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Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality
Affiliation:1. Faculty of Mathematics and Research Platform Data Science, University of Vienna, Austria;2. Johann Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences, Austria;3. Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Germany;4. School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China;5. Faculty of Mathematics, University of Vienna, Austria;1. School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;2. Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima 739-8526, Japan;1. Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA;2. Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Universytetska Str. 1, Lviv, 79000, Ukraine;3. Department of Mathematics, University of Houston, Houston, TX 77204, USA;4. Department of Computational Mathematics, Ivan Franko National University of Lviv, Universytetska Str. 1, Lviv, 79000, Ukraine
Abstract:
Keywords:Artificial neural networks  Artificial neural network approximations  Curse of dimensionality  Overcoming the curse of dimensionality  Lower bounds
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