Quantifying Training Membership Information in the Hyperspherical Embedding Geometry of Face Recognition Models

Face recognition models represent each face as an embedding vector on the unit hypersphere by clustering embeddings of the same identity while pushing different identities apart through angular-margin losses. Because these losses act only on training identities, non-member identities may form clusters with different geometric properties. In this paper, we quantify the magnitude of this difference and what training-time factors control it. We compute four statistics based on cluster geometry across 180 face recognition models in a factorial design over IResNet backbone size, loss head, training duration, and the number of training identities, and evaluate each configuration on nine benchmarks. Our results indicate that the number of training identities has the largest effect on member/non-member separability, while backbone and loss head contribute far less, and that, on a same-domain held-out reference, the geometric membership signal decreases monotonically as more identities are added to training. We provide an analysis of cross-domain (pose, age, quality, ethnicity) non-member benchmarks and report that these inflate the apparent membership signal. Finally, we fuse all four statistics with a learned classifier to reveal additional membership information beyond the best individual statistic.