Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913379156754432 |
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| author | Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail |
| author_facet | Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail |
| contents | In this paper, we first present an explanation regarding the common occurrence of spikes in the training loss when neural networks are trained with stochastic gradient descent (SGD). We provide evidence that the spikes in the training loss of SGD are "catapults", an optimization phenomenon originally observed in GD with large learning rates in [Lewkowycz et al. 2020]. We empirically show that these catapults occur in a low-dimensional subspace spanned by the top eigenvectors of the tangent kernel, for both GD and SGD. Second, we posit an explanation for how catapults lead to better generalization by demonstrating that catapults promote feature learning by increasing alignment with the Average Gradient Outer Product (AGOP) of the true predictor. Furthermore, we demonstrate that a smaller batch size in SGD induces a larger number of catapults, thereby improving AGOP alignment and test performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04815 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning Zhu, Libin Liu, Chaoyue Radhakrishnan, Adityanarayanan Belkin, Mikhail Machine Learning Optimization and Control In this paper, we first present an explanation regarding the common occurrence of spikes in the training loss when neural networks are trained with stochastic gradient descent (SGD). We provide evidence that the spikes in the training loss of SGD are "catapults", an optimization phenomenon originally observed in GD with large learning rates in [Lewkowycz et al. 2020]. We empirically show that these catapults occur in a low-dimensional subspace spanned by the top eigenvectors of the tangent kernel, for both GD and SGD. Second, we posit an explanation for how catapults lead to better generalization by demonstrating that catapults promote feature learning by increasing alignment with the Average Gradient Outer Product (AGOP) of the true predictor. Furthermore, we demonstrate that a smaller batch size in SGD induces a larger number of catapults, thereby improving AGOP alignment and test performance. |
| title | Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2306.04815 |