SIKeD: Self-guided Iterative Knowledge Distillation for Mathematical Reasoning

Shivam Adarsh, Kumar Shridhar, Caglar Gulcehre, Nicholas Monath, Mrinmaya Sachan

Keywords: Reasoning, Knowledge Distillation, LLM, SLM

TL;DR: Our approach enables smaller models to learn and choose from multiple reasoning strategies by iteratively combining LLM data and self-generated outputs

Abstract:

Large Language Models (LLMs) can transfer their reasoning skills to smaller models by teaching them to generate the intermediate reasoning process required to solve multistep reasoning tasks. While LLMs can accurately solve reasoning tasks through a variety of strategies, even without fine-tuning, smaller models are not expressive enough to fit the LLMs distribution on all strategies when distilled and tend to prioritize one strategy over the others.
This reliance on one strategy poses a challenge for smaller models when attempting to solve reasoning tasks that may be difficult with their preferred strategy.
To address this, we propose a distillation method *SIKeD*: **S**elf-guided **I**terative **K**nowledge **D**istillation, where the LLM teaches the smaller model to approach a task using different strategies and the smaller model uses its self-generated on-policy outputs to choose the most suitable strategy for the given task. The training continues in a *self-guided* iterative manner, where for each training iteration, a decision is made on how to combine the LLM data with the self-generated outputs. Unlike traditional distillation methods, *SIKeD* allows the smaller model to learn *which* strategy is suitable for a given task while continuously learning to solve a task using different strategies.
Our experiments on various mathematical reasoning datasets show that *SIKeD* significantly outperforms traditional distillation techniques across smaller models of different sizes.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 4366