Angular Gap: Reducing the Uncertainty of Image Difficulty through Model Calibration

Curriculum learning needs example difficulty to proceed from easy to hard. However, the credibility of image difficulty is rarely investigated, which can seriously affect the effectiveness of curricula. In this work, we propose Angular Gap, a measure of difficulty based on the difference in angular distance between feature embeddings and class-weight embeddings built by hyperspherical learning. To ascertain difficulty estimation, we introduce class-wise model calibration, as a post-training technique, to the learnt hyperbolic space. This bridges the gap between probabilistic model calibration and angular distance estimation of hyperspherical learning. We show the superiority of our calibrated Angular Gap over recent difficulty metrics on CIFAR10-H and ImageNetV2. We further propose Angular Gap based curriculum learning for unsupervised domain adaptation that can translate from learning easy samples to mining hard samples. We combine this curriculum with a state-of-the-art self-training method, Cycle Self Training (CST). The proposed Curricular CST learns robust representations and outperforms recent baselines on Office31 and VisDA 2017.