Implicit Reward as the Bridge: A Unified View of SFT and DPO Connections

• URL: http://arxiv.org/abs/2507.00018v2
• Date: Fri, 04 Jul 2025 08:16:16 GMT
• Title: Implicit Reward as the Bridge: A Unified View of SFT and DPO Connections
• Authors: Bo Wang, Qinyuan Cheng, Runyu Peng, Rong Bao, Peiji Li, Qipeng Guo, Linyang Li, Zhiyuan Zeng, Yunhua Zhou, Xipeng Qiu,
• Abstract summary: We present a unified theoretical framework bridgingSupervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training.<n>We propose a simple yet effective learning rate reduction approach that yields significant performance improvements.
• Score: 65.36449542323277
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical framework bridging Supervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training. Through rigorous mathematical derivation, we demonstrate that both SFT and preference learning methods like Direct Preference Optimization (DPO) operate within the same optimal policy-reward subspace, with SFT representing a special case of implicit reward learning. Our analysis reveals a critical limitation in conventional SFT: the KL divergence term in distribution matching becomes constant with respect to the policy during optimization, failing to constrain model updates. To address this, we propose a simple yet effective learning rate reduction approach that yields significant performance improvements (up to \textbf{25\%} relative gain and \textbf{6\%} absolute win rate increase in instruction following tasks. Additionally, we derive alternative SFT objectives from various f-divergence functions that preserve the KL term during optimization, further enhancing post-DPO model performance. Finally, we extend the theoretical relationship between LLM logits and Q-functions from preference learning to the SFT context, providing mathematical derivations and experimental validation.

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