Complex-valued deep learning with differential privacy

Alexander Ziller, Dmitrii Usynin, Moritz Knolle, Kerstin Hammernik, Daniel Rueckert, Georgios Kaissis

Keywords: Differential privacy, complex-valued deep learning

Abstract: We present $\zeta$-DP, an extension of differential privacy (DP) to complex-valued functions. After introducing the complex Gaussian mechanism, whose properties we characterise in terms of $(\varepsilon, \delta)$-DP and Rényi-DP, we present $\zeta$-DP stochastic gradient descent ($\zeta$-DP-SGD), a variant of DP-SGD for training complex-valued neural networks. We experimentally evaluate $\zeta$-DP-SGD on three complex-valued tasks, i.e. electrocardiogram classification, speech classification and magnetic resonance imaging (MRI) reconstruction. Moreover, we provide $\zeta$-DP-SGD benchmarks for a large variety of complex-valued activation functions and on a complex-valued variant of the MNIST dataset. Our experiments demonstrate that DP training of complex-valued neural networks is possible with rigorous privacy guarantees and excellent utility.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.03478/code)