Rethinking Quadratic Regularizers: Explicit Movement Regularization for Continual Learning

Quadratic regularizers are often used for mitigating catastrophic forgetting in deep neural networks (DNNs), but are unable to compete with recent continual learning methods. To understand this behavior, we analyze parameter updates under quadratic regularization and demonstrate such regularizers prevent forgetting of past tasks by implicitly performing a weighted average between current and previous values of model parameters. Our analysis shows the inferior performance of quadratic regularizers arises from (a) dependence of weighted averaging on training hyperparameters, which often results in unstable training and (b) assignment of lower importance to deeper layers, which are generally the cause for forgetting in DNNs. To address these limitations, we propose Explicit Movement Regularization (EMR), a continual learning algorithm that modifies quadratic regularization to remove the dependence of weighted averaging on training hyperparameters and uses a relative measure for importance to avoid problems caused by lower importance assignment to deeper layers. Compared to quadratic regularization, EMR achieves 6.2% higher average accuracy and 4.5% lower average forgetting.