Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps

In this paper, we introduce a new decomposition of multivariate maps that generalizes the decoupling problem recently proposed in the system identification community. In the context of neural networks, this decomposition can be seen as a two-layer feedforward network with flexible activation functions. We show that for such maps the Jacobian and Hessian tensors admit Para Tuck and CP decompositions respectively. We propose a methodology to perform the two-layer decoupling of the given polynomial maps based on joint Para Tuck and CP decomposition, by combining first and second-order information.