# Distilling Mathematical Reasoning Capabilities into Small Language Models

arXiv: https://arxiv.org/abs/2401.11864 · HTML: https://mlsanity.com/paper/2401.11864/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [PaD: Program-aided Distillation Can Teach Small Models Reasoning Better than Chain-of-thought Fine-tuning](https://mlsanity.com/paper/2305.13888/) (2023)

## Built on by (most cited first, 14 of 14)

- [Distilling LLM Agent into Small Models with Retrieval and Code Tools](https://mlsanity.com/paper/2505.17612/) (2025)
- [Towards Reasoning Ability of Small Language Models](https://mlsanity.com/paper/2502.11569/) (2025)
- [Learning to Focus: Causal Attention Distillation via Gradient-Guided Token Pruning](https://mlsanity.com/paper/2506.07851/) (2025)
- [Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Tasks](https://mlsanity.com/paper/2410.22296/) (2024)
- [Failure Modes in LLM Systems: A System-Level Taxonomy for Reliable AI Applications](https://mlsanity.com/paper/2511.19933/) (2025)
- [SIKeD: Self-guided Iterative Knowledge Distillation for mathematical reasoning](https://mlsanity.com/paper/2410.18574/) (2024)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [LUK: Empowering Log Understanding with Expert Knowledge from Large Language Models](https://mlsanity.com/paper/2409.01909/) (2024)
- [Small Language Models are Equation Reasoners](https://mlsanity.com/paper/2409.12393/) (2024)
- [Key-Point-Driven Mathematical Reasoning Distillation of Large Language Model](https://mlsanity.com/paper/2407.10167/) (2024)
- [UNDO: Understanding Distillation as Optimization](https://mlsanity.com/paper/2504.02521/) (2025)
- [Validity-Calibrated Reasoning Distillation](https://mlsanity.com/paper/2605.04078/) (2026)
- [MARBLE: A Multi-Agent Rule-Based LLM Reasoning Engine for Accident Severity Prediction](https://mlsanity.com/paper/2507.04893/) (2025)
- [ReAD: Reinforcement-Guided Capability Distillation for Large Language Models](https://mlsanity.com/paper/2605.11290/) (2026)

## Abstract (arXiv)

This work addresses the challenge of democratizing advanced Large Language Models (LLMs) by compressing their mathematical reasoning capabilities into sub-billion parameter Small Language Models (SLMs) without compromising performance. We introduce Equation-of-Thought Distillation (EoTD), a novel technique that encapsulates the reasoning process into equation-based representations to construct an EoTD dataset for fine-tuning SLMs. Additionally, we propose the Ensemble Thoughts Distillation (ETD) framework to enhance the reasoning performance of SLMs. This involves creating a reasoning dataset with multiple thought processes, including Chain-of-Thought (CoT), Program-of-Thought (PoT), and Equation-of-Thought (EoT), and using it for fine-tuning. Our experimental performance demonstrates that EoTD significantly boosts the reasoning abilities of SLMs, while ETD enables these models to achieve state-of-the-art reasoning performance.