A Proposal on Machine Learning via Dynamical Systems


We discuss the idea of using continuous dynamical systems to model general high-dimensional nonlinear functions used in machine learning. We also discuss the connection with deep learning.

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This is part of an ongoing project with several collaborators, including Jiequn Han, Qianxiao Li, Jianfeng Lu and Cheng Tai. The author benefitted a great deal from discussions with them, particularly Jiequn Han. This work is supported in part by the Major Program of NNSFC under Grant 91130005, ONR N00014-13-1-0338 and DOE DE-SC0009248.

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Correspondence to Weinan E.

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Dedicated to Professor Chi-Wang Shu on the occasion of his 60th birthday.

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E, W. A Proposal on Machine Learning via Dynamical Systems. Commun. Math. Stat. 5, 1–11 (2017). https://doi.org/10.1007/s40304-017-0103-z

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  • Deep learning
  • Machine learning
  • Dynamical systems

Mathematics Subject Classification

  • 37N99