The year/Independent research

Paper 2509.04419

Towards a Unified View of Large Language Model Post-Training

Published
Sep 2025
Research lab
Independent
Citations
39
GitHub
211 stars

01 In brief

Summary

This paper introduces a unified theoretical framework for large language model (LLM) post-training, showing that Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) are not contradictory but instances of a single optimization process.

The authors derive a Unified Policy Gradient Estimator (UPGE) that subsumes the gradients of various post-training algorithms (SFT, PPO, GRPO, REINFORCE, CISPO, GSPO, SRFT, LUFFY) into one expression with four interchangeable components: stabilization mask, reference policy denominator, advantage estimate, and likelihood gradient.

They demonstrate that SFT and RL optimize a common objective with different bias-variance tradeoffs.

Based on this, they propose Hybrid Post-Training (HPT), an algorithm that dynamically switches between SFT and RL losses based on real-time rollout performance (using a gate threshold γ).

Experiments on six mathematical reasoning benchmarks and two out-of-distribution suites show that HPT consistently outperforms strong baselines (SFT, GRPO, SFT→GRPO, LUFFY, SRFT) across models of varying scales (Qwen2.5-Math-1.5B, Qwen2.5-Math-7B, LLaMA3.1-8B).

Key findings include that HPT achieves the highest Pass@1024, indicating enhanced exploration, and that dynamic integration of SFT and RL improves both exploitation and exploration, with γ=0 yielding the best average performance (41.9 on Qwen2.5-Math-1.5B).

02 From the paper

Abstract

Two major sources of training data exist for post-training modern language models: online (model-generated rollouts) data, and offline (human or other-model demonstrations) data. These two types of data are typically used by approaches like Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT), respectively. In this paper, we show that these approaches are not in contradiction, but are instances of a single optimization process. We derive a Unified Policy Gradient Estimator, and present the calculations of a wide spectrum of post-training approaches as the gradient of a common objective under different data distribution assumptions and various bias-variance tradeoffs. The gradient estimator is constructed with four interchangeable parts: stabilization mask, reference policy denominator, advantage estimate, and likelihood gradient. Motivated by our theoretical findings, we propose Hybrid Post-Training (HPT), an algorithm that dynamically selects different training signals. HPT is designed to yield both effective exploitation of demonstration and stable exploration without sacrificing learned reasoning patterns. We provide extensive experiments and ablation studies to verify the effectiveness of our unified theoretical framework and HPT. Across six mathematical reasoning benchmarks and two out-of-distribution suites, HPT consistently surpasses strong baselines across models of varying scales and families.