Building fair deep neural networks (DNNs) is a crucial step towards achieving trustworthy artificial intelligence. Delving into deeper factors that affect the fairness of DNNs is paramount and serves as the foundation for mitigating model biases. However, current methods are limited in accurately predicting DNN biases, relying solely on the number of training samples and lacking more precise measurement tools. Here, we establish a geometric perspective for analyzing the fairness of DNNs, comprehensively exploring how DNNs internally shape the intrinsic geometric characteristics of datasets-the intrinsic dimensions (IDs) of perceptual manifolds, and the impact of IDs on the fairness of DNNs. Based on multiple findings, we propose Intrinsic Dimension Regularization (IDR), which enhances the fairness and performance of models by promoting the learning of concise and ID-balanced class perceptual manifolds. In various image recognition benchmark tests, IDR significantly mitigates model bias while improving its performance.
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