  We derive a new margin-based regularization formulation, termed multi-margin
regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by
principles that were applied in margin analysis of shallow linear classifiers,
e.g., support vector machine (SVM). Unlike SVM, MMR is continuously scaled by
the radius of the bounding sphere (i.e., the maximal norm of the feature vector
in the data), which is constantly changing during training. We empirically
demonstrate that by a simple supplement to the loss function, our method
achieves better results on various classification tasks across domains. Using
the same concept, we also derive a selective sampling scheme and demonstrate
accelerated training of DNNs by selecting samples according to a minimal margin
score (MMS). This score measures the minimal amount of displacement an input
should undergo until its predicted classification is switched. We evaluate our
proposed methods on three image classification tasks and six language text
classification tasks. Specifically, we show improved empirical results on
CIFAR10, CIFAR100 and ImageNet using state-of-the-art convolutional neural
networks (CNNs) and BERT-BASE architecture for the MNLI, QQP, QNLI, MRPC, SST-2
and RTE benchmarks.
