Paper:
Deep artificial neural networks with spatially repeated processing (a.k.a., deep convolutional ANNs) have been established as the best class of candidate models of visual processing in the primate ventral visual processing stream. Over the past five years, these ANNs have evolved from a simple feedforward eight-layer architecture in AlexNet to extremely deep and branching NASNet architectures, demonstrating increasingly better object categorization performance. Here we ask, as ANNs have continued to evolve in performance, are they also strong candidate models for the brain? To answer this question, we developed Brain-Score, a composite of neural and behavioral benchmarks for determining how brain-like a model is, together with an online platform where models can receive a BrainScore and compare against other models. Despite high scores, typical deep models from the machine learning community are often hard to map onto the brain's anatomy due to their vast number of layers and missing biologically-important connections, such as recurrence. To further map onto anatomy and validate our approach, we built CORnet-S: an ANN guided by Brain-Score with the anatomical constraints of compactness and recurrence. Although a shallow model with four anatomically mapped areas and recurrent connectivity, CORnet-S is a top model on Brain-Score and outperforms similarly compact models on ImageNet. Analyzing CORnet-S circuitry variants revealed recurrence as the main predictive factor of both Brain-Score and ImageNet top-1 performance.

Review:
This is an interesting paper in which the authors propose a shallow neural network, the architecture of which was optimized to maximize brain score, and show that it outperforms other shallow networks at imagenet classification. The goal of this paper — allowing brain data to improve our neural nets — is great. The paper is well written (except for a comment on clarity right below), and presents an interesting take on solving this problem. 
It is a little unclear how the authors made CORnet optimize brain score: “However, note that CORnet-S was developed using Brain-Score as a guiding benchmark and although it was never directly used in model search or optimization, testing CORnet-S on Brain-Score is not a completely independent test.” Making these steps clearer is crucial for evaluating better what the model means. In the discussion “We have tested hundreds of architectures before finding CORnet-S circuitry and thus it is possible that the proposed circuits could have a strong relation to biological implementations.” implies that the authors trained models with different architectures until the brain score was maximized after training. A hundred(s) times of training on 2760 + 2400 datapoints are probably plenty to overfit the brainscore datasets. The brain score is probably compromised after this, and it would be hard to make claims about the results on the brain modeling side. The author acknowledge this limitation, but perhaps a better thing is to add an additional dataset, perhaps one from different animal recordings, or from human fMRI? 
Arguably, the goal of the paper is to obtain a model that overpowers other simpler models, and not necessarily to make claims about the brain. The interesting part of the paper is that the shallow model does work better than other shallow models. The authors mention that brain score helps CORnet be better at generalizing to other datasets. Including these results would definitely strengthen the claim since both brain score and imagenet have been trained on hundreds of times so far. 
Another way to show that brain score helps is to show it generalizes above or differently from optimizing other models. What would have happened if the authors stuck to a simple, shallow model and instead of optimizing brain score optimized performance (hundreds of times) on some selected image dataset (this selection dataset is separate from imagenet, but the actual training is done on imagenet) and then tested performance on imagenet? Is the effect due to the brain or to the independent testing on another dataset?