Corpus ID: 4601550

Identification of Shallow Neural Networks by Fewest Samples

  title={Identification of Shallow Neural Networks by Fewest Samples},
  author={M. Fornasier and J. Vyb{\'i}ral and I. Daubechies},
  • M. Fornasier, J. Vybíral, I. Daubechies
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • We address the uniform approximation of sums of ridge functions $\sum_{i=1}^m g_i(a_i\cdot x)$ on ${\mathbb R}^d$, representing the shallowest form of feed-forward neural network, from a small number of query samples, under mild smoothness assumptions on the functions $g_i$'s and near-orthogonality of the ridge directions $a_i$'s. The sample points are randomly generated and are universal, in the sense that the sampled queries on those points will allow the proposed recovery algorithms to… CONTINUE READING
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