Realizing data features by deep nets
This addresses the theoretical understanding of deep learning's advantages and limitations for researchers, though it is incremental in nature.
The paper investigates the capability of deep neural networks to realize data features, showing they outperform shallow networks for complex features without extra capacity costs, but have similar asymptotic approximation rates for simple features like smoothness when depth is fixed.
This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additional capacity costs. This verifies the advantage of deep nets in realizing complex features. On the other hand, to realize some simple data feature like the smoothness, we prove that, up to a logarithmic factor, the approximation rate of deep nets is asymptotically identical to that of shallow nets, provided that the depth is fixed. This exhibits a limitation of deep nets in realizing simple features.