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 systematically propose a series of geometric measurements for perceptual manifolds in deep neural networks, and then 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. Therefore, 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. The code and model will be made public.

翻译：为解决长尾分类的挑战，研究者提出了多种减少模型偏差的方法，其中大多数假设样本量小的类别为弱类。然而，近期研究表明尾部类别并非总是难以学习，且在样本平衡数据集上也观察到模型偏差现象，暗示存在其他影响模型偏差的因素。本工作系统地提出了一套深度神经网络感知流形的几何度量方法，进而探究感知流形的几何特征对分类难度的影响，以及学习过程如何塑造感知流形的几何特征。一个出乎意料的发现是：训练过程中类别准确率与感知流形分离度之间的相关性逐渐减弱，而与曲率之间的负相关性逐渐增强，表明曲率不平衡导致了模型偏差。为此，我们提出曲率正则化方法，促使模型学习曲率平衡且更平缓的感知流形。在多个长尾与非长尾数据集上的评估表明，本方法具有卓越的性能和令人兴奋的泛化能力，尤其能基于现有最优技术实现显著的性能提升。本工作开启了模型偏差的几何分析视角，并提醒研究者关注非长尾甚至样本平衡数据集上的模型偏差问题。代码与模型将公开发布。