ONG: Orthogonal Natural Gradient Descent

Abstract: Orthogonal gradient descent has emerged as a powerful method for continual learning tasks. However, its Euclidean projections overlook the underlying information-geometric structure of the space of distributions parametrized by neural networks, which can lead to suboptimal convergence in learning tasks. To counteract this, we combine it with the idea of the natural gradient and present ONG (Orthogonal Natural Gradient Descent). ONG preconditions each new task gradient with an efficient EKFAC approximation of the inverse Fisher information matrix, yielding updates that follow the steepest descent direction under a Riemannian metric. To preserve performance on previously learned tasks, ONG projects these natural gradients onto the orthogonal complement of prior task gradients. We provide a theoretical justification for this procedure, introduce the ONG algorithm, and benchmark its performance on the Permuted and Rotated MNIST datasets. All code for our experiments/reproducibility can be found at https://github.com/yajatyadav/orthogonal-natural-gradient.