Differential Information Distribution: A Bayesian Perspective on Direct Preference Optimization

Fuente: arXiv
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Main Authors: Won, Yunjae, Lee, Hyunji, Hwang, Hyeonbin, Seo, Minjoon
Format: Preprint
Published: 2025
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author Won, Yunjae
Lee, Hyunji
Hwang, Hyeonbin
Seo, Minjoon
author_facet Won, Yunjae
Lee, Hyunji
Hwang, Hyeonbin
Seo, Minjoon
contents Direct Preference Optimization (DPO) has been widely used for aligning language models with human preferences in a supervised manner. However, several key questions remain unresolved: the rationale behind its log-ratio reward, how the statistical structure of preference datasets shapes its training dynamics, and how those dynamics impact downstream capabilities. We approach these questions from a Bayesian perspective, interpreting the goal of preference optimization as learning the differential information required to update a reference policy into a target policy. To formalize this view, we introduce the Differential Information Distribution (DID), defined as the distribution over samples that carry the Bayesian evidence required to update policies. We introduce three complementary insights by viewing preference optimization through the DID. First, we find that DPO's log-ratio reward is uniquely justified when preferences encode the Differential Information needed to update a reference policy into the target policy. Second, we discuss how commonly observed training dynamics in DPO, including changes in log-likelihood and policy exploration, stem from a power-law DID relationship. Finally, we analyze how training dynamics influence downstream performance using the entropy of DID, a principled measure of uncertainty in the learned information. We observe that learning high-entropy DID improves open-ended instruction-following, while low-entropy DID benefits knowledge-intensive QA. Taken together, our results show that DPO's reward design, training dynamics, and downstream capabilities all emerge as natural consequences of learning Differential Information, offering both a principled theoretical foundation and practical guidance for preference-based alignment.
format Preprint
id arxiv_https___arxiv_org_abs_2505_23761
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Differential Information Distribution: A Bayesian Perspective on Direct Preference Optimization
Won, Yunjae
Lee, Hyunji
Hwang, Hyeonbin
Seo, Minjoon
Machine Learning
Artificial Intelligence
Computation and Language
Direct Preference Optimization (DPO) has been widely used for aligning language models with human preferences in a supervised manner. However, several key questions remain unresolved: the rationale behind its log-ratio reward, how the statistical structure of preference datasets shapes its training dynamics, and how those dynamics impact downstream capabilities. We approach these questions from a Bayesian perspective, interpreting the goal of preference optimization as learning the differential information required to update a reference policy into a target policy. To formalize this view, we introduce the Differential Information Distribution (DID), defined as the distribution over samples that carry the Bayesian evidence required to update policies. We introduce three complementary insights by viewing preference optimization through the DID. First, we find that DPO's log-ratio reward is uniquely justified when preferences encode the Differential Information needed to update a reference policy into the target policy. Second, we discuss how commonly observed training dynamics in DPO, including changes in log-likelihood and policy exploration, stem from a power-law DID relationship. Finally, we analyze how training dynamics influence downstream performance using the entropy of DID, a principled measure of uncertainty in the learned information. We observe that learning high-entropy DID improves open-ended instruction-following, while low-entropy DID benefits knowledge-intensive QA. Taken together, our results show that DPO's reward design, training dynamics, and downstream capabilities all emerge as natural consequences of learning Differential Information, offering both a principled theoretical foundation and practical guidance for preference-based alignment.
title Differential Information Distribution: A Bayesian Perspective on Direct Preference Optimization
topic Machine Learning
Artificial Intelligence
Computation and Language
url https://arxiv.org/abs/2505.23761