# Improving Mathematical Reasoning Capabilities of Small Language Models via Feedback-Driven Distillation

arXiv: https://arxiv.org/abs/2411.14698 · HTML: https://mlsanity.com/paper/2411.14698/

## Key facts

- Cited by 1 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 8 of its 25 references that are in the map.
- First posted on arXiv 22 Nov 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, 8 of 8)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (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)
- [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)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (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, 1 of 1)

- [VeriThinker: Learning to Verify Makes Reasoning Model Efficient](https://mlsanity.com/paper/2505.17941/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) demonstrate exceptional reasoning capabilities, often achieving state-of-the-art performance in various tasks. However, their substantial computational and memory demands, due to billions of parameters, hinder deployment in resource-constrained environments. A promising solution is knowledge distillation, where LLMs transfer reasoning capabilities to Small Language Models (SLMs, ≤ 1B parameters), enabling wider deployment on low-resource devices. Existing methods primarily focus on generating high-quality reasoning rationales for distillation datasets but often neglect the critical role of data quantity and quality. To address these challenges, we propose a Feedback-Driven Distillation (FDD) framework to enhance SLMs' mathematical reasoning capabilities. In the initialization stage, a distillation dataset is constructed by prompting LLMs to pair mathematical problems with corresponding reasoning rationales. We classify problems into easy and hard categories based on SLM performance. For easy problems, LLMs generate more complex variations, while for hard problems, new questions of similar complexity are synthesized. In addition, we propose a multi-round distillation paradigm to iteratively enrich the distillation datasets, thereby progressively improving the mathematical reasoning abilities of SLMs. Experimental results demonstrate that our method can make SLMs achieve SOTA mathematical reasoning performance.