Complex-valued amplitude-phase interference modeling for adversarially robust classification

Deep neural networks have achieved remarkable progress in computer vision and related tasks. However, their high sensitivity to even subtle adversarial perturbations still limits their deployment in safety-critical applications. Although adversarial training can substantially improve model robustness, existing classification heads remain primarily based on softmax and its margin-based angular variants. Such decision formulations are constrained by fixed linear or angular spaces, making it difficult to capture more flexible decision boundaries. To this end, we propose a complex-valued amplitude-phase interference method (CAPI), inspired by the idea of probabilistic amplitude superposition in quantum interference. By adopting a multi-branch complex-amplitude formulation, in which phase differences govern constructive or destructive interference and amplitudes modulate the interference strength, CAPI introduces structured constraints at the decision stage, thereby improving model robustness against adversarial perturbations. Experimental results on benchmark datasets demonstrate that CAPI exhibits robust classification performance under FGSM, BIM, MIM, PGD, and AA attacks, validating its effectiveness under adversarial perturbations.