Distal Interference: Exploring the Limits of Model-Based Continual Learning

Continual learning is the sequential learning of different tasks by a machine learning model. Continual learning is known to be hindered by catastrophic interference or forgetting, i.e. rapid unlearning of earlier learned tasks when new tasks are learned. Despite their practical success, artificial neural networks (ANNs) are prone to catastrophic interference. This study analyses how gradient descent and overlapping representations between distant input points lead to distal interference and catastrophic interference. Distal interference refers to the phenomenon where training a model on a subset of the domain leads to non-local changes on other subsets of the domain. This study shows that uniformly trainable models without distal interference must be exponentially large. A novel antisymmetric bounded exponential layer B-spline ANN architecture named ABEL-Spline is proposed that can approximate any continuous function, is uniformly trainable, has polynomial computational complexity, and provides some guarantees for distal interference. Experiments are presented to demonstrate the theoretical properties of ABEL-Splines. ABEL-Splines are also evaluated on benchmark regression problems. It is concluded that the weaker distal interference guarantees in ABEL-Splines are insufficient for model-only continual learning. It is conjectured that continual learning with polynomial complexity models requires augmentation of the training data or algorithm.