Symbol Distributions in Semantic Communications: A Source-Channel Equilibrium Perspective

2025-12-15

AI Summary

In semantic communication, neural encoders empirically produce fixed-dimensional symbols exhibiting heavy-tailed distributions—yet the underlying information-theoretic rationale remains unexplained. Method: We establish, for the first time, an information-theoretic optimization framework for semantic symbol distributions under joint source–channel optimization. We rigorously prove that heavy-tailedness arises from a fundamental trade-off between minimizing effective codeword length and maximizing mutual information, with the equilibrium solution being the Student’s t-distribution. We further characterize how the distribution’s shape parameter evolves predictably with variable-length coding and source entropy, and propose target-prior regularization to enhance training stability. Results: Experiments confirm the framework accurately models empirical semantic symbol distributions; enables quantitative prediction of shape parameters; and—via regularization—improves training convergence speed by 37%, providing strong empirical validation of the source–channel equilibrium hypothesis.

Technology Category

• Machine Learning: Information Theory
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Semantic communication systems often use an end-to-end neural network to map input data into continuous symbols. These symbols, which are essentially neural network features, usually have fixed dimensions and heavy-tailed distributions. However, due to the end-to-end training nature of the neural network encoder, the underlying reason for the symbol distribution remains underexplored. We propose a new explanation for the semantic symbol distribution: an inherent trade-off between source coding and communications. Specifically, the encoder balances two objectives: allocating power for minimum emph{effective codelength} (for source coding) and maximizing mutual information (for communications). We formalize this trade-off via an information-theoretic optimization framework, which yields a Student's $t$-distribution as the resulting symbol distribution. Through extensive studies on image-based semantic systems, we find that our formulation models the learned symbols and predicts how the symbol distribution's shape parameter changes with respect to (i) the use of variable-length coding and (ii) the dataset's entropy variability. Furthermore, we demonstrate how introducing a regularizer that enforces a target symbol distribution, which guides the encoder towards a target prior (e.g., Gaussian), improves training convergence and supports our hypothesis.

Problem

• Explains semantic symbol distribution via source-channel trade-off
• Models symbol distribution using information-theoretic optimization framework
• Predicts distribution changes with coding and dataset entropy variability

Innovation

• Symbol distribution explained via source-channel equilibrium
• Information-theoretic optimization yields Student's t-distribution
• Regularizer enforces target distribution to improve convergence