Multilayer feedforward networks are universal approximators
Neural Networks
Clifford algebra multilayer prceptrons
Geometric computing with Clifford algebras
Algebraic Aspects of Designing Behaviour Based Systems
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Learning Geometric Transformations with Clifford Neurons
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
Approximation by fully complex multilayer perceptrons
Neural Computation
Complex backpropagation neural network using elementary transcendental activation functions
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 200. on IEEE International Conference - Volume 02
Optimal learning rates for clifford neurons
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
The complex backpropagation algorithm
IEEE Transactions on Signal Processing
A conic higher order neuron based on geometric algebra and its implementation
MICAI'12 Proceedings of the 11th Mexican international conference on Advances in Computational Intelligence - Volume Part II
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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.