Paper:
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 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 for completely fixed capacity continual learning.

Review:
This paper proposes a method for mitigating catastrophic forgetting in neural networks, which is an important and unsolved problem in the sequential training of multiple tasks.  The method works by (i) identifying an active subnetwork after training on one task that can perform the task to a sufficient degree of accuracy, (ii) freezing the subnetwork and pruning interfering connections to it from the rest of the network, and (iii) training the rest of the network on the next task and iterating. The contribution is a method that allows for training of sequential tasks in a fixed capacity architecture with zero catastrophic forgetting guaranteed, while still allowing for transfer between tasks via feature sharing. Additionally, it allows for controlled fine-tuning of the trade-off between accuracy and network capacity, which the authors refer to as ‘graceful forgetting’, by adjusting two hyperparameters that adjust the level of sparsity during the training of a task. The method is shown to outperform several other continual learning methods on permuted MNIST and one other method on split CIFAR-100, both standard evaluations in continual learning.
While the model demonstrates the enviable properties for a continual learning algorithm of zero forgetting and ability to transfer in a fixed network, it suffers from a significant limitation (acknowledged by the authors) that leads me to recommend it for rejection in its current incarnation: 
* Due to the progressive freezing of the parameters, the network eventually reaches full capacity, making it theoretically difficult (in the multi-head setting, depending on the degree of transfer between tasks) or impossible (in the single-head setting) to learn how to perform new tasks.
* This is particularly problematic because the mechanism for 'graceful forgetting’ can only be applied on the subnetwork for a task that has just been trained on; once N tasks have been learnt, the subnetwork for task k<N cannot be altered without potentially affecting the performance on tasks k to N.
* In the paper, subnetworks are sparsified to within a fixed margin of the maximum accuracy of each task - with this procedure, you cannot predict how much capacity will be taken up by each task, and so you cannot know in advance how many tasks will fit into the network. If instead you chose to sparsify to a given subnetwork capacity per task in order to guarantee being able to fit a certain number in, then you can not control the accuracy level for each task. 
* Another consequence of the method is that it is not clear how one can easily resume training on a previous task (perhaps to take advantage of transfer from subsequent tasks). You could reinstate connections from the features of subsequent tasks to the earlier task and train, but presumably these would initially interfere with the original subnetwork. Have the authors considered any ways of achieving this?
In fairness to the authors, they (a) show that the growth in utilised capacity slows as more tasks are added and (b) propose that the layers of the network could be dynamically extended as a way of overcoming a network at full capacity. For the reasons given above, however, it is not a practical fixed capacity algorithm for a lifelong learning setting, which constitutes an indefinite stream of sequential tasks, since at capacity it can suffer from sudden 'catastrophic remembering’, as opposed to the ‘graceful forgetting’ advertised in the paper. I do think that the idea has potential and that the algorithm would be *significantly* strengthened if there were a mechanism for graceful forgetting of all or selected previous tasks when the network is at capacity.
Further Comments / questions:
* The method is claimed to be the “first viable algorithm for single-head continual learning”. This statement is unspecific - what does ‘viable’ mean in this context? Online EWC [1] is a continual learning algorithm that can theoretically applied in a single-head setting - what makes it non-viable?
Minor comments not affecting review:
* Better to label the weight types in the caption of Figure 1 rather than just in the main text
* In order to see the effect of depletion more clearly, it would also be useful to see the performance of the current task in isolation rather than just the average of all previous tasks.
* Section 2, line 8: “speci[c]fic"
* The main text reference to Figure 5b compares it to the single-head MNIST usage graph - where is this?
[1] Schwarz, Jonathan, et al. "Progress & Compress: A scalable framework for continual learning." International Conference on Machine Learning. 2018.