Robust Group Synchronization via Cycle-Edge Message Passing
This work addresses robust synchronization in group settings, which is incremental as it builds on existing methods by incorporating cycle consistency for improved corruption handling.
The paper tackles the group synchronization problem under adversarial or uniform corruption and small noise by proposing a message passing procedure that uses cycle consistency to estimate corruption levels, achieving exact recovery and linear convergence guarantees as long as corrupted cycles per edge are bounded by a constant.
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.