  In this paper, we aim at introducing a new machine learning model, namely
reconciled polynomial machine, which can provide a unified representation of
existing shallow and deep machine learning models. Reconciled polynomial
machine predicts the output by computing the inner product of the feature
kernel function and variable reconciling function. Analysis of several concrete
models, including Linear Models, FM, MVM, Perceptron, MLP and Deep Neural
Networks, will be provided in this paper, which can all be reduced to the
reconciled polynomial machine representations. Detailed analysis of the
learning error by these models will also be illustrated in this paper based on
their reduced representations from the function approximation perspective.
