Causal Manifold Fairness: Enforcing Geometric Invariance in Representation Learning
Vidhi Rathore
TL;DR
This work addresses fairness by enforcing invariance of the local Riemannian geometry of latent representations under counterfactual interventions on sensitive attributes. It introduces Causal Manifold Fairness (CMF), which regularizes the decoder's Jacobian and Hessian to keep the pullback metric $G(z)$ and curvature $H_k(z)$ stable across factual and counterfactual worlds, within a Structural Causal Model. On a Warped Swiss Roll SCM, CMF achieves near-perfect geometric invariance while preserving predictive utility, albeit with increased reconstruction error due to trading off warping ability for invariance. The results demonstrate a principled, geometry-based fairness-utility trade-off and point to scalable extensions via Hessian-vector methods and graph-structured data.
Abstract
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.