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Recovery Theory for Projected Power Iterations in Permutation Synchronization

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

We study the projected power method (PPM) for synchronizing \(n\) unknown permutations of \(m\) objects under a possibly sparse uniform corruption model. Each pair is observed with probability \(p\), and an observed measurement is uncorrupted with probability \(π_0\) and is otherwise an independent uniform permutation. Under \(\log m=o(npπ_0^2)\), we prove exact one-step recovery (with high probability) of each prescribed block for an independent estimate with a fixed positive majority of correct blocks. When \(np\ge C_0\log n\) and \(m=o(npπ_0^2)\), we prove that one high-probability event yi

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