We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$ where $W_{ij}$ is a Gaussian random matrix and $Z_i^*$ is either an orthogonal matrix or a rotation matrix, and each $Y_{ij}$ is observed independently with probability $p$. We analyze an iterative polar decomposition algorithm for the estimation of $Z^*$ and show it has an error of $(1+o(1))\frac{\sigma ^2 d(d-1)}{2np}$ when initialized by spectral methods. A matching minimax lower bound is further established that leads to the optimality of the proposed algorithm as it achieves the exact minimax risk.
Synchronization Storage Channels (S2C): Timer-less Cache Side-Channel Attacks on the Apple M1 via Hardware Synchronization Instructions
- Award ID(s):
- 1816282
- PAR ID:
- 10477383
- Publisher / Repository:
- USENIX
- Date Published:
- Journal Name:
- 32nd USENIX Security Symposium
- Format(s):
- Medium: X
- Location:
- Anaheim, CA, USA
- Sponsoring Org:
- National Science Foundation
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