# Towards Expressive Priors for Bayesian Neural Networks: Poisson Process Radial Basis Function Networks

arXiv: https://arxiv.org/abs/1912.05779 · HTML: https://mlsanity.com/paper/1912.05779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Understanding Activation Patterns in Artificial Neural Networks by Exploring Stochastic Processes](https://mlsanity.com/paper/2308.00858/) (2023)

## Abstract (arXiv)

While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationarity and input-dependent lengthscale. We prove that our novel formulation allows for a decoupled specification of these properties, and that the estimated regression function is consistent as the number of observations tends to infinity. We demonstrate its behavior on synthetic and real examples.