  Regularization is an effective way to promote the generalization performance
of machine learning models. In this paper, we focus on label smoothing, a form
of output distribution regularization that prevents overfitting of a neural
network by softening the ground-truth labels in the training data in an attempt
to penalize overconfident outputs. Existing approaches typically use
cross-validation to impose this smoothing, which is uniform across all training
data. In this paper, we show that such label smoothing imposes a quantifiable
bias in the Bayes error rate of the training data, with regions of the feature
space with high overlap and low marginal likelihood having a lower bias and
regions of low overlap and high marginal likelihood having a higher bias. These
theoretical results motivate a simple objective function for data-dependent
smoothing to mitigate the potential negative consequences of the operation
while maintaining its desirable properties as a regularizer. We call this
approach Structural Label Smoothing (SLS). We implement SLS and empirically
validate on synthetic, Higgs, SVHN, CIFAR-10, and CIFAR-100 datasets. The
results confirm our theoretical insights and demonstrate the effectiveness of
the proposed method in comparison to traditional label smoothing.
