Abstract We extend the entropy formula of Menon and Yu for the real Deep Linear Network (DLN) to its complex and quaternionic analogues, obtaining a unified formula for DLNs over R \mathbb{R} R C \mathbb{C} C H \mathbb{H} H
Explore similar work May 29, 2026 · Joseph Wilson, Chris van der Heide, Liam Hodgkinson +1 Reliable Uncertainty Quantification Logistic Regression
Jun 3, 2026 · cs.LG J/K move · Enter open · S save
Andrew Gracyk
Department of Mathematics Purdue University West Lafayette, IN 47907, United States
We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class. We use weights drawn from the complex Gaussian, which converge asymptotically in norm to the square root of dimension almost surely. Our methods depend on Gardner volume-type comparisons at critical capacity. Our proof relies on an application of the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, nonstandard in literature. With the HCIZ formula, we may obtain a more robust approximation for the final asymptotic ratio. This strategy is applicable to our work specifically since we integrate over the unitary and orthogonal compact manifolds, facilitated via the Weyl integration formula and the Haar measure.