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We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps.
Markov Processes: Characterization and Convergence
S. Ethier and T. Kurtz · 1986
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Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
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Convergence of learning algorithms with constant learning rates
C. Kuan and K. Hornik · 1991
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Nonlinearity creates linear independence
Yoshifusa Ito · 1996
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Gradient Descent Finds Global Minima of Deep Neural Networks
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Gradient Descent Provably Optimizes Over-Parameterized Neural Networks
S. Du, X. Zhai, B. Poczos, and A. Singh · 2019
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Mean Field Analysis of Neural Networks: A Law of Large Numbers
J. Sirignano and K. Spiliopoulos · 2020
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Mean Field Analysis of Neural Networks: A Central Limit Theorem
J. Sirignano and K. Spiliopoulos · 2020
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Mean Field Analysis of Deep Neural Networks
J. Sirignano and K. Spiliopoulos · 2021
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