IsoAct: Geometry-Aware Post-hoc Debiasing via Isometric Actions

Learning representations that are robust to nuisance factors is essential for reliable deployment, but remains challenging when the representations lie on non-Euclidean manifolds. Existing debiasing methods typically assume Euclidean representations or apply linear interventions, which can distort the geometry of structured latent spaces. We propose IsoAct, a post-hoc framework that accounts for geometry in both nuisance identification and representation editing. It identifies nuisance-predictive directions using Fisher discriminant analysis (FDA) in tangent coordinates and applies corrections through manifold-native actions that preserve manifold membership. Controlled and real-world experiments on hyperspherical, hyperbolic, and $\mathrm{SE}(3)$ representations evaluate nuisance reduction, utility preservation, and manifold validity jointly. IsoAct reduces nuisance recoverability while retaining competitive utility. Its clearest joint result is on KLIFS, combining reduced kinase-group recoverability, strong structural prediction, and valid rigid poses.