Title: Continual Learning via Principal Components Projection. Abstract: Continual learning in neural networks (NN) often suffers from catastrophic forgetting. That is, when learning a sequence of tasks on an NN, the learning of a new task will cause weight changes that may destroy the learned knowledge embedded in the weights for previous tasks. Without solving this problem, it is difficult to use an NN to perform continual or lifelong learning. Although researchers have attempted to solve the problem in many ways, it remains to be challenging. In this paper, we propose a new approach, called principal components projection (PCP). The idea is that in learning a new task, if we can ensure that the gradient updates will only occur in the orthogonal directions to the input vectors of the previous tasks, then the weight updates for learning the new task will not affect the previous tasks. We propose to compute the principal components of the input vectors and use them to transform the input and to project the gradient updates for learning each new task. PCP does not need to store any sampled data from previous tasks or to generate pseudo data of previous tasks and use them to help learn a new task. Empirical evaluation shows that the proposed method PCP markedly outperforms the state-of-the-art baseline methods.