SuperCorrect: Supervising and Correcting Language Models with
  Error-Driven Insights
Authors: name: Ling Yang, name: Zhaochen Yu, name: Tianjun Zhang, name: Minkai Xu, name: Joseph E. Gonzalez, name: Bin Cui, name: Shuicheng Yan

Large language models (LLMs) like GPT-4, PaLM, and LLaMA have shown
significant improvements in various reasoning tasks. However, smaller models
such as Llama-3-8B and DeepSeekMath-Base still struggle with complex
mathematical reasoning because they fail to effectively identify and correct
reasoning errors. Recent reflection-based methods aim to address these issues
by enabling self-reflection and self-correction, but they still face challenges
in independently detecting errors in their reasoning steps. To overcome these
limitations, we propose SuperCorrect, a novel two-stage framework that uses a
large teacher model to supervise and correct both the reasoning and reflection
processes of a smaller student model. In the first stage, we extract
hierarchical high-level and detailed thought templates from the teacher model
to guide the student model in eliciting more fine-grained reasoning thoughts.
In the second stage, we introduce cross-model collaborative direct preference
optimization (DPO) to enhance the self-correction abilities of the student
model by following the teacher's correction traces during training. This
cross-model DPO approach teaches the student model to effectively locate and
resolve erroneous thoughts with error-driven insights from the teacher model,
breaking the bottleneck of its thoughts and acquiring new skills and knowledge
to tackle challenging problems. Extensive experiments consistently demonstrate
our superiority over previous methods. Notably, our SuperCorrect-7B model
significantly surpasses powerful DeepSeekMath-7B by 7.8%/5.3% and
Qwen2.5-Math-7B by 15.1%/6.3% on MATH/GSM8K benchmarks, achieving new SOTA
performance among all 7B models. Code:
https://github.com/YangLing0818/SuperCorrect-llm