Debiasing Mini-Batch Quadratics for Applications in Deep Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913667402956800 |
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| author | Tatzel, Lukas Mucsányi, Bálint Hackel, Osane Hennig, Philipp |
| author_facet | Tatzel, Lukas Mucsányi, Bálint Hackel, Osane Hennig, Philipp |
| contents | Quadratic approximations form a fundamental building block of machine learning methods. E.g., second-order optimizers try to find the Newton step into the minimum of a local quadratic proxy to the objective function; and the second-order approximation of a network's loss function can be used to quantify the uncertainty of its outputs via the Laplace approximation. When computations on the entire training set are intractable - typical for deep learning - the relevant quantities are computed on mini-batches. This, however, distorts and biases the shape of the associated stochastic quadratic approximations in an intricate way with detrimental effects on applications. In this paper, we (i) show that this bias introduces a systematic error, (ii) provide a theoretical explanation for it, (iii) explain its relevance for second-order optimization and uncertainty quantification via the Laplace approximation in deep learning, and (iv) develop and evaluate debiasing strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Debiasing Mini-Batch Quadratics for Applications in Deep Learning Tatzel, Lukas Mucsányi, Bálint Hackel, Osane Hennig, Philipp Machine Learning Quadratic approximations form a fundamental building block of machine learning methods. E.g., second-order optimizers try to find the Newton step into the minimum of a local quadratic proxy to the objective function; and the second-order approximation of a network's loss function can be used to quantify the uncertainty of its outputs via the Laplace approximation. When computations on the entire training set are intractable - typical for deep learning - the relevant quantities are computed on mini-batches. This, however, distorts and biases the shape of the associated stochastic quadratic approximations in an intricate way with detrimental effects on applications. In this paper, we (i) show that this bias introduces a systematic error, (ii) provide a theoretical explanation for it, (iii) explain its relevance for second-order optimization and uncertainty quantification via the Laplace approximation in deep learning, and (iv) develop and evaluate debiasing strategies. |
| title | Debiasing Mini-Batch Quadratics for Applications in Deep Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.14325 |