# Neural Bayesian Filtering

arXiv: https://arxiv.org/abs/2510.03614 · HTML: https://mlsanity.com/paper/2510.03614/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 67 references that are in the map.
- First posted on arXiv 4 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)
- [Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors](https://mlsanity.com/paper/1805.11122/) (2018)
- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [Rethinking Formal Models of Partially Observable Multiagent Decision Making](https://mlsanity.com/paper/1906.11110/) (2019)
- [Student of Games: A unified learning algorithm for both perfect and imperfect information games](https://mlsanity.com/paper/2112.03178/) (2021)
- [Scalable Online Planning via Reinforcement Learning Fine-Tuning](https://mlsanity.com/paper/2109.15316/) (2021)
- [Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction](https://mlsanity.com/paper/1901.08096/) (2019)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Generative Distribution Embeddings: Lifting autoencoders to the space of distributions for multiscale representation learning](https://mlsanity.com/paper/2505.18150/) (2025)
- [History Filtering in Imperfect Information Games: Algorithms and Complexity](https://mlsanity.com/paper/2311.14651/) (2023)

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

- [Test-time Reinforcement Learning in Imperfect Information Games](https://mlsanity.com/paper/2608.30635/) (2026)
- [Belief Embedding Tree Search](https://mlsanity.com/paper/2610.15046/) (2026)

## Abstract (arXiv)

Sequential estimation under partial observability requires tracking beliefs that may be high-dimensional, multimodal, and non-Gaussian. Classical Bayesian filters generalize zero-shot to any system whose dynamics can be evaluated, but their representations scale poorly: parametric filters struggle to capture multimodality, and particle filters require exponentially many particles in the state dimension. Generative Distribution Embeddings (GDEs) learn compact representations of complex distributions but have no sequential update. We present Neural Bayesian Filtering (NBF), which represents beliefs as embeddings and approximates their Bayesian update. At each step, NBF samples particles from a learned conditional generator, propagates them through the dynamics, and embeds the propagated set, weighted by the likelihood of the new observation. Regenerating the set from the embedding at each step, rather than resampling a surviving pool, mitigates the risk of impoverishment that degrades particle filters. The system dynamics and likelihood enter only through propagation and weighting, so NBF retains zero-shot adaptability to new dynamics as long as the beliefs they produce fall within the family the embedding was trained on. Training the GDE to represent that family requires only the states realized at training time. We validate NBF on Lorenz-96 and a pursuit--evasion domain, showing graceful scaling with state dimension, accurate tracking of multimodal posteriors, and zero-shot generalization to dynamics and likelihoods held out from training.