$\textit{SKIntern}$: Internalizing Symbolic Knowledge for Distilling Better CoT Capabilities into Small Language Models

TL;DR

SKIntern is a novel method that internalizes symbolic knowledge into small language models through progressive fine-tuning, enhancing reasoning capabilities, reducing inference costs, and outperforming existing methods across various tasks.

Contribution

It introduces a curriculum learning-based progressive fine-tuning approach for small language models to internalize symbolic knowledge efficiently.

Findings

Outperforms state-of-the-art baselines by over 5%

Reduces inference FLOPs by up to 4x

Improves reasoning and out-of-domain generalization

Abstract

Small Language Models (SLMs) are attracting attention due to the high computational demands and privacy concerns of Large Language Models (LLMs). Some studies fine-tune SLMs using Chains of Thought (CoT) data distilled from LLMs, aiming to enhance their reasoning ability. Furthermore, Some CoT distillation methods introduce external symbolic knowledge into the generation process to improve the limited knowledge memory, reasoning ability and out-of-domain (OOD) generalization of SLMs. However, the introduction of symbolic knowledge increases computational overhead and introduces potential noise. In this paper, we introduce $\textit{SKIntern}$, an innovative approach that empowers SLMs to internalize symbolic knowledge and few-shot examples gradually through a progressive fine-tuning process, guided by a predefined linear decay schedule under curriculum learning. By efficiently internalizing knowledge, $\textit{SKIntern}$ reduces computational overhead and speeds up the reasoning process by focusing solely on the question during inference. It outperforms state-of-the-art baselines by over 5\%, while reducing inference costs (measured in FLOPs) by up to $4\times$ across a wide range of SLMs in both in-domain (ID) and out-of-domain (OOD) tasks. Our code will be available at \url{https://github.com/Xnhyacinth/SKIntern}.