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We show that the core reasons that complex and hypercomplex valued neuralnetworks offer improvements over their real-valued counterparts is the weightsharing mechanism and treating multidimensional data as a single entity. Theiralgebra linearly combines the dimensions, making each dimension related to theothers. However, both are constrained to a set number of dimensions, two forcomplex and four for quaternions. Here we introduce novel vector mapconvolutions which capture both of these properties provided bycomplex/hypercomplex convolutions, while dropping the unnatural dimensionalityconstraints they impose. This is achieved by introducing a system that mimicsthe unique linear combination of input dimensions, such as the Hamilton productfor quaternions. We perform three experiments to show that these novel vectormap convolutions seem to capture all the benefits of complex and hyper-complexnetworks, such as their ability to capture internal latent relations, whileavoiding the dimensionality restriction.

Generalizing Complex/Hyper-complex Convolutions to Vector Map Convolutions