# Uncertainty Quantification with the Empirical Neural Tangent Kernel

Source: [Uncertainty Quantification with the Empirical Neural Tangent Kernel](<https://www.sota2.com/research/paper/68fa7c2f1e209131cea8ce7f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-12T05:02:43.297Z

Authors: Joseph Wilson, Chris van der Heide, Liam Hodgkinson, Fred Roosta

Published: 2025-02-05T04:01:34.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Uncertainty Quantification on ImageNet](<https://www.sota2.com/research/sota/uncertainty-quantification-on-imagenet.md>): Uncertainty Quantification; ImageNet; V-ID: 0.813.

- [Uncertainty Quantification on FashionMNIST (using V-ID, V-OOD, MI metrics)](<https://www.sota2.com/research/sota/uncertainty-quantification-on-fashionmnist-using-v-id-v-ood-mi-metrics.md>): Uncertainty Quantification; FashionMNIST; V-ID: 92.08.

- [Uncertainty Quantification on SVHN](<https://www.sota2.com/research/sota/uncertainty-quantification-on-svhn.md>): Uncertainty Quantification; SVHN; V-ID Score: 90.97.

- [Uncertainty Quantification on CIFAR-100](<https://www.sota2.com/research/sota/uncertainty-quantification-on-cifar-100.md>): Uncertainty Quantification; CIFAR-100; V-ID: 0.7703.

- [Uncertainty Quantification on CIFAR-10](<https://www.sota2.com/research/sota/uncertainty-quantification-on-cifar-10.md>): Uncertainty Quantification; CIFAR-10; V-ID: 0.9063.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2502.02870>)

[PDF](<https://arxiv.org/pdf/2502.02870.pdf>)