# textitSKIntern: Internalizing Symbolic Knowledge for Distilling Better CoT Capabilities into Small Language Models

arXiv: https://arxiv.org/abs/2409.13183 · HTML: https://mlsanity.com/paper/2409.13183/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2024.

## Built on by (most cited first, 3 of 3)

- [Reasoning Scaffolding: Distilling the Flow of Thought from LLMs](https://mlsanity.com/paper/2509.23619/) (2025)
- [The Thinking Spectrum: An Empirical Study of Tunable Reasoning in LLMs through Model Merging](https://mlsanity.com/paper/2509.22034/) (2025)
- [ReaLM: Reflection-Enhanced Autonomous Reasoning with Small Language Models](https://mlsanity.com/paper/2508.12387/) (2025)

## Abstract (arXiv)

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 textitSKIntern, 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, textitSKIntern 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× across a wide range of SLMs in both in-domain (ID) and out-of-domain (OOD) tasks. Our code will be available at urlhttps://github.com/Xnhyacinth/SKIntern.