Piecewise Linear Neural Networks and Deep Learning

TL;DR

This paper systematically reviews Piecewise Linear Neural Networks (PWLNNs), their representations, learning algorithms, theoretical foundations, and applications in deep learning, highlighting their evolution and recent successes.

Contribution

It provides a comprehensive overview of PWLNN methodologies, including models, algorithms, theory, and applications, with a focus on deep learning advancements.

Findings

PWLNNs have evolved from shallow to deep architectures.

ReLU has popularized PWLNNs in deep learning.

PWLNNs achieve advantageous performance in various tasks.

Abstract

As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In 1977, the canonical representation pioneered the works of shallow PWLNNs learned by incremental designs, but the applications to large-scale data were prohibited. In 2010, the Rectified Linear Unit (ReLU) advocated the prevalence of PWLNNs in deep learning. Ever since, PWLNNs have been successfully applied to extensive tasks and achieved advantageous performances. In this Primer, we systematically introduce the methodology of PWLNNs by grouping the works into shallow and deep networks. Firstly, different PWLNN representation models are constructed with elaborated examples. With PWLNNs, the evolution of learning algorithms for data is presented and fundamental theoretical analysis follows up for in-depth understandings. Then, representative applications are introduced together with discussions and outlooks.