Uncertainty Quantification with the Empirical Neural Tangent Kernel
This addresses the need for both cheap and reliable uncertainty quantification in neural networks for critical systems, representing a strong specific gain rather than a foundational breakthrough.
The paper tackles the problem of uncertainty quantification in neural networks by proposing a post-hoc, sampling-based method that constructs efficient deep ensembles using gradient-descent sampling on linearized networks. The method approximates the posterior of a Gaussian process with the empirical Neural Tangent Kernel, achieving state-of-the-art performance across UQ metrics while reducing computational costs by multiple factors.
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.