IsoAct: Geometry-Aware Post-hoc Debiasing via Isometric Actions
Sumin Park, Taero Kim, Minhyeong Cho, Subeen Park, Jong Hwan Lee, Kyungwoo Song
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.
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