LEMMA: Learning from Errors for MatheMatical Advancement in LLMs
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913867263639552 |
|---|---|
| author | Pan, Zhuoshi Li, Yu Lin, Honglin Pei, Qizhi Tang, Zinan Wu, Wei Ming, Chenlin Zhao, H. Vicky He, Conghui Wu, Lijun |
| author_facet | Pan, Zhuoshi Li, Yu Lin, Honglin Pei, Qizhi Tang, Zinan Wu, Wei Ming, Chenlin Zhao, H. Vicky He, Conghui Wu, Lijun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LEMMA: Learning from Errors for MatheMatical Advancement in LLMs Pan, Zhuoshi Li, Yu Lin, Honglin Pei, Qizhi Tang, Zinan Wu, Wei Ming, Chenlin Zhao, H. Vicky He, Conghui Wu, Lijun Machine Learning Artificial Intelligence 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. |
| title | LEMMA: Learning from Errors for MatheMatical Advancement in LLMs |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2503.17439 |