On Clifford neurons and Clifford multi-layer perceptrons.
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.
Buchholz
Sven
S
Cognitive Systems Group, University of Kiel, Christian-Albrechts-Platz 4, 24118 Kiel, Germany. sbh@ks.informatik.uni-kiel.de
Sommer
Gerald
G
D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D012815:Signal Processing, Computer-Assisted