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Vector-valued neural learning has emerged as a promising direction in deeplearning recently. Traditionally, training data for neural networks (NNs) areformulated as a vector of scalars; however, its performance may not be optimalsince associations among adjacent scalars are not modeled. In this paper, wepropose a new vector neural architecture called the Arbitrary BIlinear ProductNeural Network (ABIPNN), which processes information as vectors in each neuron,and the feedforward projections are defined using arbitrary bilinear products.Such bilinear products can include circular convolution, seven-dimensionalvector product, skew circular convolution, reversed- time circular convolution,or other new products not seen in previous work. As a proof-of-concept, weapply our proposed network to multispectral image denoising and singing voicesepa- ration. Experimental results show that ABIPNN gains substantialimprovements when compared to conventional NNs, suggesting that associationsare learned during training.

Backpropagation with N-D Vector-Valued Neurons Using Arbitrary Bilinear Products