An Overview of Uncertainty Quantification Methods for Infinite Neural Networks

Florian Juengermann; Maxime Laasri; Marius Merkle

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arXiv · 2201.04746

An Overview of Uncertainty Quantification Methods for Infinite Neural Networks

Florian Juengermann·Maxime Laasri·Marius Merkle

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Abstract

To better understand the theoretical behavior of large neural networks, several works have analyzed the case where a network's width tends to infinity. In this regime, the effect of random initialization and the process of training a neural network can be formally expressed with analytical tools like Gaussian processes and neural tangent kernels. In this paper, we review methods for quantifying uncertainty in such infinite-width neural networks and compare their relationship to Gaussian processes in the Bayesian inference framework. We make use of several equivalence results along the way to obtain exact closed-form solutions for predictive uncertainty.

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Florian Juengermann, Maxime Laasri, Marius Merkle. 2022-01-13. An Overview of Uncertainty Quantification Methods for Infinite Neural Networks. https://arxiv.org/abs/2201.04746

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