Representation of Neural Networks on Tensor- Product Basis

The paper introduces a tensor-product-based alternative to approximate neural network models based on locally identified ones. The proposed approach may be a useful tool for solving many kind of black-box like identification problems. The main idea is based upon the approximation of a parameter varying system by locally identified neural network (NN) models in the parameter space on tensor-product form basis. The weights in the corresponding layers of the input local models are jointly expressed in tensor-product form such a way ensuring the efficient approximation. First the theoretical background of the higher order singular value decomposition and the tensor-product representation are introduced followed by the description of how this form can be applied for NN model approximation.