# A brief note on understanding neural networks as Gaussian processes

arXiv: https://arxiv.org/abs/2107.11892 · HTML: https://mlsanity.com/paper/2107.11892/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 9 references that are in the map.
- First posted on arXiv 25 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [A Priori Estimates of the Population Risk for Two-layer Neural Networks](https://mlsanity.com/paper/1810.06397/) (2018)

## Built on by (most cited first, 1 of 1)

- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)

## Abstract (arXiv)

As a generalization of the work in [Lee et al., 2017], this note briefly discusses when the prior of a neural network output follows a Gaussian process, and how a neural-network-induced Gaussian process is formulated. The posterior mean functions of such a Gaussian process regression lie in the reproducing kernel Hilbert space defined by the neural-network-induced kernel. In the case of two-layer neural networks, the induced Gaussian processes provide an interpretation of the reproducing kernel Hilbert spaces whose union forms a Barron space.