@inproceedings{tan-etal-2026-scaling,
title = "Scaling Behaviors of {LLM} Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning",
author = "Tan, Zelin and
Geng, Hejia and
Yu, Xiaohang and
Zhang, Mulei and
Wan, Guancheng and
Zhou, Yifan and
He, Qiang and
Xue, Xiangyuan and
Zhou, Heng and
Fan, Yutao and
Li, Zhong-Zhi and
Zhang, Zaibin and
Zhang, Guibin and
Zhang, Chen and
Yin, Zhenfei and
Torr, Philip and
Bai, Lei",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.1444/",
pages = "31300--31319",
ISBN = "979-8-89176-390-6",
abstract = "While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper investigates the scaling behavior of Large Language Model (LLM) reinforcement learning post-training, focusing on mathematical reasoning. Through experiments across the Qwen2.5 series (0.5B to 72B), we characterize how model scale, data, and compute interact. Our analysis yields four key findings: 1. Larger models consistently demonstrate superior compute and data efficiency. 2. The relationship between model performance and training resources follows a **predictive power-law** across both base and instruction-tuned models. 3. RL learning efficiency exhibits a latent **saturation trend** with increasing model scale. 4. In data-constrained regimes, performance is primarily driven by the **total volume of training data** rather than sample uniqueness. These results offer practical guidelines for scaling reasoning capabilities through reinforcement learning post-training."
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<abstract>While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper investigates the scaling behavior of Large Language Model (LLM) reinforcement learning post-training, focusing on mathematical reasoning. Through experiments across the Qwen2.5 series (0.5B to 72B), we characterize how model scale, data, and compute interact. Our analysis yields four key findings: 1. Larger models consistently demonstrate superior compute and data efficiency. 2. The relationship between model performance and training resources follows a **predictive power-law** across both base and instruction-tuned models. 3. RL learning efficiency exhibits a latent **saturation trend** with increasing model scale. 4. In data-constrained regimes, performance is primarily driven by the **total volume of training data** rather than sample uniqueness. These results offer practical guidelines for scaling reasoning capabilities through reinforcement learning post-training.</abstract>
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%0 Conference Proceedings
%T Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning
%A Tan, Zelin
%A Geng, Hejia
%A Yu, Xiaohang
%A Zhang, Mulei
%A Wan, Guancheng
%A Zhou, Yifan
%A He, Qiang
%A Xue, Xiangyuan
%A Zhou, Heng
%A Fan, Yutao
%A Li, Zhong-Zhi
%A Zhang, Zaibin
%A Zhang, Guibin
%A Zhang, Chen
%A Yin, Zhenfei
%A Torr, Philip
%A Bai, Lei
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F tan-etal-2026-scaling
%X While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper investigates the scaling behavior of Large Language Model (LLM) reinforcement learning post-training, focusing on mathematical reasoning. Through experiments across the Qwen2.5 series (0.5B to 72B), we characterize how model scale, data, and compute interact. Our analysis yields four key findings: 1. Larger models consistently demonstrate superior compute and data efficiency. 2. The relationship between model performance and training resources follows a **predictive power-law** across both base and instruction-tuned models. 3. RL learning efficiency exhibits a latent **saturation trend** with increasing model scale. 4. In data-constrained regimes, performance is primarily driven by the **total volume of training data** rather than sample uniqueness. These results offer practical guidelines for scaling reasoning capabilities through reinforcement learning post-training.
%U https://aclanthology.org/2026.acl-long.1444/
%P 31300-31319
Markdown (Informal)
[Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning](https://aclanthology.org/2026.acl-long.1444/) (Tan et al., ACL 2026)
ACL
- Zelin Tan, Hejia Geng, Xiaohang Yu, Mulei Zhang, Guancheng Wan, Yifan Zhou, Qiang He, Xiangyuan Xue, Heng Zhou, Yutao Fan, Zhong-Zhi Li, Zaibin Zhang, Guibin Zhang, Chen Zhang, Zhenfei Yin, Philip Torr, and Lei Bai. 2026. Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 31300–31319, San Diego, California, United States. Association for Computational Linguistics.