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Research questionHow does restricting complex-valued neural networks to real pre-activations change asymptotic storage capacity?Complex-valued neural hypothesis classes may store different numbers of patterns depending on whether their pre-activations can remain complex or must be real. The key difficulty is quantifying this capacity change in the asymptotic limit.
Neural and Evolutionary Computing
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Shortcomings and capacities of real-constrained neural networks in complex spacesThe analysis studies complex-valued neural hypothesis classes with weights drawn from a complex Gaussian and derives an asymptotic capacity ratio using Gardner-volume comparisons. Its evidence is mathematical and asymptotic, relying on integrations over unitary and orthogonal compact manifolds; no empirical or finite-dimensional performance results are specified.research paper · Sep 2, 2026
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