Universal characteristics of deep neural network loss surfaces from random matrix theory
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917988112793600 |
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| author | Baskerville, Nicholas P Keating, Jonathan P Mezzadri, Francesco Najnudel, Joseph Granziol, Diego |
| author_facet | Baskerville, Nicholas P Keating, Jonathan P Mezzadri, Francesco Najnudel, Joseph Granziol, Diego |
| contents | This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning gradient descent algorithms. We also present insights into deep neural network loss surfaces from quite general arguments based on tools from statistical physics and random matrix theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08601 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Universal characteristics of deep neural network loss surfaces from random matrix theory Baskerville, Nicholas P Keating, Jonathan P Mezzadri, Francesco Najnudel, Joseph Granziol, Diego Mathematical Physics Disordered Systems and Neural Networks Machine Learning This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning gradient descent algorithms. We also present insights into deep neural network loss surfaces from quite general arguments based on tools from statistical physics and random matrix theory. |
| title | Universal characteristics of deep neural network loss surfaces from random matrix theory |
| topic | Mathematical Physics Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2205.08601 |