LEMMA: Learning from Errors for MatheMatical Advancement in LLMs

ACL ARR 2025 February Submission3405 Authors

Abstract:

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model's reflective ability. Though some studies attempted to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes.

In this work, we propose to enhance LLM's reasoning ability by Learning from Errors for MatheMatical Advancement (LEMMA). LEMMA constructs data consists of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an *error-type grounded mistake augmentation* method to collect diverse and representative errors.
Correct solutions are either from fixing the errors or generating a fresh start.
By fine-tuning on the constructed dataset, the model is able to *self-correct errors autonomously* within the generation process *without relying on external critique models*.
Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong models with less than $90k$ data.

Paper Type: Long

Research Area: NLP Applications

Research Area Keywords: mathematical NLP, data synthesis, reflection, self-correction

Contribution Types: NLP engineering experiment, Data resources, Data analysis

Languages Studied: English

Submission Number: 3405