Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning
The message is that the statistical cost of depth is the metric entropy of the set $B(k,F)$ of compositions, and it separates the models whose estimation error is independent of the depth from those whose estimation error grows with it.
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa et al.
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