Preventing catastrophic forgetting while continually learning new tasks is an essential problem in lifelong learning. Structural regularization (SR) refers to a family of algorithms that mitigate catastrophic forgetting by penalizing the network for changing its critical parameters from previous tasks while learning a new one. The penalty is often induced via a quadratic regularizer defined by an emph{importance matrix}, e.g., the (empirical) Fisher information matrix in the Elastic Weight Consolidation framework. In practice and due to computational constraints, most SR methods crudely approximate the importance matrix by its diagonal. In this paper, we propose emph{Sketched Structural Regularization} (Sketched SR) as an alternative approach to compress the importance matrices used for regularizing in SR methods. Specifically, we apply emph{linear sketching methods} to better approximate the importance matrices in SR algorithms. We show that sketched SR: (i) is computationally efficient and straightforward to implement, (ii) provides an approximation error that is justified in theory, and (iii) is method oblivious by construction and can be adapted to any method that belongs to the structural regularization class. We show that our proposed approach consistently improves various SR algorithms performance on both synthetic experiments and benchmark continual learning tasks, including permuted-MNIST and CIFAR-100.
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