# Robust Group Synchronization via Quadratic Programming

arXiv: https://arxiv.org/abs/2206.08994 · HTML: https://mlsanity.com/paper/2206.08994/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [Message Passing Least Squares Framework and its Application to Rotation Synchronization](https://mlsanity.com/paper/2007.13638/) (2020)
- [Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC](https://mlsanity.com/paper/1805.12279/) (2018)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Synchronizing Probability Measures on Rotations via Optimal Transport](https://mlsanity.com/paper/2004.00663/) (2020)
- [Near-Optimal Performance Bounds for Orthogonal and Permutation Group Synchronization via Spectral Methods](https://mlsanity.com/paper/2008.05341/) (2020)
- [Near-Optimal Joint Object Matching via Convex Relaxation](https://mlsanity.com/paper/1402.1473/) (2014)
- [Random Laplacian matrices and convex relaxations](https://mlsanity.com/paper/1504.03987/) (2015)
- [Synchronization over Z2 and community detection in multiplex signed networks with constraints](https://mlsanity.com/paper/1504.04061/) (2015)

## Built on by (most cited first, 10 of 10)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [ReSync: Riemannian Subgradient-based Robust Rotation Synchronization](https://mlsanity.com/paper/2305.15136/) (2023)
- [Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization](https://mlsanity.com/paper/2511.02329/) (2025)
- [OSP: Boosting Distributed Model Training with 2-stage Synchronization](https://mlsanity.com/paper/2306.16926/) (2023)
- [Robust Angular Synchronization via Directed Graph Neural Networks](https://mlsanity.com/paper/2310.05842/) (2023)
- [Certifiably Optimal Anisotropic Rotation Averaging](https://mlsanity.com/paper/2503.07353/) (2025)
- [Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares](https://mlsanity.com/paper/2306.04961/) (2023)
- [Incremental Rotation Averaging Revisited](https://mlsanity.com/paper/2309.16924/) (2023)
- [Higher-Order Group Synchronization](https://mlsanity.com/paper/2505.21932/) (2025)
- [TriDE: Triangle-Consistent Translation Directions for Global Camera Pose Estimation](https://mlsanity.com/paper/2605.06889/) (2026)

## Abstract (arXiv)

We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we thus refer to our method as detection and estimation of structural consistency (DESC). This general framework can be extended to other algebraic and geometric structures. Our formulation has the following advantages: it can tolerate corruption as high as the information-theoretic bound, it does not require a good initialization for the estimates of group elements, it has a simple interpretation, and under some mild conditions the global minimum of our objective function exactly recovers the corruption levels. We demonstrate the competitive accuracy of our approach on both synthetic and real data experiments of rotation averaging.