# An Overview of Uncertainty Quantification Methods for Infinite Neural Networks

arXiv: https://arxiv.org/abs/2201.04746 · HTML: https://mlsanity.com/paper/2201.04746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 7 of 7)

- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [Wide Mean-Field Variational Bayesian Neural Networks Ignore the Data](https://mlsanity.com/paper/2106.07052/) (2021)
- [Uncertainty-Aware (UNA) Bases for Deep Bayesian Regression Using Multi-Headed Auxiliary Networks](https://mlsanity.com/paper/2006.11695/) (2020)

## Abstract (arXiv)

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.