# Robust Angular Synchronization via Directed Graph Neural Networks

arXiv: https://arxiv.org/abs/2310.05842 · HTML: https://mlsanity.com/paper/2310.05842/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Nonconvex phase synchronization](https://mlsanity.com/paper/1601.06114/) (2016)
- [Tightness of the maximum likelihood semidefinite relaxation for angular synchronization](https://mlsanity.com/paper/1411.3272/) (2014)
- [Message Passing Least Squares Framework and its Application to Rotation Synchronization](https://mlsanity.com/paper/2007.13638/) (2020)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Understanding Notions of Stationarity in Non-Smooth Optimization](https://mlsanity.com/paper/2006.14901/) (2020)
- [A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group](https://mlsanity.com/paper/2009.07514/) (2020)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [Sync-Rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and Semidefinite Programming Synchronization](https://mlsanity.com/paper/1504.01070/) (2015)
- [GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks](https://mlsanity.com/paper/2202.00211/) (2022)
- [Robust Group Synchronization via Quadratic Programming](https://mlsanity.com/paper/2206.08994/) (2022)
- [Solving Jigsaw Puzzles By the Graph Connection Laplacian](https://mlsanity.com/paper/1811.03188/) (2018)
- [Multi-Frequency Phase Synchronization](https://mlsanity.com/paper/1901.08235/) (2019)
- [On recovery guarantees for angular synchronization](https://mlsanity.com/paper/2005.02032/) (2020)
- [An extension of the angular synchronization problem to the heterogeneous setting](https://mlsanity.com/paper/2012.14932/) (2020)
- [Unrolled algorithms for group synchronization](https://mlsanity.com/paper/2207.09418/) (2022)

## Built on by (most cited first, 2 of 2)

- [Dynamic angular synchronization under smoothness constraints](https://mlsanity.com/paper/2406.04071/) (2024)
- [Learning to Fuse Temporal Proximity Networks: A Case Study in Chimpanzee Social Interactions](https://mlsanity.com/paper/2502.00302/) (2025)

## Abstract (arXiv)

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles θ1, dots, θn∈[0, 2π) from m noisy measurements of their offsets θi-θj ;mboxmod ; 2π. 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.