Impact of Regularization on Calibration and Robustness: from the Representation Space Perspective

Recent studies have shown that regularization techniques using soft labels, e.g., label smoothing, Mixup, and CutMix, not only enhance image classification accuracy but also improve model calibration and robustness against adversarial attacks. However, the underlying mechanisms of such improvements remain underexplored. In this paper, we offer a novel explanation from the perspective of the representation space (i.e., the space of the features obtained at the penultimate layer). Our investigation first reveals that the decision regions in the representation space form cone-like shapes around the origin after training regardless of the presence of regularization. However, applying regularization causes changes in the distribution of features (or representation vectors). The magnitudes of the representation vectors are reduced and subsequently the cosine similarities between the representation vectors and the class centers (minimal loss points for each class) become higher, which acts as a central mechanism inducing improved calibration and robustness. Our findings provide new insights into the characteristics of the high-dimensional representation space in relation to training and regularization using soft labels.