A Theory of Neural Computation with Clifford Algebras

The present thesis introduces Clifford Algebra as a framework for neural computation. Neural computation with Clifford algebras is model-based. This principle is established by constructing Clifford algebras from quadratic spaces. Then the subspace grading inherent to any Clifford algebra is introduced. The above features of Clifford algebras are then taken as motivation for introducing the Basic Clifford Neuron (BCN). As a second type of Clifford neuron the Spinor Clifford Neuron is presented. A systematic basis for Clifford neural computation is provided by the important notions of isomorphic Clifford neurons and isomorphic representations. After the neuron level is established, the discussion continues with (Spinor) Clifford Multilayer Perceptrons. First, (Spinor) Clifford Multilayer Perceptrons with real-valued activation functions ((S)CMLPs) are studied. A generic Backpropagation algorithm for CMLPs is derived. Also, universal approximation theorems for (S)CMLPs are presented. Finally, CMLPs with Clifford-valued activation functions are studied.

Preview

Rights

Use and reproduction:

No license. The provisions of the German Copyright Act (UrhG) apply.

Please note that individual components of the publication may be subject to other licensing or copyright conditions.

Cite

Citation style:
Could not load citation form.