On the existence of optimal shallow feedforward networks with ReLU activation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916487355170816 |
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| author | Dereich, Steffen Kassing, Sebastian |
| author_facet | Dereich, Steffen Kassing, Sebastian |
| contents | We prove existence of global minima in the loss landscape for the approximation of continuous target functions using shallow feedforward artificial neural networks with ReLU activation. This property is one of the fundamental artifacts separating ReLU from other commonly used activation functions. We propose a kind of closure of the search space so that in the extended space minimizers exist. In a second step, we show under mild assumptions that the newly added functions in the extension perform worse than appropriate representable ReLU networks. This then implies that the optimal response in the extended target space is indeed the response of a ReLU network. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_03950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the existence of optimal shallow feedforward networks with ReLU activation Dereich, Steffen Kassing, Sebastian Machine Learning Numerical Analysis Optimization and Control Primary 68T07, Secondary 68T05, 41A50 We prove existence of global minima in the loss landscape for the approximation of continuous target functions using shallow feedforward artificial neural networks with ReLU activation. This property is one of the fundamental artifacts separating ReLU from other commonly used activation functions. We propose a kind of closure of the search space so that in the extended space minimizers exist. In a second step, we show under mild assumptions that the newly added functions in the extension perform worse than appropriate representable ReLU networks. This then implies that the optimal response in the extended target space is indeed the response of a ReLU network. |
| title | On the existence of optimal shallow feedforward networks with ReLU activation |
| topic | Machine Learning Numerical Analysis Optimization and Control Primary 68T07, Secondary 68T05, 41A50 |
| url | https://arxiv.org/abs/2303.03950 |