The deep arbitrary polynomial chaos neural network or how Deep Artificial Neural Networks could benefit from data-driven homogeneous chaos theory

Sergey Oladyshkin, Timothy Praditia, Ilja Kröker, Farid Mohammadi, Wolfgang Nowak, Sebastian Otte

Abstract: Highlights•Kernel structure reformulation of deep artificial neural networks in terms of homogeneous chaos theory.•Response on each node of the deep network represented through polynomial chaos expansion.•Orthonormal decomposition mitigates the non-optimal representation while processing the neural signal.•Accounting for high-order effects reflecting simultaneous neural impacts.•Analytical estimation of mean and variance of neural signal on each node is provided.