Multiscale FFT
An algorithm that uses uniform grids of different granularity within dyadic intervals and computes convolutions by FFT within each interval under a divide-and-conquer strategy. It reduces the time complexity of the PLD accountant from O(alpha^{-2}) to O(alpha^{-1} log(1/alpha)).
Timeline (last 90 days)
The multi-scale FFT algorithm proposed in the paper represents the likelihood ratio on a special grid: within each dyadic interval the grid is uniform, but different intervals have different granularity.
The multi-scale FFT algorithm reduces the runtime's dependence on α from O(α^{-2}) to O(α^{-1} log(1/α)).
Experiments show that under high-precision requirements, the multi-scale FFT algorithm can bring speedups of several orders of magnitude.
When combined with DP-SGD and the PREAMBLE mechanism, the multi-scale FFT algorithm can give improved privacy bounds.
In the future, the multi-scale FFT technique is expected to be integrated into mainstream DP libraries, promoting the standardization and practical adoption of privacy-preserving technologies.
All Facts (5)
The multi-scale FFT algorithm proposed in the paper represents the likelihood ratio on a special grid: within each dyadic interval the grid is uniform, but different intervals have different granularity.
50%UnverifiedThe multi-scale FFT algorithm reduces the runtime's dependence on α from O(α^{-2}) to O(α^{-1} log(1/α)).
50%UnverifiedExperiments show that under high-precision requirements, the multi-scale FFT algorithm can bring speedups of several orders of magnitude.
50%UnverifiedWhen combined with DP-SGD and the PREAMBLE mechanism, the multi-scale FFT algorithm can give improved privacy bounds.
50%UnverifiedIn the future, the multi-scale FFT technique is expected to be integrated into mainstream DP libraries, promoting the standardization and practical adoption of privacy-preserving technologies.
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