Tensor-based Polynomial Features Generation for High-order Neural Networks

This paper discusses the methods and algorithms for polynomial features generation. The polynomial features generation is the very first step for the High-order Neural Units evaluation. The algorithms for polynomial features generation based on recursive calls are memory effective; however, these algorithms can not benefit from the modern hardware optimizations for neural networks focused on fast tensor operations on GPUs (Graphic Processing Units) and TPUs (Tensor Processing units). Moreover, the recursive calls with many operations are limiting for the application of automatic differentiation algorithms. That makes the design of a high order neural network with HONU in the later than the first hidden layer challenging. The tensor-based algorithm for polynomial features generation that tries to leverage TPU and GPU hardware architecture is introduced in this paper. The tensor-based algorithm's implementation is tested and compared with a straight-forward recursive algorithm and with SciKit-learn library implementation in Python programming language.