Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs

2025-06-02

AI Summary

Quantization-induced noise accumulation severely degrades performance in distributed graph filtering under bandwidth-constrained communication. Method: This paper proposes an error spectral shaping–based quantization error feedback mechanism—first introducing the spectral shaping concept from state-space digital filtering into graph signal processing. It establishes an exact quantization error model and a closed-loop compensation framework, deriving a closed-form solution for the optimal feedback coefficients. The method unifies graph signal processing, random graph theory, asynchronous distributed optimization, and quantized control to support deterministic graphs, stochastic graphs, and node-asynchronous updates. Contribution/Results: Theoretical analysis proves that the proposed method significantly lowers the steady-state error lower bound. Experiments demonstrate superior accuracy and robustness over existing quantized graph filtering approaches across diverse topologies and under stringent communication constraints, including low-bitwidth quantization and irregular connectivity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper introduces an innovative error feedback framework designed to mitigate quantization noise in distributed graph filtering, where communications are constrained to quantized messages. It comes from error spectrum shaping techniques from state-space digital filters, and therefore establishes connections between quantized filtering processes over different domains. In contrast to existing error compensation methods, our framework quantitatively feeds back the quantization noise for exact compensation. We examine the framework under three key scenarios: (i) deterministic graph filtering, (ii) graph filtering over random graphs, and (iii) graph filtering with random node-asynchronous updates. Rigorous theoretical analysis demonstrates that the proposed framework significantly reduces the effect of quantization noise, and we provide closed-form solutions for the optimal error feedback coefficients. Moreover, this quantitative error feedback mechanism can be seamlessly integrated into communication-efficient decentralized optimization frameworks, enabling lower error floors. Numerical experiments validate the theoretical results, consistently showing that our method outperforms conventional quantization strategies in terms of both accuracy and robustness.

Problem

• Mitigates quantization noise in distributed graph filtering
• Connects quantized filtering processes across different domains
• Reduces quantization noise effects with optimal feedback coefficients

Innovation

• Error feedback framework reduces quantization noise
• Connects quantized filtering across different domains
• Optimal coefficients for exact noise compensation