Perturbing the Phase: Analyzing Adversarial Robustness of Complex-Valued Neural Networks

Complex-valued neural networks (CVNNs) are rising in popularity for all kinds of applications. To safely use CVNNs in practice, analyzing their robustness against outliers is crucial. One well known technique to understand the behavior of deep neural networks is to investigate their behavior under adversarial attacks, which can be seen as worst case minimal perturbations. We design Phase Attacks, a kind of attack specifically targeting the phase information of complex-valued inputs. Additionally, we derive complex-valued versions of commonly used adversarial attacks. We show that in some scenarios CVNNs are more robust than RVNNs and that both are very susceptible to phase changes with the Phase Attacks decreasing the model performance more, than equally strong regular attacks, which can attack both phase and magnitude.

Key Contributions

• Phase Attack: a novel adversarial attack specifically targeting the phase information of complex-valued inputs, shown to be more effective than standard attacks of equal perturbation strength
• Complex-valued formulations of standard gradient-based adversarial attacks (e.g., FGSM, PGD) applicable to CVNNs
• Comparative robustness analysis between CVNNs and RVNNs under phase, magnitude, and standard adversarial attacks, with an open-source PyTorch toolbox

🛡️ Threat Analysis

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