@inproceedings{ding-etal-2026-rethinking,
title = "Rethinking Expert Trajectory Utilization in {LLM} Post-training for Mathematical Reasoning",
author = "Ding, Bowen and
Chen, Yuhan and
Lyu, Jiayang and
Yuan, Jiyao and
Zhu, Qi and
Tian, Shuangshuang and
Zhu, Dantong and
Wang, Futing and
Deng, Heyuan and
Mi, Fei and
Shang, Lifeng and
Lin, Tao",
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.1528/",
pages = "33081--33106",
ISBN = "979-8-89176-390-6",
abstract = "Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) dominate the post-training landscape for mathematical reasoning, yet differ fundamentally in their reliance on expert trajectories. To understand the optimal way to harness these trajectories for maximizing performance, we propose the Plasticity-Ceiling Framework. This framework empirically grounds the post-training landscape by decomposing the final performance ceiling into the foundational SFT performance and the subsequent RL plasticity (i.e., the maximum improvement via RL). Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability and premature convergence deficits inherent in synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the Stable or Mild Overfitting Regime of SFT maximizes the final ceiling by securing a robust SFT foundation with substantial RL plasticity; (2) Refuting the ``Less is More'' hypothesis in SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) The Minimum Validation Loss of SFT serves as a reliable indicator for selecting the expert trajectories that maximize the ultimate performance ceiling. Our findings provide actionable guidelines for extracting maximum value from expert trajectories."
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<abstract>Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) dominate the post-training landscape for mathematical reasoning, yet differ fundamentally in their reliance on expert trajectories. To understand the optimal way to harness these trajectories for maximizing performance, we propose the Plasticity-Ceiling Framework. This framework empirically grounds the post-training landscape by decomposing the final performance ceiling into the foundational SFT performance and the subsequent RL plasticity (i.e., the maximum improvement via RL). Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability and premature convergence deficits inherent in synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the Stable or Mild Overfitting Regime of SFT maximizes the final ceiling by securing a robust SFT foundation with substantial RL plasticity; (2) Refuting the “Less is More” hypothesis in SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) The Minimum Validation Loss of SFT serves as a reliable indicator for selecting the expert trajectories that maximize the ultimate performance ceiling. Our findings provide actionable guidelines for extracting maximum value from expert trajectories.</abstract>
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%0 Conference Proceedings
%T Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning
%A Ding, Bowen
%A Chen, Yuhan
%A Lyu, Jiayang
%A Yuan, Jiyao
%A Zhu, Qi
%A Tian, Shuangshuang
%A Zhu, Dantong
%A Wang, Futing
%A Deng, Heyuan
%A Mi, Fei
%A Shang, Lifeng
%A Lin, Tao
%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 ding-etal-2026-rethinking
%X Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) dominate the post-training landscape for mathematical reasoning, yet differ fundamentally in their reliance on expert trajectories. To understand the optimal way to harness these trajectories for maximizing performance, we propose the Plasticity-Ceiling Framework. This framework empirically grounds the post-training landscape by decomposing the final performance ceiling into the foundational SFT performance and the subsequent RL plasticity (i.e., the maximum improvement via RL). Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability and premature convergence deficits inherent in synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the Stable or Mild Overfitting Regime of SFT maximizes the final ceiling by securing a robust SFT foundation with substantial RL plasticity; (2) Refuting the “Less is More” hypothesis in SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) The Minimum Validation Loss of SFT serves as a reliable indicator for selecting the expert trajectories that maximize the ultimate performance ceiling. Our findings provide actionable guidelines for extracting maximum value from expert trajectories.
%U https://aclanthology.org/2026.acl-long.1528/
%P 33081-33106
Markdown (Informal)
[Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning](https://aclanthology.org/2026.acl-long.1528/) (Ding et al., ACL 2026)
ACL
- Bowen Ding, Yuhan Chen, Jiayang Lyu, Jiyao Yuan, Qi Zhu, Shuangshuang Tian, Dantong Zhu, Futing Wang, Heyuan Deng, Fei Mi, Lifeng Shang, and Tao Lin. 2026. Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 33081–33106, San Diego, California, United States. Association for Computational Linguistics.