Discovering Intersectional Bias via Directional Alignment in Face Recognition Embeddings

Modern face recognition models embed identities on a unit hypersphere, where identity variation forms tight clusters. Conversely, shared semantic attributes can often be effectively approximated as linear directions in the latent space. Existing bias evaluation methods rely on predefined attribute labels, synthetic counterfactuals, or proximity-based clustering, all of which fail to capture intersectional subpopulations that emerge along latent directions. We introduce LatentAlign, an attribute-free algorithm that discovers semantically coherent and interpretable subpopulations by iteratively aligning embeddings along dominant latent directions. Unlike distance-based clustering, LatentAlign exploits the geometry of hyperspherical embeddings to isolate directional structures shared across identities, allowing for the interpretable discovery of attributes. Across four state-of-the-art recognition backbones (ArcFace, CosFace, ElasticFace, PartialFC) and two benchmarks (RFW, CelebA), LatentAlign consistently yields more semantically coherent groups than $k$-means, spherical $k$-means, nearest-neighbor search, and DBSCAN. Crucially, the discovered subpopulations expose severe intersectional vulnerabilities, with False Match Rates up to 4x higher than groups defined by explicit annotations. Our results show that by treating semantic attributes as directional features rather than spatial clusters, we can effectively isolate intersectional subpopulations and expose hidden biases that standard audits miss.