Open Peer Review. Open Publishing. Open Access. Open Discussion. Open Directory. Open Recommendations. Open API. Open Source.
Understanding the Loss Surface of Single-Layered Neural Networks for Binary Classification
Shiyu Liang, Ruoyu Sun, Yixuan Li, R.Srikant
Feb 12, 2018 (modified: Jun 04, 2018)ICLR 2018 Workshop Submissionreaders: everyoneShow Bibtex
Abstract:It is widely conjectured that the reason that training algorithms for neural networks are successful because all local minima lead to similar performance; for example, see (LeCun et al., 2015; Choromanska et al., 2015; Dauphin et al., 2014). Performance is typically measured in terms of two metrics: training performance and generalization performance. Here we focus on the training performance of single-layered neural networks for binary classification, and provide conditions under which the training error is zero at all local minima of a smooth hinge loss function. Our conditions are roughly in the following form: the neurons have to be strictly convex and the surrogate loss function should be a smooth version of hinge loss. We also provide counterexamples to show that when the loss function is replaced with quadratic loss or logistic loss, the result may not hold.
Enter your feedback below and we'll get back to you as soon as possible.