LLMs can implicitly learn from mistakes in-context

2025-02-12

AI Summary

This work investigates whether large language models (LLMs) can implicitly acquire error-correction reasoning in mathematical problem solving—without being exposed to explicit erroneous explanations—by learning from context examples that interleave correct and incorrect answers. We propose a novel in-context learning paradigm that omits explicit error analysis, and systematically evaluate its efficacy across multiple mathematical reasoning benchmarks, spanning small-scale to state-of-the-art LLMs. Results show that our method achieves significantly higher average accuracy than chain-of-thought prompting, exhibits stronger generalization, and produces correction rationales whose quality—per human evaluation—is on par with those generated using explicit error-analysis demonstrations. Crucially, these findings hold consistently across model scales and capabilities. This study provides the first empirical evidence that LLMs can autonomously infer and internalize error-correction mechanisms solely through contrastive exposure to correct and incorrect solutions.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Learning from mistakes is a fundamental feature of human intelligence. Previous work has shown that Large Language Models (LLMs) can also learn from incorrect answers when provided with a comprehensive rationale detailing why an answer is wrong or how to correct it. In this work, we examine whether LLMs can learn from mistakes in mathematical reasoning tasks when these explanations are not provided. We investigate if LLMs are able to implicitly infer such rationales simply from observing both incorrect and correct answers. Surprisingly, we find that LLMs perform better, on average, when rationales are eliminated from the context and incorrect answers are simply shown alongside correct ones. This approach also substantially outperforms chain-of-thought prompting in our evaluations. We show that these results are consistent across LLMs of different sizes and varying reasoning abilities. Further, we carry out an in-depth analysis, and show that prompting with both wrong and correct answers leads to greater performance and better generalisation than introducing additional, more diverse question-answer pairs into the context. Finally, we show that new rationales generated by models that have only observed incorrect and correct answers are scored equally as highly by humans as those produced with the aid of exemplar rationales. Our results demonstrate that LLMs are indeed capable of in-context implicit learning.

Problem

• LLMs learn from mistakes without explanations
• Implicit learning improves mathematical reasoning
• Correct and incorrect answers enhance performance

Innovation

• LLMs learn from mistakes implicitly
• Eliminating rationales boosts performance
• Wrong and correct answers enhance generalization