Paper:
Human and animals continuously acquire, adapt as well as transfer knowledge throughout their lifespan. The ability to learn continuously is crucial for the effective functioning of agents interacting with the real world and processing continuous streams of information. Continuous learning has been a long-standing challenge for neural networks as the repeated acquisition of information from nonuniform data distributions generally lead to catastrophic forgetting or interference. This work proposes a modular architecture capable of continuous acquisition of tasks while averting catastrophic forgetting. Specifically, our contributions are: (i) Efficient Architecture: a modular architecture emulating the visual cortex that can learn meaningful representations with limited labelled examples, (ii) Knowledge Retention: retention of learned knowledge via limited replay of past experiences, (iii) Forward Transfer: efficient and relatively faster learning on new tasks, and (iv) Naturally Skewed Distributions: The learning in the above-mentioned claims is performed on non-uniform data distributions which better represent the natural statistics of our ongoing experience. Several experiments that substantiate the above-mentioned claims are demonstrated on the CIFAR-100 dataset.

Review:
I think there might be some interesting ideas in the work, but I think the authors somehow did not manage to position themselves well within the *recent* works on the topic or even with respect to what continual learning (CL) is understood to be in these recent works. 
E.g. CL is a generic learning problem, and most algorithms are generic (with a few caveats in terms of what information is available) in the sense that they can be applied regardless of task (be it RL, be it sequence modelling etc.). This work seems limited to image classification. The SHDL wavelets pre-processing, if I understood it, is specific for images and probably even there under some assumption (e.g natural images). 
The autoencoder (middle bit) is trained on all tasks the CL needs to face, if I understood the work correctly (phase 0 + phase 1). This potentially makes the CL problem much simpler because you are limiting yourself to the top layer only when dealing with CL, not the rest. Not to mention that I don't understand the motivation of the autoencoder. I think ample results show that unsupervised learning fails in many instances to provide the right features and underperforms compared to learning discriminative features by just backproping from the cross entropy (discriminative loss) all the way down. The only instance I know of for doing this is in low data regime where there is no alternative. 
I think the modularity used needs to be better introduced. Why the autoencoder, why the first layer of wavelets? Is it for the benefit for CL? I can understand the wavelets, since they are not learnt. But the autoencoder? The autoencoder being trained on all data feels like a cheat. 
I think the citation of the perceptron a bit strange. Do you really use the original perceptrion from 58? Why? We have much better tools now !?
I think the different metrics introduced are interesting and useful. Though you should somehow find common ground to existing works as well to ensure a point of comparison. In the results section I almost got lost. What is the final performance on Cifar. How does this compare to a model that is not trained in a CL regime? What loss do you get from the proposed parametrizaton?
In the comparison with EWC and iCarl, there the whole model was dealing with the CL problem, right? (all intermediary layers). I'm actually surprised iCarl is not doing better (I expect it can do better than EWC). Maybe provide a few more information of hyperparam used for this comparison.
Overall I think the paper is not ready for being published. Not without addressing these points:
 * role of modularity (if not CL -- then why? ; is the modular structure original or part of the previous works cited, e.g. where the wavelets are introduced and so forth)
 * better integration with recent literature; provide answers and settings that allow apple to apple comparison so one can easily understand where this approach falls; if the method is not meant for this "traditional settings and metrics" please still provide them, and then motivate why this regime is not interesting and explain better the regime the method is meant for
 * as it stands the work is light on the low level details; Hyper-params and other details are not carefully provided (maybe consider adding an appendix with all of these). I have doubts that the work is reproducible without these details.