Title: Continual Learning via Neural Pruning. Abstract: We introduce Continual Learning via Neural Pruning~(CLNP), a new method aimed at lifelong learning in fixed capacity models based on neuronal model sparsification. In this method, subsequent tasks are trained using the inactive neurons and filters of the sparsified network and cause zero deterioration to the performance of previous tasks. In order to deal with the possible compromise between model sparsity and performance, we formalize and incorporate the concept of \emph{graceful forgetting}: the idea that it is preferable to suffer a small amount of forgetting in a controlled manner if it helps regain network capacity and prevents uncontrolled loss of performance during the training of future tasks. CLNP also provides simple continual learning diagnostic tools in terms of the number of free neurons left for the training of future tasks as well as the number of neurons that are being reused. In particular,  we see in experiments that CLNP verifies and automatically takes advantage of the fact that the features of earlier layers are more transferable.   We show empirically that CLNP leads to significantly improved results over current weight elasticity based methods. CLNP can also be applied in single-head architectures providing the first viable such algorithm for continual learning. 