A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff

2026-04-16

AI Summary

Traditional rate–distortion theory struggles to account for perceptual quality in compression, while existing rate–distortion–perception (RDP) frameworks lack a solid theoretical foundation. This work addresses this gap by introducing a semantic perspective based on synonymous information, defining perceptual reconstruction as the recovery of any sample within the ideal synonymous set to which the source signal belongs. It proposes a synonymous source coding architecture and a synonymous variational inference (SVI) analytical framework. Leveraging the principle of synonymy–perception consistency, the study theoretically establishes, for the first time, the alignment between perceptual optimization and semantic recognition, naturally yielding a distribution divergence term. This leads to a synonymous rate–distortion–perception trade-off theory that subsumes both classical rate–distortion theory and current RDP formulations, demonstrating the theoretical advantages of synonymous coding in perceptual compression.

Technology Category

• Computer Vision: Computational Photography, Image & Video Synthesis
• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

The fundamental limit of natural signal compression has traditionally been characterized by classical rate-distortion (RD) theory through the tradeoff between coding rate and reconstruction distortion, while the rate-distortion-perception (RDP) framework introduces a divergence-based measure of perceptual quality as a modeling principle rather than a theoretically-derived principle, leaving its theoretical origin unclear. In this paper, motivated by a synonymity-based semantic information perspective, we reformulate perceptual reconstruction as recovering any admissible sample within an ideal synonymous set (synset) associated with the source, rather than the source sample itself, and correspondingly establish a synonymous source coding architecture. On this basis, we develop a synonymous variational inference (SVI) analysis framework with a synonymous variational lower bound (SVLBO) for tractable analysis of synset-oriented compression. Within this framework, we establish a synonymity-perception consistency principle, showing that optimal identification of semantic information is theoretically consistent with perceptual optimization. Based on its derivation result, we prove a synonymous RDP tradeoff for the proposed synonymous source coding. These analytical results show that the distributional divergence term arises naturally from the synset-based reconstruction objective, clarify its compatibility with existing RDP formulations and classical RD theory, and suggest the potential advantages of synonymous source coding.

Problem

• rate-distortion-perception
• perceptual quality
• semantic information
• synonymous set
• theoretical foundation

Innovation

• synonymous source coding
• rate-distortion-perception tradeoff
• semantic information
• variational inference
• perceptual quality