  Real-world data are long-tailed, the lack of tail samples leads to a
significant limitation in the generalization ability of the model. Although
numerous approaches of class re-balancing perform well for moderate class
imbalance problems, additional knowledge needs to be introduced to help the
tail class recover the underlying true distribution when the observed
distribution from a few tail samples does not represent its true distribution
properly, thus allowing the model to learn valuable information outside the
observed domain. In this work, we propose to leverage the geometric information
of the feature distribution of the well-represented head class to guide the
model to learn the underlying distribution of the tail class. Specifically, we
first systematically define the geometry of the feature distribution and the
similarity measures between the geometries, and discover four phenomena
regarding the relationship between the geometries of different feature
distributions. Then, based on four phenomena, feature uncertainty
representation is proposed to perturb the tail features by utilizing the
geometry of the head class feature distribution. It aims to make the perturbed
features cover the underlying distribution of the tail class as much as
possible, thus improving the model's generalization performance in the test
domain. Finally, we design a three-stage training scheme enabling feature
uncertainty modeling to be successfully applied. Experiments on
CIFAR-10/100-LT, ImageNet-LT, and iNaturalist2018 show that our proposed
approach outperforms other similar methods on most metrics. In addition, the
experimental phenomena we discovered are able to provide new perspectives and
theoretical foundations for subsequent studies.
