Series of Hessian-Vector Products for Tractable Saddle-Free Newton Optimisation of Neural Networks
| Autor: | Oldewage, Elre T., Clarke, Ross M., Hernández-Lobato, José Miguel |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the need to address non-convexity, for instance by modifying the Hessian's eigenvalues as in Saddle-Free Newton methods. We propose an optimisation algorithm which addresses both of these concerns - to our knowledge, the first efficiently-scalable optimisation algorithm to asymptotically use the exact inverse Hessian with absolute-value eigenvalues. Our method frames the problem as a series which principally square-roots and inverts the squared Hessian, then uses it to precondition a gradient vector, all without explicitly computing or eigendecomposing the Hessian. A truncation of this infinite series provides a new optimisation algorithm which is scalable and comparable to other first- and second-order optimisation methods in both runtime and optimisation performance. We demonstrate this in a variety of settings, including a ResNet-18 trained on CIFAR-10. Comment: 37 pages, 10 figures, 5 tables. To appear in TMLR. First two authors' order randomised |
| Databáze: | arXiv |
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