Reliable one-bit quantization of bandlimited graph data via single-shot noise shaping

2026-02-09

AI Summary

This work addresses the challenge of efficiently quantizing bandlimited graph signals to extremely low bit depths—such as 1-bit—while preserving their low-pass spectral characteristics. To this end, the authors propose a one-shot noise-shaping quantization framework that, for the first time, enables reliable quantization of graph signals at arbitrary bit depths, including the single-bit regime. By integrating graph Fourier analysis with quantization error control theory, the method provides rigorous theoretical bounds on signal reconstruction error. Experimental evaluations across multiple graph signal datasets demonstrate that the proposed approach significantly outperforms existing techniques, achieving state-of-the-art reconstruction performance particularly in the 1-bit setting.

Technology Category

Machine Learning: Graph-based Machine LearningReasoning under Uncertainty: Graphical ModelsCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasetsSecurity and Privacy: Large-scale security measurements

Abstract

Graph data are ubiquitous in natural sciences and machine learning. In this paper, we consider the problem of quantizing graph structured, bandlimited data to few bits per entry while preserving its information under low-pass filtering. We propose an efficient single-shot noise shaping method that achieves state-of-the-art performance and comes with rigorous error bounds. In contrast to existing methods it allows reliable quantization to arbitrary bit-levels including the extreme case of using a single bit per data coefficient.

Problem

• graph data
• one-bit quantization
• bandlimited
• low-pass filtering
• quantization

Innovation

• one-bit quantization
• graph signal processing
• noise shaping
• bandlimited graph data
• error bounds