Training Deep Neural Networks with Virtual Smoothing Classes

Learning with softmax cross-entropy on one-hot labels often leads to overconfidence on the correct class. While label smoothing regulates this overconfidence by redistributing some confidence from the correct class to other incorrect classes, it compromises the representation in the logits about the similarity between samples of different classes and may hurt calibration if higher confidence is required for high accuracy. To overcome these limitations, we propose a Virtual Smoothing (VS) label that redistributes certain confidence from the correct class to additional VS classes to regularize overconfidence. In VS labels, the VS class nodes act as adversaries to the original class nodes, enforcing regularization by clustering samples across all classes. The zero confidence assigned to each incorrect class also allows the incorrect logits to be different from each other without erasing information about sample similarities. The prediction probability can still approach 1 when applying softmax to the logits of the original real classes, which avoids harming but consistently improves calibration. Experiments show that VS labels consistently improve accuracy and calibration while providing better logits for improved knowledge distillation. Additionally, VS labels exhibit effectiveness in improving adversarial training, robust distillation, and out-of-distribution detection.