  Continual learning aims to efficiently learn from a non-stationary stream of
data while avoiding forgetting the knowledge of old data. In many practical
applications, data complies with non-Euclidean geometry. As such, the commonly
used Euclidean space cannot gracefully capture non-Euclidean geometric
structures of data, leading to inferior results. In this paper, we study
continual learning from a novel perspective by exploring data geometry for the
non-stationary stream of data. Our method dynamically expands the geometry of
the underlying space to match growing geometric structures induced by new data,
and prevents forgetting by keeping geometric structures of old data into
account. In doing so, making use of the mixed curvature space, we propose an
incremental search scheme, through which the growing geometric structures are
encoded. Then, we introduce an angular-regularization loss and a
neighbor-robustness loss to train the model, capable of penalizing the change
of global geometric structures and local geometric structures. Experiments show
that our method achieves better performance than baseline methods designed in
Euclidean space.
