How do Quadratic Regularizers Prevent Catastrophic Forgetting: The Role of Interpolation

While several methods have been proposed to tackle this problem, there is limited work explaining why these methods work well. This paper has the goal of better explaining a popularly used technique for avoiding catastrophic forgetting: quadratic regularization. We show that quadratic regularizers prevent forgetting of past tasks by interpolating current and previous values of model parameters at every training iteration. Over multiple training iterations, this interpolation operation reduces the learning rates of more important model parameters, thereby minimizing their movement. Our analysis also reveals two drawbacks of quadratic regularization: (a) dependence of parameter interpolation on training hyperparameters, which often leads to training instability and (b) assignment of lower importance to deeper layers, which are generally the place forgetting occurs in DNNs. Via a simple modification to the order of operations, we show these drawbacks can be easily avoided, resulting in 6.2% higher average accuracy at 4.5% lower average forgetting. We confirm the robustness of our results by training over 2000 models in different settings. Learning algorithms are often designed under the assumption of independent and identical data distributions. However, this assumption is violated in several practical scenarios, such as continual learning and lifelong learning, where data distributions evolve constantly. In such settings, deep neural networks (DNNs) witness catastrophic forgetting and have difficulty adapting to new tasks without losing performance on previously learned ones. Several past works have tried to address this problem. While these works have shown promising results, a detailed understanding of their proposed methods is still to be developed. Understanding the reasons due to which existing methods for preventing catastrophic forgetting work or fail can open the possibility of developing better methods. With this motivation, in this work, we analyze quadratic regularization, a popular technique for preventing catastrophic forgetting in DNNs.