# Particle Filter Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1905.12885 · HTML: https://mlsanity.com/paper/1905.12885/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 30 of 36)

- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Structured World Belief for Reinforcement Learning in POMDP](https://mlsanity.com/paper/2107.08577/) (2021)
- [Multi-scale Attention Flow for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2205.07493/) (2022)
- [Learning Latent Graph Dynamics for Visual Manipulation of Deformable Objects](https://mlsanity.com/paper/2104.12149/) (2021)
- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [Flow-based Recurrent Belief State Learning for POMDPs](https://mlsanity.com/paper/2205.11051/) (2022)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [Learning to Assimilate in Chaotic Dynamical Systems](https://mlsanity.com/paper/2111.01058/) (2021)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters](https://mlsanity.com/paper/2111.01409/) (2021)
- [The Wasserstein Believer: Learning Belief Updates for Partially Observable Environments through Reliable Latent Space Models](https://mlsanity.com/paper/2303.03284/) (2023)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Spatial-Channel Transformer Network for Trajectory Prediction on the Traffic Scenes](https://mlsanity.com/paper/2101.11472/) (2021)
- [Differentiable Parsing and Visual Grounding of Natural Language Instructions for Object Placement](https://mlsanity.com/paper/2210.00215/) (2022)
- [Deep Learning-Based Robust Multi-Object Tracking via Fusion of mmWave Radar and Camera Sensors](https://mlsanity.com/paper/2407.08049/) (2024)
- [Unrolling Particles: Unsupervised Learning of Sampling Distributions](https://mlsanity.com/paper/2110.02915/) (2021)
- [A Survey of Machine Learning Techniques for Improving Global Navigation Satellite Systems](https://mlsanity.com/paper/2406.16873/) (2024)
- [Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving](https://mlsanity.com/paper/2212.06968/) (2022)
- [PF-GNN: Differentiable particle filtering based approximation of universal graph representations](https://mlsanity.com/paper/2401.17752/) (2024)
- [Model-Based Reinforcement Learning under Random Observation Delays](https://mlsanity.com/paper/2509.20869/) (2025)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)
- [Belief-Enriched Pessimistic Q-Learning against Adversarial State Perturbations](https://mlsanity.com/paper/2403.04050/) (2024)
- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)
- [Dynamic Analysis and an Eigen Initializer for Recurrent Neural Networks](https://mlsanity.com/paper/2307.15679/) (2023)
- [Recursive Least Squares Based Refinement Network for the Rollout Trajectory Prediction Methods](https://mlsanity.com/paper/2102.10859/) (2021)
- [Hidden State Approximation in Recurrent Neural Networks Using Continuous Particle Filtering](https://mlsanity.com/paper/2212.09008/) (2022)
- [Memory-efficient particle filter recurrent neural network for object localization](https://mlsanity.com/paper/2310.01595/) (2023)

## Abstract (arXiv)

Recurrent neural networks (RNNs) have been extraordinarily successful for prediction with sequential data. To tackle highly variable and noisy real-world data, we introduce Particle Filter Recurrent Neural Networks (PF-RNNs), a new RNN family that explicitly models uncertainty in its internal structure: while an RNN relies on a long, deterministic latent state vector, a PF-RNN maintains a latent state distribution, approximated as a set of particles. For effective learning, we provide a fully differentiable particle filter algorithm that updates the PF-RNN latent state distribution according to the Bayes rule. Experiments demonstrate that the proposed PF-RNNs outperform the corresponding standard gated RNNs on a synthetic robot localization dataset and 10 real-world sequence prediction datasets for text classification, stock price prediction, etc.