Pairwise Margin Maximization for Deep Neural Networks
This work addresses a fundamental regularization issue in deep learning for multi-class classification, offering a novel approach that could enhance generalization in various applications.
The authors identified that the standard weight decay regularization, derived from SVM maximum margin, is suboptimal for multi-class deep neural networks, and proposed Pairwise Margin Maximization (PMM) as a new regularization scheme, demonstrating substantial empirical improvements in training.
The weight decay regularization term is widely used during training to constrain expressivity, avoid overfitting, and improve generalization. Historically, this concept was borrowed from the SVM maximum margin principle and extended to multi-class deep networks. Carefully inspecting this principle reveals that it is not optimal for multi-class classification in general, and in particular when using deep neural networks. In this paper, we explain why this commonly used principle is not optimal and propose a new regularization scheme, called {\em Pairwise Margin Maximization} (PMM), which measures the minimal amount of displacement an instance should take until its predicted classification is switched. In deep neural networks, PMM can be implemented in the vector space before the network's output layer, i.e., in the deep feature space, where we add an additional normalization term to avoid convergence to a trivial solution. We demonstrate empirically a substantial improvement when training a deep neural network with PMM compared to the standard regularization terms.