# Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step

arXiv: https://arxiv.org/abs/2306.14050 · HTML: https://mlsanity.com/paper/2306.14050/

## Key facts

- Cited by 148 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 42 of its 59 references that are in the map.
- First posted on arXiv 24 Jun 2023.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 42)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)
- [Explain Yourself! Leveraging Language Models for Commonsense Reasoning](https://mlsanity.com/paper/1906.02361/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Symbolic Knowledge Distillation: from General Language Models to Commonsense Models](https://mlsanity.com/paper/2110.07178/) (2021)
- [WANLI: Worker and AI Collaboration for Natural Language Inference Dataset Creation](https://mlsanity.com/paper/2201.05955/) (2022)
- [Generating Training Data with Language Models: Towards Zero-Shot Language Understanding](https://mlsanity.com/paper/2202.04538/) (2022)
- [Generating Datasets with Pretrained Language Models](https://mlsanity.com/paper/2104.07540/) (2021)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)

## Built on by (most cited first, 30 of 148)

- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Personal LLM Agents: Insights and Survey about the Capability, Efficiency and Security](https://mlsanity.com/paper/2401.05459/) (2024)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [Efficient Large Language Models: A Survey](https://mlsanity.com/paper/2312.03863/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [MedVLM-R1: Incentivizing Medical Reasoning Capability of Vision-Language Models (VLMs) via Reinforcement Learning](https://mlsanity.com/paper/2502.19634/) (2025)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [Large Language Models Meet NLP: A Survey](https://mlsanity.com/paper/2405.12819/) (2024)
- [A Survey of Resource-efficient LLM and Multimodal Foundation Models](https://mlsanity.com/paper/2401.08092/) (2024)
- [EdgeMoE: Empowering Sparse Large Language Models on Mobile Devices](https://mlsanity.com/paper/2308.14352/) (2023)
- [Auto-Regressive Next-Token Predictors are Universal Learners](https://mlsanity.com/paper/2309.06979/) (2023)
- [SuRe: Summarizing Retrievals using Answer Candidates for Open-domain QA of LLMs](https://mlsanity.com/paper/2404.13081/) (2024)
- [Model Compression and Efficient Inference for Large Language Models: A Survey](https://mlsanity.com/paper/2402.09748/) (2024)
- [Survey on Knowledge Distillation for Large Language Models: Methods, Evaluation, and Application](https://mlsanity.com/paper/2407.01885/) (2024)
- [TopViewRS: Vision-Language Models as Top-View Spatial Reasoners](https://mlsanity.com/paper/2406.02537/) (2024)
- [Beyond Chain-of-Thought: A Survey of Chain-of-X Paradigms for LLMs](https://mlsanity.com/paper/2404.15676/) (2024)
- [Beyond Answers: Transferring Reasoning Capabilities to Smaller LLMs Using Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2402.04616/) (2024)
- [Measuring and Improving Chain-of-Thought Reasoning in Vision-Language Models](https://mlsanity.com/paper/2309.04461/) (2023)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [What is the Role of Small Models in the LLM Era: A Survey](https://mlsanity.com/paper/2409.06857/) (2024)
- [Adaptive In-conversation Team Building for Language Model Agents](https://mlsanity.com/paper/2405.19425/) (2024)
- [SiDA-MoE: Sparsity-Inspired Data-Aware Serving for Efficient and Scalable Large Mixture-of-Experts Models](https://mlsanity.com/paper/2310.18859/) (2023)
- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [EVOLvE: Evaluating and Optimizing LLMs For In-Context Exploration](https://mlsanity.com/paper/2410.06238/) (2024)
- [Speculative Decoding via Early-exiting for Faster LLM Inference with Thompson Sampling Control Mechanism](https://mlsanity.com/paper/2406.03853/) (2024)
- [How Far Are We From AGI: Are LLMs All We Need?](https://mlsanity.com/paper/2405.10313/) (2024)
- [Meteor: Mamba-based Traversal of Rationale for Large Language and Vision Models](https://mlsanity.com/paper/2405.15574/) (2024)

## Abstract (arXiv)

Chain-of-thought prompting (e.g., "Let's think step-by-step") primes large language models to verbalize rationalization for their predictions. While chain-of-thought can lead to dramatic performance gains, benefits appear to emerge only for sufficiently large models (beyond 50B parameters). We show that orders-of-magnitude smaller models (125M -- 1.3B parameters) can still benefit from chain-of-thought prompting. To achieve this, we introduce Symbolic Chain-of-Thought Distillation (SCoTD), a method to train a smaller student model on rationalizations sampled from a significantly larger teacher model. Experiments across several commonsense benchmarks show that: 1) SCoTD enhances the performance of the student model in both supervised and few-shot settings, and especially for challenge sets; 2) sampling many reasoning chains per instance from the teacher is paramount; and 3) after distillation, student chain-of-thoughts are judged by humans as comparable to the teacher, despite orders of magnitude fewer parameters. We test several hypotheses regarding what properties of chain-of-thought samples are important, e.g., diversity vs. teacher likelihood vs. open-endedness. We release our corpus of chain-of-thought samples and code.