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This paper introduces Distribution Discriminant Theory (DDT) to quantify the alignment between training data and the model-induced distribution in supervised fine-tuning (SFT) of LLMs. Based on DDT, they propose In-Distribution Finetuning (IDFT), a loss-level method, and Hinted Decoding, a data-level technique, to improve generalization by aligning the training data distribution with the model's. Experiments show that the proposed framework achieves generalization performance comparable to offline RL methods like DPO and SimPO, while retaining the efficiency of SFT.
SFT can match the generalization performance of offline RL methods like DPO, thanks to a new theory that aligns training data with the model's distribution.
Supervised fine-tuning (SFT) is computationally efficient but often yields inferior generalization compared to reinforcement learning (RL). This gap is primarily driven by RL's use of on-policy data. We propose a framework to bridge this chasm by enabling On-Policy SFT. We first present \textbf{\textit{Distribution Discriminant Theory (DDT)}}, which explains and quantifies the alignment between data and the model-induced distribution. Leveraging DDT, we introduce two complementary techniques: (i) \textbf{\textit{In-Distribution Finetuning (IDFT)}}, a loss-level method to enhance generalization ability of SFT, and (ii) \textbf{\textit{Hinted Decoding}}, a data-level technique that can re-align the training corpus to the model's distribution. Extensive experiments demonstrate that our framework achieves generalization performance on par with prominent offline RL algorithms, including DPO and SimPO, while maintaining the efficiency of an SFT pipeline. The proposed framework thus offers a practical alternative in domains where RL is infeasible. We open-source the code here: https://github.com/zhangmiaosen2000/Towards-On-Policy-SFT