Quadratic models for understanding catapult dynamics of neural networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929333035073536 |
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| author | Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail |
| author_facet | Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail |
| contents | While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" [Lewkowycz et al. 2020] that arises when training such models with large learning rates. We then empirically show that the behaviour of neural quadratic models parallels that of neural networks in generalization, especially in the catapult phase regime. Our analysis further demonstrates that quadratic models can be an effective tool for analysis of neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11787 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quadratic models for understanding catapult dynamics of neural networks Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail Machine Learning Optimization and Control While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" [Lewkowycz et al. 2020] that arises when training such models with large learning rates. We then empirically show that the behaviour of neural quadratic models parallels that of neural networks in generalization, especially in the catapult phase regime. Our analysis further demonstrates that quadratic models can be an effective tool for analysis of neural networks. |
| title | Quadratic models for understanding catapult dynamics of neural networks |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2205.11787 |