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Deep-learning architectures for classification problems involve thecross-entropy loss sometimes assisted with auxiliary loss functions like centerloss, contrastive loss and triplet loss. These auxiliary loss functionsfacilitate better discrimination between the different classes of interest.However, recent studies hint at the fact that these loss functions do not takeinto account the intrinsic angular distribution exhibited by the low-level andhigh-level feature representations. This results in less compactness betweensamples from the same class and unclear boundary separations between dataclusters of different classes. In this paper, we address this issue byproposing the use of geometric constraints, rooted in Riemannian geometry.Specifically, we propose Angular Margin Contrastive Loss (AMC-Loss), a new lossfunction to be used along with the traditional cross-entropy loss. The AMC-Lossemploys the discriminative angular distance metric that is equivalent togeodesic distance on a hypersphere manifold such that it can serve a cleargeometric interpretation. We demonstrate the effectiveness of AMC-Loss byproviding quantitative and qualitative results. We find that although theproposed geometrically constrained loss-function improves quantitative resultsmodestly, it has a qualitatively surprisingly beneficial effect on increasingthe interpretability of deep-net decisions as seen by the visual explanationsgenerated by techniques such as the Grad-CAM. Our code is available athttps://github.com/hchoi71/AMC-Loss.

AMC-Loss: Angular Margin Contrastive Loss for Improved Explainability in Image Classification