  We introduce the Kronecker factored online Laplace approximation for
overcoming catastrophic forgetting in neural networks. The method is grounded
in a Bayesian online learning framework, where we recursively approximate the
posterior after every task with a Gaussian, leading to a quadratic penalty on
changes to the weights. The Laplace approximation requires calculating the
Hessian around a mode, which is typically intractable for modern architectures.
In order to make our method scalable, we leverage recent block-diagonal
Kronecker factored approximations to the curvature. Our algorithm achieves over
90% test accuracy across a sequence of 50 instantiations of the permuted MNIST
dataset, substantially outperforming related methods for overcoming
catastrophic forgetting.
