Distal Interference: Exploring the Limits of Model-Based Continual Learning
Heinrich van Deventer, Anna Sergeevna Bosman
TL;DR
This work defines distal interference as non-local changes in model outputs under gradient updates and proves that a uniformly trainable, distal-interference-free model requires exponential parameter counts, challenging practical model-only continual learning. It introduces ABEL-Splines, a min-distal orthogonal spline-based architecture with antisymmetric exponential layers that achieve universal function approximation while maintaining sparse activity and bounded gradients. Through theoretical analysis and targeted experiments, the paper shows that weaker min-distal guarantees are insufficient for robust continual learning and that pure polynomial-complexity models still struggle without data augmentation or replay techniques. The study suggests exploring intermediate architectures or augmentation strategies to enable practical continual learning with polynomial complexity.
Abstract
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.