Uncertainty Quantification with the Empirical Neural Tangent Kernel

TL;DR

This paper introduces a post-training, sampling-based uncertainty quantification method for neural networks that efficiently approximates Gaussian process posteriors using the empirical Neural Tangent Kernel, outperforming existing methods in speed and accuracy.

Contribution

It presents a novel, efficient approach to uncertainty quantification for over-parameterized neural networks using the empirical NTK, combining the benefits of Bayesian methods and deep ensembles.

Findings

Outperforms competing UQ methods in computational efficiency.

Maintains state-of-the-art accuracy across regression and classification tasks.

Reduces computational costs by multiple factors.

Abstract

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems. Several Bayesian uncertainty quantification (UQ) methods exist that are either cheap or reliable, but not both. We propose a post-hoc, sampling-based UQ method for over-parameterized networks at the end of training. Our approach constructs efficient and meaningful deep ensembles by employing a (stochastic) gradient-descent sampling process on appropriately linearized networks. We demonstrate that our method effectively approximates the posterior of a Gaussian process using the empirical Neural Tangent Kernel. Through a series of numerical experiments, we show that our method not only outperforms competing approaches in computational efficiency-often reducing costs by multiple factors-but also maintains state-of-the-art performance across a variety of UQ metrics for both regression and classification tasks.