# Reinforcement learning fine-tuning of language model for instruction following and math reasoning

arXiv: https://arxiv.org/abs/2506.21560 · HTML: https://mlsanity.com/paper/2506.21560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [ALJP: An Arabic Legal Judgment Prediction in Personal Status Cases Using Machine Learning Models](https://mlsanity.com/paper/2309.00238/) (2023)

## Abstract (arXiv)

This study investigates the effectiveness of reinforcement learning (RL) fine-tuning techniques on a compact language model (Qwen2.5-0.5B Base) for two challenging tasks: instruction following and mathematical reasoning. We compare supervised fine-tuning (SFT), Direct Preference Optimization (DPO) using preference-labeled data, and Reinforce Leave-One-Out (RLOO) with reward models. Our experiments show that RLOO with DeBERTa reward modeling achieves the best alignment, while DPO provides strong and consistent results. For math reasoing tasks, synthetic data augmentation and best-of-N sampling with an external verifier significantly improve accuracy, showing the potential of combining fine-tuning with inference-time tools. This study highlights key trade-offs and practical strategies for training lightweight, task-aligned small-scale language models.