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 Cartesian real, polar, phase-only, magnitude-only, parameter-matched real, and FLOP-matched real baselines.
This research emerges as AI's frontier expands, requiring more sophisticated computational methods to handle complex data structures and improve model efficiency and performance.
Understanding when complex-valued neural networks offer tangible benefits can guide AI researchers and developers in selecting optimal architectures, potentially leading to breakthroughs in specific domains.
This study provides a more rigorous framework for evaluating CVNNs, moving beyond simple complex-valued inputs to a deeper understanding of their representational, geometric, and optimization advantages.
- · AI researchers
- · Machine learning developers
- · Signal processing sectors
- · AI projects using CVNNs without clear justification
- · Academic groups focusing solely on real-valued networks
- · Developers neglecting representational advantages
Improved performance and efficiency in AI applications where data is naturally complex-valued, such as telecommunications or quantum computing simulations.
A broader adoption of CVNNs in specialized AI domains, necessitating new curriculum development and tools tailored for complex arithmetic.
Potential for new AI hardware accelerators optimized for complex number operations, leading to specialized compute architectures.
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Read at arXiv cs.LG