Group Synchronization: Fast Initialization and Sheaf-Theoretic Structure
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Luo, Yiran
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Abstract
Group synchronization estimates unknown group elements from noisy pairwise relative measurements on a graph. This thesis studies the problem through two independent but connected contributions. The first develops FAST-Sync, a fast linear initialization method for synchronization over matrix Lie groups. The second develops a sheaf-theoretic formulation that interprets exact synchronization as a global-section problem and noisy residuals through a local perturbation sheaf and its Hodge decomposition.
Both contributions are organized around the same local-to-global structure: vertex states must explain edge measurements while respecting gauge freedom and cycle consistency. Together they provide a computational method for fast initialization and a geometric language for understanding the residual structure left by noisy synchronization problems.
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Date
2026-05
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Undergraduate Thesis