  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 learning strategy
that is resilient to data drift. This makes it suitable for online continual
learning, which is the problem of training neural networks on a continuous data
stream, where multiple classification tasks are presented sequentially so that
data from past tasks are no longer accessible, and data from the current task
can be seen only once. To address this challenging scenario, we propose a
memory-based representation learning technique equipped with our new loss
functions. Our approach does not require negative data or knowledge of task
boundaries and performs well with smaller batch sizes while being
computationally efficient. We demonstrate with extensive experiments that the
proposed method outperforms the current state-of-the-art methods on both
standard evaluation scenarios and realistic scenarios with blurry task
boundaries. For reproducibility, we use the same training pipeline for every
compared method and share the code at https://github.com/Nicolas1203/ocl-fd.
