An Algorithm for Training Polynomial Networks

TL;DR

This paper introduces the Basis Learner, an efficient layer-by-layer algorithm for training deep polynomial networks with quadratic nodes, capable of reducing training error to zero and outperforming shallow polynomial models.

Contribution

The paper presents a novel universal training algorithm for deep quadratic networks, with practical implementations and experimental validation.

Findings

Training error decreases at each iteration

Algorithm can reach zero training error under mild conditions

Deep polynomial networks outperform shallow models in experiments

Abstract

We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.