Shortcomings and capacities of real-constrained neural networks in complex spaces
Researchers have analyzed the storage capacities of neural networks when real pre-activations are enforced within complex hypothesis classes. Their work utilizes the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, a method not commonly found in this field, to derive a more stable approximation for the asymptotic ratio. This approach is specifically tailored for their research by integrating over unitary and orthogonal compact manifolds, employing the Weyl integration formula and the Haar measure. AI