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arXiv · 1805.07517

The global optimum of shallow neural network is attained by ridgelet transform

Sho Sonoda·Isao Ishikawa·Masahiro Ikeda·Kei Hagihara·Yoshihiro Sawano·Takuo Matsubara·Noboru Murata
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Abstract

We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform. A series of computational experiments show that there exists an interesting similarity between the scatter plot of hidden parameters in a shallow neural network after the BP training and the spectrum of the ridgelet transform. By introducing a continuous model of neural networks, we reduce the training problem to a convex optimization in an infinite dimensional Hilbert space, and obtain the explicit expression of the global optimizer via the ridgelet transform.

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Sho Sonoda, Isao Ishikawa, Masahiro Ikeda, Kei Hagihara, Yoshihiro Sawano, Takuo Matsubara, Noboru Murata. 2018-05-19. The global optimum of shallow neural network is attained by ridgelet transform. https://arxiv.org/abs/1805.07517

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