2018/02/19 by Shiyu Liang, Ruoyu Sun, Liang, Shiyu +5 · 2 citations
Computer Science · #Advanced Neural Network Applications #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.1803.00909
openalex publication_date 2018/02/19 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
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.