# Mixed Distillation Helps Smaller Language Model Better Reasoning

arXiv: https://arxiv.org/abs/2312.10730 · HTML: https://mlsanity.com/paper/2312.10730/

## Key facts

- Cited by 19 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 38 of its 60 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## 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, 30 of 38)

- [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)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Want To Reduce Labeling Cost? GPT-3 Can Help](https://mlsanity.com/paper/2108.13487/) (2021)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Ask Me Anything: A simple strategy for prompting language models](https://mlsanity.com/paper/2210.02441/) (2022)
- [Distilling Task-Specific Knowledge from BERT into Simple Neural Networks](https://mlsanity.com/paper/1903.12136/) (2019)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)

## Built on by (most cited first, 19 of 19)

- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [MAGDi: Structured Distillation of Multi-Agent Interaction Graphs Improves Reasoning in Smaller Language Models](https://mlsanity.com/paper/2402.01620/) (2024)
- [A Survey of Token Compression for Efficient Multimodal Large Language Models](https://mlsanity.com/paper/2507.20198/) (2025)
- [Symbiotic Cooperation for Web Agents: Harnessing Complementary Strengths of Large and Small LLMs](https://mlsanity.com/paper/2502.07942/) (2025)
- [VeriThinker: Learning to Verify Makes Reasoning Model Efficient](https://mlsanity.com/paper/2505.17941/) (2025)
- [Learning from Committee: Reasoning Distillation from a Mixture of Teachers with Peer-Review](https://mlsanity.com/paper/2410.03663/) (2024)
- [GLaD: Geometric Latent Distillation for Vision-Language-Action Models](https://mlsanity.com/paper/2512.09619/) (2025)
- [PatentGPT: A Large Language Model for Intellectual Property](https://mlsanity.com/paper/2404.18255/) (2024)
- [Legal Mathematical Reasoning with LLMs: Procedural Alignment through Two-Stage Reinforcement Learning](https://mlsanity.com/paper/2504.02590/) (2025)
- [Enhancing Reasoning Abilities of Small LLMs with Cognitive Alignment](https://mlsanity.com/paper/2504.09802/) (2025)
- [SIKeD: Self-guided Iterative Knowledge Distillation for mathematical reasoning](https://mlsanity.com/paper/2410.18574/) (2024)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [Efficient Turing Machine Simulation with Transformers](https://mlsanity.com/paper/2512.00003/) (2025)
- [Knowledge Distillation with Structured Chain-of-Thought for Text-to-SQL](https://mlsanity.com/paper/2512.17053/) (2025)
- [BRIDGE: Bridging Reasoning In Distillation Gap Elimination via Structure-Aware Masking](https://mlsanity.com/paper/2602.17686/) (2026)
- [Generative Spatiotemporal Intent Sequence Recommendation via Implicit Reasoning in Amap](https://mlsanity.com/paper/2605.28888/) (2026)
- [Don't Wait to Reply: Towards Responsive yet Thoughtful Dialogue through Proactive Thinking](https://mlsanity.com/paper/2607.03093/) (2026)

## Abstract (arXiv)

While large language models (LLMs) have demonstrated exceptional performance in recent natural language processing (NLP) tasks, their deployment poses substantial challenges due to high computational and memory demands in real-world applications. Recent studies have focused on enhancing smaller models through knowledge distillation from LLMs, yielding promising results. However, these models often struggle to match the performance of LLMs, especially in tasks that require reasoning. In this work, we introduce Mixed Distillation (MD) framework, which capitalizes on the strengths of Program of Thought (PoT) and Chain of Thought (CoT) capabilities within LLMs, combining multiple prompting techniques and distilling these capabilities into smaller models. Our experimental results show that MD significantly enhances the single-path and multi-path reasoning ability of smaller models in various tasks. In terms of accuracy and generality of reasoning tasks, the model generated by it exceeds the comprehensive performance of two individually distilled models. Notably, LLaMA2-7B and CodeLlama-7B using MD achieved remarkable improvements of (84.5%) and (85.5%), respectively, outperforming GPT-3.5-Turbo by (2.5%) and (3.5%), on the SVAMP benchmark.