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Asymptotic properties of one-layer artificial neural networks with sparse connectivity

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  • Hirsch, Christian
  • Neumann, Matthias
  • Schmidt, Volker

Abstract

A law of large numbers for the empirical distribution of parameters of a one-layer artificial neural network with sparse connectivity is derived for a simultaneously increasing number of both, neurons and training iterations of the stochastic gradient descent.

Suggested Citation

  • Hirsch, Christian & Neumann, Matthias & Schmidt, Volker, 2023. "Asymptotic properties of one-layer artificial neural networks with sparse connectivity," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002115
    DOI: 10.1016/j.spl.2022.109698
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    1. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    2. Sirignano, Justin & Spiliopoulos, Konstantinos, 2020. "Mean field analysis of neural networks: A central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1820-1852.
    3. Decebal Constantin Mocanu & Elena Mocanu & Peter Stone & Phuong H. Nguyen & Madeleine Gibescu & Antonio Liotta, 2018. "Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
    4. da Costa, Conrado & Freitas Paulo da Costa, Bernardo & Jara, Milton, 2019. "Reaction–Diffusion models: From particle systems to SDE’s," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4411-4430.
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