EREAL: Enhancing Mathematical Reasoning through Error-Aware Learning in Large Language Models

Official implementation of EREAL (Enhancing Reasoning through Error-Aware Learning), a novel framework that enables LLMs to learn from token-level mistakes for improved mathematical reasoning.

📖 Overview

EREAL addresses the limitations of existing error-correction methods by introducing:

• Minimal-edit Correction: Revises only erroneous segments while preserving valid reasoning steps
• Dynamic Error-Aware Loss: Adaptively weights tokens based on error proportion during training
• Fine-grained Supervision: Enables token-level learning from mistakes

🔬 Key Insight: Most model errors require only localized corrections, making coarse-grained rewriting inefficient and disruptive to valid reasoning.

🚀 Quick Start

Installation

cd EREAL
pip install -r requirements.txt

Training

To train a model using EREAL:

# Edit the paths in finetune.sh first
# - Set OUTPUT_DIR to your desired output directory
# - Set DATA_PATH to your training data
# - Set model_name_or_path to your base model path
bash ./script/finetune.sh

Evaluation

To evaluate your fine-tuned model:

# First merge the LoRA weights with the base model
# Edit the paths in evaluate.sh:
# - Set base-model to your base model path
# - Set lora-path to your checkpoint directory
# - Set save-path to where you want to save the merged model

# Then run the evaluation script
bash ./script/evaluate.sh

📊 Supported Models & Benchmarks

Tested Models

• LLaMA-3.1-8B-Instruct
• DeepSeek-Math-7B-Instruct
• Mistral-7B-Instruct-v0.3

Evaluation Benchmarks

Category	Dataset	Samples
In-Distribution	GSM8K	1,319
	MATH	5,000
Out-of-Distribution	ASDiv	2,215
	MAWPS	2,065
	SVAMP	1,000
	TabMWP	1,000
	CARP_EN	976

📚 Citation

If you find this code useful, please cite our paper:

@article{YU2027105197,
  title   = {EREAL: Enhancing Mathematical Reasoning through Error-Aware Learning in Large Language Models},
  journal = {Information Processing & Management},
  volume  = {64},
  number  = {2, Part B},
  pages   = {105197},
  year    = {2027},
  issn    = {0306-4573},
  doi     = {10.1016/j.ipm.2026.105197},
  url     = {https://www.sciencedirect.com/science/article/pii/S030645732600587X},
  author  = {Yuqing Yu and Zihao Li and Lixin Zou and Chenliang Li and Qian Wang}
}