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arXiv · 2007.04630

Maximum-and-Concatenation Networks

Xingyu Xie·Hao Kong·Jianlong Wu·Wayne Zhang·Guangcan Liu·Zhouchen Lin
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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.

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Xingyu Xie, Hao Kong, Jianlong Wu, Wayne Zhang, Guangcan Liu, Zhouchen Lin. 2020-07-09. Maximum-and-Concatenation Networks. https://arxiv.org/abs/2007.04630

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