Mathematics of Continual Learning
This work addresses the foundational problem of mathematical rigor in continual learning for researchers, though it is incremental as it primarily reviews and connects existing fields rather than introducing new methods.
This tutorial paper tackles the underdeveloped mathematical foundations of continual learning by establishing connections with the mathematically principled field of adaptive filtering, enabling enhancement of continual learning's theoretical basis and extension of adaptive filtering insights.
Continual learning is an emerging subject in machine learning that aims to solve multiple tasks presented sequentially to the learner without forgetting previously learned tasks. Recently, many deep learning based approaches have been proposed for continual learning, however the mathematical foundations behind existing continual learning methods remain underdeveloped. On the other hand, adaptive filtering is a classic subject in signal processing with a rich history of mathematically principled methods. However, its role in understanding the foundations of continual learning has been underappreciated. In this tutorial, we review the basic principles behind both continual learning and adaptive filtering, and present a comparative analysis that highlights multiple connections between them. These connections allow us to enhance the mathematical foundations of continual learning based on existing results for adaptive filtering, extend adaptive filtering insights using existing continual learning methods, and discuss a few research directions for continual learning suggested by the historical developments in adaptive filtering.