C2AM Loss: Chasing a Better Decision Boundary for Long-Tail Object Detection

Long-tail object detection suffers from poor performance on tail categories. We reveal that the real culprit lies in the extremely imbalanced distribution of the classifier's weight norm. For conventional softmax cross-entropy loss, such imbalanced weight norm distribution yields ill conditioned decision boundary for categories which have small weight norms. To get rid of this situation, we choose to maxi-mize the cosine similarity between the learned feature and the weight vector of target category rather than the inner-product of them. The decision boundary between any two categories is the angular bisector of their weight vectors. Whereas, the absolutely equal decision boundary is sub-optimal because it reduces the model's sensitivity to vari-ous categories. Intuitively, categories with rich data diver-sity should occupy a larger area in the classification space while categories with limited data diversity should occupy a slightly small space. Hence, we devise a Category-Aware Angular Margin Loss (C2AM Loss) to introduce an adaptive angular margin between any two categories. Specif-ically, the margin between two categories is proportional to the ratio of their classifiers' weight norms. As a result, the decision boundary is slightly pushed towards the cat-egory which has a smaller weight norm. We conduct comprehensive experiments on LVIS dataset. C2AM Loss brings 4.9~5.2 AP improvements on different detectors and back-bones compared with baseline.