-dimensional vector neuron

We describe a new neuron model, -dimensional vector neuron, which can deal with signals as one cluster, by extending the 3-dimensional vector neuron to dimensions naturally. The -bit parity problem which cannot be solved with a single usual real-valued neuron, can be solved with a single -dimensional vector neuron with the orthogonal decision boundary, which reveals the potent computational power of -dimensional vector neurons. Rumelhart, Hinton and Williams showed that increasing the number of layers made the computational power of neural networks high [Rumelhart et al., 1986a; Rumelhart et al., 1986b]. Here we show that extending the dimensionality of neural networks to dimensions originates the similar effect on neural networks.