LEMMA: Learning from Errors for MatheMatical Advancement in LLMs
Authors: name: Zhuoshi Pan, name: Yu Li, name: Honglin Lin, name: Qizhi Pei, name: Zinan Tang, name: Wei Wu, name: Chenlin Ming, name: H. Vicky Zhao, name: Conghui He, name: Lijun Wu

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 attempt 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 LLMs' reasoning ability by Learning
from Errors for Mathematical Advancement (LEMMA). LEMMA constructs data
consisting 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. Through a model-aware smooth reflection connection,
the erroneous solution is transferred to the correct one. 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 baselines.