Large and moderate deviations for Gaussian neural networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908925178150912 |
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| author | Macci, Claudio Pacchiarotti, Barbara Torrisi, Giovanni Luca |
| author_facet | Macci, Claudio Pacchiarotti, Barbara Torrisi, Giovanni Luca |
| contents | We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e., there is exactly one hidden layer) the large and moderate principles hold for quite general pre-activation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large and moderate deviations for Gaussian neural networks Macci, Claudio Pacchiarotti, Barbara Torrisi, Giovanni Luca Probability 60F10, 60F05, 68T07 We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e., there is exactly one hidden layer) the large and moderate principles hold for quite general pre-activation functions. |
| title | Large and moderate deviations for Gaussian neural networks |
| topic | Probability 60F10, 60F05, 68T07 |
| url | https://arxiv.org/abs/2401.01611 |