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

arXiv: https://arxiv.org/abs/2507.00018 · HTML: https://mlsanity.com/paper/2507.00018/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- Offline RL and imitation learning from data / [Language-conditioned policies and VLAs](https://mlsanity.com/offlinerl/language-conditioned-policies-and-vlas/)

## Builds on (most cited first, 30 of 33)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [A Divergence Minimization Perspective on Imitation Learning Methods](https://mlsanity.com/paper/1911.02256/) (2019)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning](https://mlsanity.com/paper/2503.01067/) (2025)
- [Imitating Language via Scalable Inverse Reinforcement Learning](https://mlsanity.com/paper/2409.01369/) (2024)

## Built on by (most cited first, 17 of 17)

- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum](https://mlsanity.com/paper/2510.00526/) (2025)
- [Entropy-Adaptive Fine-Tuning: Resolving Confident Conflicts to Mitigate Forgetting](https://mlsanity.com/paper/2601.02151/) (2026)
- [One-Token Rollout: Guiding Supervised Fine-Tuning of LLMs with Policy Gradient](https://mlsanity.com/paper/2509.26313/) (2025)
- [RFG: Test-Time Scaling for Diffusion Large Language Model Reasoning with Reward-Free Guidance](https://mlsanity.com/paper/2509.25604/) (2025)
- [RealDPO: Real or Not Real, that is the Preference](https://mlsanity.com/paper/2510.14955/) (2025)
- [Sample-efficient LLM Optimization with Reset Replay](https://mlsanity.com/paper/2508.06412/) (2025)
- [Bridging VLMs and Embodied Intelligence with Deliberate Practice Policy Optimization](https://mlsanity.com/paper/2511.16602/) (2025)
- [Knowledge Graph-Assisted LLM Post-Training for Enhanced Legal Reasoning](https://mlsanity.com/paper/2601.13806/) (2026)
- [Compatibility-Aware Dynamic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2606.11206/) (2026)
- [SSPO: Self-traced Step-wise Preference Optimization for Process Supervision and Reasoning Compression](https://mlsanity.com/paper/2508.12604/) (2025)
- [Reg-DPO: SFT-Regularized Direct Preference Optimization with GT-Pair for Improving Video Generation](https://mlsanity.com/paper/2511.01450/) (2025)
- [Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning](https://mlsanity.com/paper/2512.11470/) (2025)
- [PaperGuide: Making Small Language-Model Paper-Reading Agents More Efficient](https://mlsanity.com/paper/2601.12988/) (2026)
- [IRIS: Implicit Reward-Guided Internal Sifting for Mitigating Multimodal Hallucination](https://mlsanity.com/paper/2602.01769/) (2026)
- [RL-RIG: A Generative Spatial Reasoner via Intrinsic Reflection](https://mlsanity.com/paper/2602.19974/) (2026)
- [Scaling Near-Optimal SFT-RL Annotation Budget Allocation from Small to Large LLMs](https://mlsanity.com/paper/2609.01573/) (2026)

## Abstract (arXiv)

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 25% relative gain and 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.