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We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional structure, while a shallow network cannot exploit this knowledge.
Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen
S. Pawelke · 1972
Earlier work this paper cites.
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H. N. Mhaskar · 1993
Earlier work this paper cites.
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P. Lizorkin and K. P. Rustamov · 1994
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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