# LightReasoner: Can Small Language Models Teach Large Language Models Reasoning?

arXiv: https://arxiv.org/abs/2510.07962 · HTML: https://mlsanity.com/paper/2510.07962/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [The First Few Tokens Are All You Need: An Efficient and Effective Unsupervised Prefix Fine-Tuning Method for Reasoning Models](https://mlsanity.com/paper/2503.02875/) (2025)

## Built on by (most cited first, 3 of 3)

- [Weak-Driven Learning: How Weak Agents make Strong Agents Stronger](https://mlsanity.com/paper/2602.08222/) (2026)
- [The Master Key Hypothesis: Unlocking Cross-Model Capability Transfer via Linear Subspace Alignment](https://mlsanity.com/paper/2604.06377/) (2026)
- [TeacherGRPO: Closing the Capacity Gap in Reasoning Distillation via Teacher Alignment](https://mlsanity.com/paper/2609.33426/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated remarkable progress in reasoning, often through supervised fine-tuning (SFT). However, SFT is resource-intensive, relying on large curated datasets, rejection-sampled demonstrations, and uniform optimization across all tokens, even though only a fraction carry meaningful learning value. In this work, we explore a counterintuitive idea: can smaller language models (SLMs) teach larger language models (LLMs) by revealing high-value reasoning moments that reflect the latter's unique strength? We propose LightReasoner, a novel framework that leverages the behavioral divergence between a stronger expert model (LLM) and a weaker amateur model (SLM). LightReasoner operates in two stages: (1) a sampling stage that pinpoints critical reasoning moments and constructs supervision examples capturing the expert's advantage through expert-amateur contrast, and (2) a fine-tuning stage that aligns the expert model with these distilled examples, amplifying its reasoning strengths. Across seven mathematical benchmarks, LightReasoner improves accuracy by up to 28.1%, while reducing time consumption by 90%, sampled problems by 80%, and tuned token usage by 99%, all without relying on ground-truth labels. By turning weaker SLMs into effective teaching signals, LightReasoner offers a scalable and resource-efficient approach for advancing LLM reasoning. Code is available at: https://github.com/HKUDS/LightReasoner