On Clifford neurons and Clifford multi-layer perceptrons.

Abstract

We study the framework of Clifford algebra for the design of neural architectures capable of processing different geometric entities. The benefits of this model-based computation over standard real-valued networks are demonstrated. One particular example thereof is the new class of so-called Spinor Clifford neurons. The paper provides a sound theoretical basis to Clifford neural computation. For that purpose the new concepts of isomorphic neurons and isomorphic representations are introduced. A unified training rule for Clifford MLPs is also provided. The topic of activation functions for Clifford MLPs is discussed in detail for all two-dimensional Clifford algebras for the first time.