Parabolic Continual Learning
This addresses catastrophic forgetting for continual learning systems, representing an incremental methodological advance.
The authors tackled catastrophic forgetting in continual learning by introducing a parabolic PDE regularization approach that uses memory buffers as boundary conditions to bound expected error. They demonstrated empirical performance improvements on multiple continual learning tasks.
Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential equation (PDE) to regularize the expected behavior of the loss over time. This class of parabolic PDEs has a number of favorable properties that allow us to analyze the error incurred through forgetting and the error induced through generalization. Specifically, we do this through imposing boundary conditions where the boundary is given by a memory buffer. By using the memory buffer as a boundary, we can enforce long term dependencies by bounding the expected error by the boundary loss. Finally, we illustrate the empirical performance of the method on a series of continual learning tasks.