  Noisy labels are ubiquitous in real-world datasets, which poses a challenge
for robustly training deep neural networks (DNNs) since DNNs can easily overfit
to the noisy labels. Most recent efforts have been devoted to defending noisy
labels by discarding noisy samples from the training set or assigning weights
to training samples, where the weight associated with a noisy sample is
expected to be small. Thereby, these previous efforts result in a waste of
samples, especially those assigned with small weights. The input $x$ is always
useful regardless of whether its observed label $y$ is clean. To make full use
of all samples, we introduce a manifold regularizer, named as Paired Softmax
Divergence Regularization (PSDR), to penalize the Kullback-Leibler (KL)
divergence between softmax outputs of similar inputs. In particular, similar
inputs can be effectively generated by data augmentation. PSDR can be easily
implemented on any type of DNNs to improve the robustness against noisy labels.
As empirically demonstrated on benchmark datasets, our PSDR impressively
improve state-of-the-art results by a significant margin.
