This seems extremely harsh, given the vast successes of deep neural nets calling them 'dumb as bricks' (there are too many examples of extrapolation outside datasets to count[1]). They have proven generalization capability when care is taken against over fitting (almost any model has this ability). Also there are results showing getting stuck in local minima is unlikely in highly-dimensional parameter spaces (the curvature in a large number of directions needs to coincide), and in any case rarely you're seeking the global minimum because of said over-fitting issues.
[1] It should be self-evident because they would hardly be of any use if unable to extrapolate at all. See GANs (https://www.thispersondoesnotexist.com/), AlphaGo (https://en.wikipedia.org/wiki/AlphaGo), etc.
For a high-level discussion, see the following article, by Francois Chollet, the maintainer of the deep learning library, Keras:
https://blog.keras.io/the-limitations-of-deep-learning.html
It is also not controversial that gradient optimisation gets stuck in local optima. A good exercise to convince yourself of this is to implement a simple gradient descent algorithm and observe its behaviour.
>> [1] It should be self-evident because they would hardly be of any use if unable to extrapolate at all.
That is why deep neural nets are trained with such vast amounts of data and computing power: it's to compensate for their inability to generalise to unseen instances.
That, too, is not controversial. It is common knowledge that the recent success of deep learning is due to the availability of larger datasets and more powerful computers than in past years. For example, see this interview with Geoff Hinton:
http://techjaw.com/2015/06/07/geoffrey-hinton-deep-learning-...
Geoffrey Hinton: I think it’s mainly because of the amount of computation and the amount of data now around but it’s also partly because there have been some technical improvements in the algorithms. Particularly in the algorithms for doing unsupervised learning where you’re not told what the right answer is but the main thing is the computation and the amount of data.
The algorithms we had in the old days would have worked perfectly well if computers had been a million times faster and datasets had been a million times bigger but if we’d said that thirty years ago people would have just laughed.
I hope this is helpful. I understand there are misconceptions about the strengths and limitations of deep neural nets that are not very easy to see with the naked eye. But it's a good idea to approach such an overhypoted technology with a skeptical mind and, e.g., ask yourself: why is all that data necessary, if they are so good at learning?
>> What seems novel here is how significant architecture alone is (I wouldn't guess it being this powerful), and this possibly has implications on the connection with the human brain -- in which my vague impression is that connections themselves are much more tuned than weights; also possibly giving greater emphasis on architecture training.
You are surprised by how significant architecture is. I am not surprised at all. I think it's been very clear for a while now that the success of deep neural networks is entirely due to their architectures that are fine-tuned to specific tasks. On the one hand, it's obvious that this is the case if you look at the two major successes of deep learning: CNNs for vision and LSTMs (and variants) for sequence learning. Both are extremely precise, extremely intricate architectures with an intense focus one one kind of task, and that kind of task, alone. On the other hand, the vast majority of neural net publications are specifically about new architectures, or, rather, tweaks to existing architectures.
In fact, in my boldest moments I'd go as far as to suggest that weight training with gradient optimisation has kept deep neural nets back. Gradient optimisation gets stuck in local minima, and it will always get stuck in local minima, and therefore always be dumb as bricks. Which is evident in the way deep neural nets overfit and are incapable of extrapolating outside their training datasets.