Exploring Data Geometry for Continual Learning

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 in-ferior 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 pre-vents forgetting by keeping geometric structures of old data into account. In doing so, making use of the mixed cur-vature space, we propose an incremental search scheme, through which the growing geometric structures are en-coded. Then, we introduce an angular-regularization loss and a neighbor-robustness loss to train the model, capa-ble 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.