Pretty dense paper. Always happy to see new theoretical work on deep learning. We need more of it.
Depth matters: expressivity in DNNs goes thru a phase transition with depth. https://arxiv.org/pdf/1606.05340v2.pdf … (warning: contains Riemannian geometry)
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Surya'a lab is doing great work in this area. Both topically and geographically.
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expressivity of NN can have a direction? what does it mean?
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if you define a measure of expressivity as a scalar (or vector), then sure.
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also an archived general relativity course from 2008 with different lectures http://theoreticalminimum.com/courses/general-relativity/2008/fall …
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from the depth matters dept http://www.cs.huji.ac.il/~shashua/papers/colt16.pdf … http://www.cs.huji.ac.il/~shashua/papers/simnets-icml16.pdf … shallow nets req exp size to match polynomial deep
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