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To address the challenges of long-tailed classification, researchers haveproposed several approaches to reduce model bias, most of which assume thatclasses with few samples are weak classes. However, recent studies have shownthat tail classes are not always hard to learn, and model bias has beenobserved on sample-balanced datasets, suggesting the existence of other factorsthat affect model bias. In this work, we first establish a geometricperspective for analyzing model fairness and then systematically propose aseries of geometric measurements for perceptual manifolds in deep neuralnetworks. Subsequently, we comprehensively explore the effect of the geometriccharacteristics of perceptual manifolds on classification difficulty and howlearning shapes the geometric characteristics of perceptual manifolds. Anunanticipated finding is that the correlation between the class accuracy andthe separation degree of perceptual manifolds gradually decreases duringtraining, while the negative correlation with the curvature graduallyincreases, implying that curvature imbalance leads to model bias.Building uponthese observations, we propose curvature regularization to facilitate the modelto learn curvature-balanced and flatter perceptual manifolds. Evaluations onmultiple long-tailed and non-long-tailed datasets show the excellentperformance and exciting generality of our approach, especially in achievingsignificant performance improvements based on current state-of-the-arttechniques. Our work opens up a geometric analysis perspective on model biasand reminds researchers to pay attention to model bias on non-long-tailed andeven sample-balanced datasets.

Predicting and Enhancing the Fairness of DNNs with the Curvature of Perceptual Manifolds