# Effective Learning for Small Reasoning Models: An Empirical Study on 0.5B Reasoning LLMs

arXiv: https://arxiv.org/abs/2506.13404 · HTML: https://mlsanity.com/paper/2506.13404/

## 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 26 of its 42 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [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)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Challenges and Applications of Large Language Models](https://mlsanity.com/paper/2307.10169/) (2023)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Small Language Models: Survey, Measurements, and Insights](https://mlsanity.com/paper/2409.15790/) (2024)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [SQL-R1: Training Natural Language to SQL Reasoning Model By Reinforcement Learning](https://mlsanity.com/paper/2504.08600/) (2025)
- [A Survey of Text-to-SQL in the Era of LLMs: Where are we, and where are we going?](https://mlsanity.com/paper/2408.05109/) (2024)
- [MM-MATH: Advancing Multimodal Math Evaluation with Process Evaluation and Fine-grained Classification](https://mlsanity.com/paper/2404.05091/) (2024)
- [A Survey of Small Language Models](https://mlsanity.com/paper/2410.20011/) (2024)
- [High-Similarity-Pass Attention for Single Image Super-Resolution](https://mlsanity.com/paper/2305.15768/) (2023)
- [Code Generation with Small Language Models: A Codeforces-Based Study](https://mlsanity.com/paper/2504.07343/) (2025)

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

- [G2RPO-A: Guided Group Relative Policy Optimization with Adaptive Guidance](https://mlsanity.com/paper/2508.13023/) (2025)
- [ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models](https://mlsanity.com/paper/2610.07803/) (2026)
- [StartLux-Decision: AutoThink Decision Models with Reinforcement Learning for Calibrated Deliberative Decisions](https://mlsanity.com/paper/2610.17309/) (2026)

## Abstract (arXiv)

The ongoing evolution of language models has led to the development of large-scale architectures that demonstrate exceptional performance across a wide range of tasks. However, these models come with significant computational and energy demands, as well as potential privacy implications. In this context, Small Reasoning Language Models (SRLMs) with approximately 0.5 billion parameters present a compelling alternative due to their remarkable computational efficiency and cost-effectiveness, particularly in resource-constrained environments. Despite these advantages, the limited capacity of 0.5 billion parameter models poses challenges in handling complex tasks such as mathematical reasoning. This research investigates various training strategies, including supervised fine-tuning (SFT), knowledge distillation (KD), and reinforcement learning (RL), as well as their hybrid implementations, to enhance the performance of 0.5B SRLMs. We analyze effective methodologies to bridge the performance gap between SRLMS and larger models and present insights into optimal training pipelines tailored for these smaller architectures. Through extensive experimental validation and analysis, our work aims to provide actionable recommendations for maximizing the reasoning capabilities of 0.5B models.