Shortcomings and capacities of real-constrained neural networks in complex spaces
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Computer Science > Machine Learning
Title:Shortcomings and capacities of real-constrained neural networks in complex spaces
Abstract: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. Our methods depend on Gardner volume 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.
| Comments: | First version |
| Subjects: | Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Probability (math.PR) |
| Cite as: | arXiv:2606.04390 [cs.LG] |
| (or arXiv:2606.04390v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.04390
arXiv-issued DOI via DataCite (pending registration)
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