# ReSync: Riemannian Subgradient-based Robust Rotation Synchronization

arXiv: https://arxiv.org/abs/2305.15136 · HTML: https://mlsanity.com/paper/2305.15136/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 17 of 17)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Spectral Method and Regularized MLE Are Both Optimal for Top-K Ranking](https://mlsanity.com/paper/1707.09971/) (2017)
- [Subgradient methods for sharp weakly convex functions](https://mlsanity.com/paper/1803.02461/) (2018)
- [Near-optimal bounds for phase synchronization](https://mlsanity.com/paper/1703.06605/) (2017)
- [Nonconvex phase synchronization](https://mlsanity.com/paper/1601.06114/) (2016)
- [Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval](https://mlsanity.com/paper/1705.02356/) (2017)
- [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)
- [Strong Consistency, Graph Laplacians, and the Stochastic Block Model](https://mlsanity.com/paper/2004.09780/) (2020)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Near-Optimal Performance Bounds for Orthogonal and Permutation Group Synchronization via Spectral Methods](https://mlsanity.com/paper/2008.05341/) (2020)
- [A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group](https://mlsanity.com/paper/2009.07514/) (2020)
- [Random Laplacian matrices and convex relaxations](https://mlsanity.com/paper/1504.03987/) (2015)
- [Robust Group Synchronization via Quadratic Programming](https://mlsanity.com/paper/2206.08994/) (2022)
- [Multi-Frequency Phase Synchronization](https://mlsanity.com/paper/1901.08235/) (2019)

## Built on by (most cited first, 3 of 3)

- [Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization](https://mlsanity.com/paper/2407.04260/) (2024)
- [NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization](https://mlsanity.com/paper/2604.07372/) (2026)
- [ℓ1-norm rank-one symmetric matrix factorization has no spurious second-order stationary points](https://mlsanity.com/paper/2410.05025/) (2024)

## Abstract (arXiv)

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSync yields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSync to the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.