  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.
