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.

构建公平的深度神经网络是实现可信的人工智能的关键步骤。深入研究影响深度神经网络公平性的因素是减轻模型偏见的基础，但目前的方法在准确预测深度神经网络偏见方面存在局限性，仅依赖于训练样本数量并缺乏更精确的测量工具。在这里，我们建立了一个几何学视角来分析深度神经网络的公平性，全面探索了深度神经网络内部如何塑造数据集的本质几何特征-感知流形的本质维度和维度对深度神经网络公平性的影响。基于多项发现，我们提出了内在维度正则化（IDR）的方法，通过促进学习简洁而平衡的类别感知流形，增强模型的公平性和性能。在各种图像识别基准测试中，IDR显著减轻模型偏见并改善其性能。

揭示和减缓DNNs的一般偏差通过感知流形的内在维度