Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race, gender) do not merely shift data distributions but causally warp the geometry of the data manifold itself. To address this, we introduce Causal Manifold Fairness (CMF), a novel framework that bridges causal inference and geometric deep learning. CMF learns a latent representation where the local Riemannian geometry, defined by the metric tensor and curvature, remains invariant under counterfactual interventions on sensitive attributes. By enforcing constraints on the Jacobian and Hessian of the decoder, CMF ensures that the rules of the latent space (distances and shapes) are preserved across demographic groups. We validate CMF on synthetic Structural Causal Models (SCMs), demonstrating that it effectively disentangles sensitive geometric warping while preserving task utility, offering a rigorous quantification of the fairness-utility trade-off via geometric metrics.

翻译：机器学习公平性日益关键，然而标准方法通常将数据视为高维空间中的静态点，忽略了底层的生成结构。我们认为敏感属性（如种族、性别）不仅会移动数据分布，还会因果性地扭曲数据流形本身的几何结构。为解决此问题，我们提出了因果流形公平性（CMF），这是一个连接因果推断与几何深度学习的新颖框架。CMF学习一种潜在表示，其中由度量张量和曲率定义的局部黎曼几何在对敏感属性进行反事实干预时保持不变。通过对解码器的雅可比矩阵和海森矩阵施加约束，CMF确保了潜在空间的规则（距离和形状）在不同人口群体间得以保持。我们在合成结构因果模型（SCMs）上验证了CMF，证明其能有效解耦敏感的几何扭曲，同时保持任务效用，并通过几何度量提供了对公平性-效用权衡的严格量化。