Learning Representations on the Unit Sphere: Investigating Angular Gaussian and von Mises-Fisher Distributions for Online Continual Learning

arXiv:2306.03364v4 Announce Type: replace
Abstract: We use the maximum a posteriori estimation principle for learning representations distributed on the unit sphere. We propose to use the angular Gaussian distribution, which corresponds to a Gaussian projected on the unit-sphere and derive the associated loss function. We also consider the von Mises-Fisher distribution, which is the conditional of a Gaussian in the unit-sphere. The learned representations are pushed toward fixed directions, which are the prior means of the Gaussians; allowing for a …

angular arxiv continual cs.cv cs.lg fisher sphere type