Robust Angular Synchronization via Directed Graph Neural Networks

TL;DR

This paper introduces GNNSync, a neural network-based framework using directed graph neural networks for robust angular synchronization, outperforming traditional methods especially in high-noise scenarios.

Contribution

The paper presents a novel, theoretically-grounded neural network approach for angular synchronization and its heterogeneous extension, with new loss functions and superior robustness.

Findings

GNNSync achieves superior accuracy over baselines.

The method is robust in high-noise environments.

Experimental validation on extensive datasets.

Abstract

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \;\mbox{mod} \; 2\pi.$ Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed $k$-synchronization) is to estimate $k$ groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels.