Robust Group Synchronization via Cycle-Edge Message Passing

Gilad Lerman, Yunpeng Shi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently solve the synchronization problem in our setting. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish exact recovery with high probability under a common uniform corruption model.

Original languageEnglish (US)
Pages (from-to)1665-1741
Number of pages77
JournalFoundations of Computational Mathematics
Issue number6
StatePublished - Dec 2022

Bibliographical note

Funding Information:
This work was supported by NSF award DMS-1821266.

Publisher Copyright:
© 2021, The Author(s).


  • Exact recovery
  • Group synchronization
  • Message passing
  • Robust estimation


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