Debiasing Mini-Batch Quadratics for Applications in Deep Learning

• URL: http://arxiv.org/abs/2410.14325v1
• Date: Fri, 18 Oct 2024 09:37:05 GMT
• Title: Debiasing Mini-Batch Quadratics for Applications in Deep Learning
• Authors: Lukas Tatzel, Bálint Mucsányi, Osane Hackel, Philipp Hennig,
• Abstract summary: Quadratic approximations form a fundamental building block of machine learning methods. When computations on the entire training set are intractable - typical for deep learning - the relevant quantities are computed on mini-batches. We 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 via the Laplace approximation in deep learning, and (iv) develop and evaluate debiasing strategies.
• Score: 22.90473935350847
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• Abstract: 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.

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