"Identification of neural networks: from one neuron to deep networks"Fornasier, MassimoArtificial neural networks are nonlinear parametric functions. For identification of a network from finite samples we mean computing the parameters of a network (up to natural symmetries) from observation of a finite number of input-output pairs, which is a well-known NP hard problem due to nonlinearity. Nevertheless a network remains determined by a finite number of parameters and it is not at all expected that for generic networks one would need a much larger number of samples to identify the network. In this talk we review results of finite sample identifiability of networks, starting with the simplest model of one single artificial neuron to understanding deep neural networks. The presented identification results are constructive and can be realized by algorithms with polynomial complexity with respect to input dimension and size of the network. |
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