The loss surface of deep and wide neural networks

• DOI: 10.48550/arxiv.1704.08045
• Publication Date: 2017-01-01
• Authors: Nguyen, Quynh; Hein, Matthias
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; Computer Science - Artificial Intelligence; Computer Vision and Pattern Recognition (cs.CV); Computer Science - Computer Vision and Pattern Recognition; Computer Science - Neural and Evolutionary Computing; Machine Learning (stat.ML); 02 engineering and technology; Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Statistics - Machine Learning; 0202 electrical engineering, electronic engineering, information engineering; Neural and Evolutionary Computing (cs.NE)

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is the case as all local minima are close to being globally optimal. We show that this is (almost) true, in fact almost all local minima are globally optimal, for a fully connected network with squared loss and analytic activation function given that the number of hidden units of one layer of the network is larger than the number of training points and the network structure from this layer on is pyramidal.<br/>ICML 2017. Main results now hold for larger classes of loss functions<br/>