoning capabilities of large language models (LLMs) Our methodology reveals significant gaps in LLMs' learning of logical rules, with identified reasoning failures ranging from 29% to 90% across different models. We leverage these findings to construct targeted demonstration examples and fine-tune data, notably enhancing logical reasoning in models like GPT-4o by up to 5%.
  arXiv  Detail & Related papers  (2024-01-01T13:53:53Z)
• MR-GSM8K: A Meta-Reasoning Benchmark for Large Language Model Evaluation [60.65820977963331]
  We introduce a novel evaluation paradigm for Large Language Models (LLMs) This paradigm shifts the emphasis from result-oriented assessments, which often neglect the reasoning process, to a more comprehensive evaluation. By applying this paradigm in the GSM8K dataset, we have developed the MR-GSM8K benchmark.
  arXiv  Detail & Related papers  (2023-12-28T15:49:43Z)
• Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Models [56.34029644009297]
  Large language models (LLMs) have demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. LLMs excel most in abductive reasoning, followed by deductive reasoning, while they are least effective at inductive reasoning. We study single-task training, multi-task training, and "chain-of-thought" knowledge distillation fine-tuning technique to assess the performance of model.
  arXiv  Detail & Related papers  (2023-10-02T01:00:50Z)
• Improving Open Information Extraction with Large Language Models: A Study on Demonstration Uncertainty [52.72790059506241]
  Open Information Extraction (OIE) task aims at extracting structured facts from unstructured text. Despite the potential of large language models (LLMs) like ChatGPT as a general task solver, they lag behind state-of-the-art (supervised) methods in OIE tasks.
  arXiv  Detail & Related papers  (2023-09-07T01:35:24Z)
• Metacognitive Prompting Improves Understanding in Large Language Models [12.112914393948415]
  We introduce Metacognitive Prompting (MP), a strategy inspired by human introspective reasoning processes. We conduct experiments on four prevalent Large Language Models (LLMs) across ten natural language understanding (NLU) datasets. MP consistently outperforms existing prompting methods in both general and domain-specific NLU tasks.
  arXiv  Detail & Related papers  (2023-08-10T05:10:17Z)
• Knowledge-Augmented Reasoning Distillation for Small Language Models in Knowledge-Intensive Tasks [90.11273439036455]
  Large Language Models (LLMs) have shown promising performance in knowledge-intensive reasoning tasks. We propose Knowledge-Augmented Reasoning Distillation (KARD), a novel method that fine-tunes small LMs to generate rationales from LLMs with augmented knowledge retrieved from an external knowledge base. We empirically show that KARD significantly improves the performance of small T5 and GPT models on the challenging knowledge-intensive reasoning datasets.
  arXiv  Detail & Related papers  (2023-05-28T13:00:00Z)
• Large Language Models are In-Context Semantic Reasoners rather than Symbolic Reasoners [75.85554779782048]
  Large Language Models (LLMs) have excited the natural language and machine learning community over recent years. Despite of numerous successful applications, the underlying mechanism of such in-context capabilities still remains unclear. In this work, we hypothesize that the learned textitsemantics of language tokens do the most heavy lifting during the reasoning process.
  arXiv  Detail & Related papers  (2023-05-24T07:33:34Z)
• Exploring Self-supervised Logic-enhanced Training for Large Language Models [59.227222647741094]
  In this paper, we make the first attempt to investigate the feasibility of incorporating logical knowledge through self-supervised post-training. We devise an auto-regressive objective variant of MERIt and integrate it with two LLM series, i.e., FLAN-T5 and LLaMA, with parameter size ranging from 3 billion to 13 billion. The results on two challenging logical reasoning benchmarks demonstrate the effectiveness of LogicLLM.
  arXiv  Detail & Related papers  (2023-05-23T06:13:10Z)
• Information Extraction in Low-Resource Scenarios: Survey and Perspective [56.5556523013924]
  Information Extraction seeks to derive structured information from unstructured texts. This paper presents a review of neural approaches to low-resource IE from emphtraditional and emphLLM-based perspectives.
  arXiv  Detail & Related papers  (2022-02-16T13:44:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.