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Neural networks constitute a class of functions that are typically non-surjective, with high-dimensional fibers and complicated image. We prove two main results concerning the geometry of the loss landscape of a neural network. First, we provide an explicit effective bound on the sizes of the hidden layers so that the loss landscape has no spurious valleys, which guarantees the success of gradient descent methods. Second, we present a novel method for analyzing whether a given neural network architecture with monomial activation function can represent a target function of interest. The core of our analysis method is the study of a specific set of error values, and its behavior depending on different training datasets.
|Title of host publication||Proceedings of the 40th International Conference on Machine Learning|
|Editors||Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, Jonathan Scarlett|
|Publisher||Proceedings of Machine Learning Research (PMLR)|
|Number of pages||21|
|Publication status||Published - Jul 2023|
|Event||Fortieth International Conference on Machine Learning - Hawaiʻi Convention Center, 1801 Kalākaua Avenue , Honolulu, United States|
Duration: 23 Jul 2023 → 29 Jul 2023
Conference number: 40
|Name||Proceedings of Machine Learning Research|
|Conference||Fortieth International Conference on Machine Learning|
|Abbreviated title||ICML 2023|
|Period||23/07/23 → 29/07/23|
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