Maximum-and-Concatenation Networks

TL;DR

This paper introduces Maximum-and-Concatenation Networks (MCN), a novel deep learning architecture that improves local minima quality, enhances generalization, and can be integrated into existing models to boost performance.

Contribution

The paper proposes MCN, a new network architecture with theoretical guarantees on local minima improvement and approximation efficiency, advancing deep neural network training and generalization.

Findings

Every local minimum of an (l+1)-layer MCN can outperform the global minima of its first l layers.

MCN can approximate certain functions arbitrarily well with high efficiency.

MCN has a smaller covering number than many existing DNNs, leading to better generalization bounds.

Abstract

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, \emph{every local minimum of an $(l+1)$-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first $l$ layers}. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, \emph{it is easy to plug MCN into an existing deep model to make it also have this property}. Finally, under mild conditions, we show that MCN can approximate certain continuous functions arbitrarily well with \emph{high efficiency}; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.