# Stochastic Neural Network with Kronecker Flow

arXiv: https://arxiv.org/abs/1906.04282 · HTML: https://mlsanity.com/paper/1906.04282/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Computable Lipschitz Bounds for Deep Neural Networks](https://mlsanity.com/paper/2410.21053/) (2024)
- [Concentration inequalities and optimal number of layers for stochastic deep neural networks](https://mlsanity.com/paper/2206.11241/) (2022)

## Abstract (arXiv)

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner that adequately captures the dependencies among the various parameters. In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks. We apply our method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits. In all setups, our methods prove to be competitive with existing methods and better than the baselines.