  In speaker recognition, where speech segments are mapped to embeddings on the
unit hypersphere, two scoring back-ends are commonly used, namely cosine
scoring and PLDA. We have recently proposed PSDA, an analog to PLDA that uses
Von Mises-Fisher distributions instead of Gaussians. In this paper, we present
toroidal PSDA (T-PSDA). It extends PSDA with the ability to model within and
between-speaker variabilities in toroidal submanifolds of the hypersphere. Like
PLDA and PSDA, the model allows closed-form scoring and closed-form EM updates
for training. On VoxCeleb, we find T-PSDA accuracy on par with cosine scoring,
while PLDA accuracy is inferior. On NIST SRE'21 we find that T-PSDA gives large
accuracy gains compared to both cosine scoring and PLDA.
