As large language models (LLMs) have demonstrated impressive multiple step-by-step reasoning capabilities in recent natural language processing (NLP) reasoning tasks, many studies are interested in distilling reasoning abilities into smaller language models (SLMs) via fine-tuning. Previous distillation methods usually utilize the capabilities of LLMs to generate chain-of-thought (CoT) samples to teach SLMs. However, this distillation approach performs poorly in certain scenarios due to the limitations of CoT. In this work, we introduce a novel Mixed Distillation (MD) framework, distilling multiple step-by-step reasoning abilities into SLMs. First, we leverage LLMs to generate multiple step-by-step reasoning rationales by sampling automatically. Then, we create high-quality, well-balanced mixed thought data and design a novel multi-task loss to help SLMs better learn and adaptively activate multiple step-by-step reasoning. Our extensive experiments demonstrate that MD enhances both single-path (using either CoT or PoT) and multi-path (using both CoT and PoT) reasoning abilities of SLMs during inference across reasoning tasks. Notably, a single model generated by MD exceeds the comprehensive performance of an ensemble of two individual CoT and PoT distilled models. Mistral-7B using MD can achieve remarkable improvements of 87.5%, 74.0% and 77.1% on SVAMP, GSM8K and ASDIV, respectively, outperforming the teacher model, GPT-3.5-Turbo. We hope our work provides insight into SLMs’ multiple step-by-step reasoning abilities.

Instruction tuning is a crucial technique for aligning language models with humans’ actual goals in the real world. Extensive research has highlighted the quality of instruction data is essential for the success of this alignment. However, creating high-quality data manually is labor-intensive and time-consuming, which leads researchers to explore using LLMs to synthesize data. Recent studies have focused on using a stronger LLM to iteratively enhance existing instruction data, showing promising results. Nevertheless, previous work often lacks control over the evolution direction, resulting in high uncertainty in the data synthesis process and low-quality instructions. In this paper, we introduce a general and scalable framework, IDEA-MCTS (Instruction Data Enhancement using Monte Carlo Tree Search), a scalable framework for efficiently synthesizing instructions. With tree search and evaluation models, it can efficiently guide each instruction to evolve into a high-quality form, aiding in instruction fine-tuning. Experimental results show that IDEA-MCTS significantly enhances the seed instruction data, raising the average evaluation scores of quality, diversity, and complexity from 2.19 to 3.81. Furthermore, in open-domain benchmarks, experimental results show that IDEA-MCTS improves the accuracy of real-world instruction-following skills in LLMs by an average of 5% in low-resource settings.