When do complex-valued neural networks help? A study of representation, geometry, and optimization

arXiv:2605.27673v1 Announce Type: new Abstract: Complex-valued Neural Networks (CVNNs) are often motivated by domains where information is naturally encoded in magnitude and phase. Yet complex-valued inputs alone do not determine when complex arithmetic improves learning: the label signal may lie in amplitude, phase, their coupling, or a symmetry that real-valued models can also represent under suitable coordinates. We study this through a representation-first evaluation of CVNNs against Cartes