# Can LLMs Learn by Teaching for Better Reasoning? A Preliminary Study

arXiv: https://arxiv.org/abs/2406.14629 · HTML: https://mlsanity.com/paper/2406.14629/

## Key facts

- Cited by 5 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 28 of its 101 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## 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, 28 of 28)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Exploring Large Language Model based Intelligent Agents: Definitions, Methods, and Prospects](https://mlsanity.com/paper/2401.03428/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [An Overview of Machine Teaching](https://mlsanity.com/paper/1801.05927/) (2018)
- [Learning from Teaching Regularization: Generalizable Correlations Should be Easy to Imitate](https://mlsanity.com/paper/2402.02769/) (2024)
- [What Do Language Models Learn in Context? The Structured Task Hypothesis](https://mlsanity.com/paper/2406.04216/) (2024)
- [Bias at a Second Glance: A Deep Dive into Bias for German Educational Peer-Review Data Modeling](https://mlsanity.com/paper/2209.10335/) (2022)
- [Black-box Generalization of Machine Teaching](https://mlsanity.com/paper/2206.15205/) (2022)

## Built on by (most cited first, 5 of 5)

- [Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoning](https://mlsanity.com/paper/2503.01642/) (2025)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [VTBench: Evaluating Visual Tokenizers for Autoregressive Image Generation](https://mlsanity.com/paper/2505.13439/) (2025)
- [Scaling Textual Gradients via Sampling-Based Momentum](https://mlsanity.com/paper/2506.00400/) (2025)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)

## Abstract (arXiv)

Teaching to improve student models (e.g., knowledge distillation) is an extensively studied methodology in LLMs. However, for humans, teaching improves not only students but also teachers, by fostering more rigorous and clear reasoning as well as knowledge building. We ask: Can LLMs also learn by teaching (LbT) for better reasoning? If the answer is yes, we can potentially unlock the possibility of continuously advancing the models without solely relying on human-produced data or stronger models. In this paper, we provide a preliminary exploration on this question. We show that LbT ideas can be incorporated into existing LLM training/prompting pipelines and bring improvements. Specifically, we design three methods, each mimicking one of the three levels of LbT: observing students' feedback, learning from the feedback, and learning iteratively, with the goals of improving answer accuracy without training or improving models' inherent capability with fine-tuning. We reveal some findings: (1) Teaching materials that make it easier for students to learn have clearer and more accurate logic when using in-context learning as the student's "learning" method; (2) Weak-to-strong generalization: LbT might help improve strong models by teaching weak models; (3) Diversity in students might help: teaching multiple students could be better than teaching one student or the teacher itself. We hope that our exploration can inspire future research on LbT and more broadly adopting the advanced techniques in education to improve LLMs. The code and website are at https://github.com/imagination-research/lbt and https://sites.google.com/view/llm-learning-by-teaching.