让模型学习对敏感属性不变的几何结构，提升公平性。
Causal Manifold Fairness: Enforcing Geometric Invariance in Representation Learning
- 通过因果干预约束潜在空间的度量与曲率，保持几何不变性。
- 在合成数据上实现敏感属性引起的几何扭曲有效解耦。
- 适合关注公平性与表示学习结合的研究者。
机器学习中的公平性日益重要，但传统方法常将数据视为高维空间中的静态点，忽略了其生成结构。我们提出敏感属性（如种族、性别）不仅改变数据分布，更会因果性地扭曲数据流形的几何结构。为此，我们引入因果流形公平性（CMF），融合因果推断与几何深度学习。CMF 学习一个潜在表示，其中局部黎曼几何（由度量张量和曲率定义）在对敏感属性进行反事实干预时保持不变。通过约束解码器的雅可比矩阵和海森矩阵，确保不同人口群体间的潜在空间规则（距离与形状）一致。我们在合成结构性因果模型（SCMs）上验证了该方法，证明其能有效解耦敏感属性导致的几何扭曲，同时保留任务性能，并通过几何度量精确量化公平性与效用的权衡。
原文摘要 · Abstract (English)
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.
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