A backpropagation algorithm for neural networks based an 3D vector product

A 3D vector version of the backpropagation algorithm is proposed for multilayered neural networks in which vector product operation is performed, and whose weights, threshold values, input and output signals are all 3D real numbered vectors. This new algorithm can be used to learn patterns consisted of 3D vectors in a natural way. The XOR problem was used to successfully test the new formulation.

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