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Limitations of shallow nets approximation
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DOI：10.1016/j.neunet.2017.06.016.png)
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In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. (C) 2017 Elsevier Ltd. All rights reserved.
Keyword:
Shallow nets
Deep nets
Approximation
Reproducing kernel Hilbert space
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