# Radial and Directional Posteriors for Bayesian Neural Networks

arXiv: https://arxiv.org/abs/1902.02603 · HTML: https://mlsanity.com/paper/1902.02603/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Matching Normalizing Flows and Probability Paths on Manifolds](https://mlsanity.com/paper/2207.04711/) (2022)
- [Structured Dropout Variational Inference for Bayesian Neural Networks](https://mlsanity.com/paper/2102.07927/) (2021)
- [On The Distribution of Penultimate Activations of Classification Networks](https://mlsanity.com/paper/2107.01900/) (2021)
- [Shapley Pruning for Neural Network Compression](https://mlsanity.com/paper/2407.15875/) (2024)

## Abstract (arXiv)

We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The dependencies learned via the directional density provide better modeling performance compared to the widely-used Gaussian mean-field-type variational family. In addition, the strength of input and output neurons learned via the radial density provides a structured way to compress neural networks. Indeed, experiments show that our variational family improves predictive performance and yields compressed networks simultaneously.