  To address the challenges of long-tailed classification, researchers have
proposed several approaches to reduce model bias, most of which assume that
classes with few samples are weak classes. However, recent studies have shown
that tail classes are not always hard to learn, and model bias has been
observed on sample-balanced datasets, suggesting the existence of other factors
that affect model bias. In this work, we first establish a geometric
perspective for analyzing model fairness and then systematically propose a
series of geometric measurements for perceptual manifolds in deep neural
networks. Subsequently, we comprehensively explore the effect of the geometric
characteristics of perceptual manifolds on classification difficulty and how
learning shapes the geometric characteristics of perceptual manifolds. An
unanticipated finding is that the correlation between the class accuracy and
the separation degree of perceptual manifolds gradually decreases during
training, while the negative correlation with the curvature gradually
increases, implying that curvature imbalance leads to model bias.Building upon
these observations, we propose curvature regularization to facilitate the model
to learn curvature-balanced and flatter perceptual manifolds. Evaluations on
multiple long-tailed and non-long-tailed datasets show the excellent
performance and exciting generality of our approach, especially in achieving
significant performance improvements based on current state-of-the-art
techniques. Our work opens up a geometric analysis perspective on model bias
and reminds researchers to pay attention to model bias on non-long-tailed and
even sample-balanced datasets.
