# Hidden Markov Neural Networks

arXiv: https://arxiv.org/abs/2004.06963 · HTML: https://mlsanity.com/paper/2004.06963/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2020.

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

- [BAM: Bayes with Adaptive Memory](https://mlsanity.com/paper/2202.02405/) (2022)
- [Differentiable Filtering for Learning Hidden Markov Models](https://mlsanity.com/paper/2511.10571/) (2025)
- [Tempering the Bayes Filter towards Improved Model-Based Estimation](https://mlsanity.com/paper/2512.02823/) (2025)

## Abstract (arXiv)

We define an evolving in-time Bayesian neural network called a Hidden Markov Neural Network, which addresses the crucial challenge in time-series forecasting and continual learning: striking a balance between adapting to new data and appropriately forgetting outdated information. This is achieved by modelling the weights of a neural network as the hidden states of a Hidden Markov model, with the observed process defined by the available data. A filtering algorithm is employed to learn a variational approximation of the evolving-in-time posterior distribution over the weights. By leveraging a sequential variant of Bayes by Backprop, enriched with a stronger regularization technique called variational DropConnect, Hidden Markov Neural Networks achieve robust regularization and scalable inference. Experiments on MNIST, dynamic classification tasks, and next-frame forecasting in videos demonstrate that Hidden Markov Neural Networks provide strong predictive performance while enabling effective uncertainty quantification.