MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning
This work addresses the problem of inefficient reliance on large language models for mathematical reasoning in small models, offering an incremental improvement with a novel training paradigm.
The paper tackles the challenge of mathematical reasoning for small language models by introducing a multi-view fine-tuning method that uses diverse annotation formats as different views, enabling a LLaMA-7B model to outperform prior knowledge distillation approaches and baselines while improving generalization across datasets and noisy data.
Reasoning in mathematical domains remains a significant challenge for relatively small language models (LMs). Many current methods focus on specializing LMs in mathematical reasoning and rely heavily on knowledge distillation from powerful but inefficient large LMs (LLMs). In this work, we explore a new direction that avoids over-reliance on LLM teachers, introducing a multi-view fine-tuning method that efficiently exploits existing mathematical problem datasets with diverse annotation styles. Our approach uniquely considers the various annotation formats as different "views" and leverages them in training the model. By postpending distinct instructions to input questions, models can learn to generate solutions in diverse formats in a flexible manner. Experimental results show that our strategy enables a LLaMA-7B model to outperform prior approaches that utilize knowledge distillation, as well as carefully established baselines. Additionally, the proposed method grants the models promising generalization ability across various views and datasets, and the capability to learn from inaccurate or incomplete noisy data. We hope our multi-view training paradigm could inspire future studies in other machine reasoning domains.