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Understanding the Loss Surface of Single-Layered Neural Networks for Binary Classification
Shiyu Liang, Ruoyu Sun, Yixuan Li, R.Srikant
Feb 12, 2018 (modified: Feb 12, 2018)ICLR 2018 Workshop Submissionreaders: everyone
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.
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