2024/10/18 by Lukas Tatzel, Tatzel, Lukas, Bálint Mucsányi +5 · 1 citation
Computer Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2410.14325
openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.