README.md

---
license: llama3
library_name: transformers
pipeline_tag: text-generation
---

# Model Card for Model ID

**Key Takeaways**

💡 **Systematic analysis on error types**: Categorizes common model-generated mathematical reasoning errors, revealing consistent error patterns across models and guiding targeted improvements.

💡 **Error-type grounded error augmentation**: Introduces diverse and meaningful errors by leveraging a teacher model to _intentionally inject representative mistakes_ with type sampled from the analyzed distribution, enhancing the model’s ability to learn from failures.

💡 **Two complementary self-correction mechanisms**: Combines _Fix & Continue_ (correcting mistakes within the original reasoning) and _Fresh & Restart_ (restarting the reasoning process from scratch) to generate effective revision trajectories.

✅ **LEMMA** – A novel framework that fine-tunes LLMs on error-corrective trajectories, enabling autonomous error detection and correction during mathematical reasoning.

📊 **Result** – Up to 13.3% accuracy improvement for LLaMA3-8B with only 90k synthesized data.

<!-- Provide a quick summary of what the model is/does. -->

The LEMMA series models are trained on the [LEMMA Dataset](https://huggingface.co/datasets/panzs19/LEMMA). This dataset uses the training set of MATH and GSM8K to generate error-corrective reasoning trajectories. For each question in these datasets, the student model (LLaMA3-8B) generates self-generated errors, and the teacher model (GPT-4o) deliberately introduces errors based on the error type distribution of the student model. Then, both "Fix & Continue" and "Fresh & Restart" correction strategies are applied to these errors to create error-corrective revision trajectories. After filtering out trajectories with incorrect final answers, we obtain this dataset. Fine-tuning on this dataset achieves up to 13.3% average accuracy improvement for LLaMA3-8B with less than 90k synthesized data. For more details, please refer to our paper [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://arxiv.org/abs/2503.17439).

## Model Details

### Model Description

- **Finetuned from model [optional]:** [Llama-3-70B](https://huggingface.co/meta-llama/Meta-Llama-3-70B)

### Model Sources [optional]

- **Repository:** [https://github.com/pzs19/LEMMA/](https://github.com/pzs19/LEMMA/)
- **Paper:** [https://arxiv.org/abs/2503.17439](https://arxiv.org/abs/2503.17439)

### Direct Use

The same as Llama-3-70B.

### Recommendations

Users (both direct and downstream) should be made aware of the risks, biases and limitations of the model.

## Training Details

The LEMMA series models are trained on the [LEMMA Dataset](https://huggingface.co/datasets/panzs19/LEMMA) using [LLaMA-Factory](https://github.com/hiyouga/LLaMA-Factory). For more details, please refer to our [paper](https://arxiv.org/abs/2503.17439).

### Results

| Model | Checkpoint | Paper  | GSM8k | MATH  | License |
| ----- |------| ---- |------|-------| ----- |
| LEMMA-LLAMA-3-8B | 🤗 <a href="https://huggingface.co/panzs19/LEMMA-LLAMA-3-8B" target="_blank">HF Link</a> |  📃 <a href="" target="_blank">[LEMMA]</a>| **79.2**  |  **38.3**	| <a href="https://www.llama.com/llama3/license/" target="_blank">Llama 3  </a> |
| LEMMA-LLAMA-3-70B | 🤗 <a href="https://huggingface.co/panzs19/LEMMA-LLAMA-3-70B" target="_blank">HF Link</a> |  📃 <a href="" target="_blank">[LEMMA]</a>| **91.5**  |  **51.8** | <a href="https://www.llama.com/llama3/license/" target="_blank">Llama 3 </a> |

## Citation [optional]

Please cite the paper if you refer to our model, code, data or paper from MetaMath.

```
@article{LEMMA,
  title={LEMMA: Learning from Errors for MatheMatical Advancement in LLMs},
  author={Zhuoshi Pan, Yu Li, Honglin Lin, Qizhi Pei, Zinan Tang, Wei Wu, Chenlin Ming, H. Vicky Zhao, Conghui He, Lijun Wu},
  journal={arXiv preprint arXiv:2503.17439},
  year={2025}
}
```