Recent research about margin theory has proved that maximizing the minimum margin like support vector machines does not necessarily lead to better performance, and instead, it is crucial to optimize the margin distribution. In the meantime, margin theory has been used to explain the empirical success of deep network in recent studies. In this paper, we present ODN (the Optimal margin Distribution Network), a network which embeds a loss function in regard to the optimal margin distribution. We give a theoretical analysis for our method using the PAC-Bayesian framework, which confirms the significance of the margin distribution for classification within the framework of deep networks. In addition, empirical results show that the ODN model always outperforms the baseline cross-entropy loss model consistently across different regularization situations. And our ODN
 model also outperforms the cross-entropy loss (Xent), hinge loss and soft hinge loss model in generalization task through limited training data.
This paper presents a deep neural network embedding a loss function in regard to the optimal margin distribution, which alleviates the overfitting problem theoretically and empirically. Presents a PAC-Bayesian bound for a margin loss