# KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertainty

arXiv: https://arxiv.org/abs/2406.15131 · HTML: https://mlsanity.com/paper/2406.15131/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 45 of its 55 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [DayDreamer: World Models for Physical Robot Learning](https://mlsanity.com/paper/2206.14176/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model](https://mlsanity.com/paper/1907.00953/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [TransDreamer: Reinforcement Learning with Transformer World Models](https://mlsanity.com/paper/2202.09481/) (2022)
- [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Temporal Predictive Coding For Model-Based Planning In Latent Space](https://mlsanity.com/paper/2106.07156/) (2021)

## Built on by (most cited first, 9 of 9)

- [Advancing Intelligent Sequence Modeling: Evolution, Trade-offs, and Applications of State-Space Architectures from S4 to Mamba](https://mlsanity.com/paper/2503.18970/) (2025)
- [Kalman Linear Attention: Parallel Bayesian Filtering For Efficient Language Modelling and State Tracking](https://mlsanity.com/paper/2602.10743/) (2026)
- [Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2409.16824/) (2024)
- [Unraveling the Complexity of Memory in RL Agents: an Approach for Classification and Evaluation](https://mlsanity.com/paper/2412.06531/) (2024)
- [MEMBOT: Memory-Based Robot in Intermittent POMDP](https://mlsanity.com/paper/2509.11225/) (2025)
- [VariBASed: Variational Bayes-Adaptive Sequential Monte-Carlo Planning for Deep Reinforcement Learning](https://mlsanity.com/paper/2602.18857/) (2026)
- [Geometry of Uncertainty: Learning Metric Spaces for Multimodal State Estimation in RL](https://mlsanity.com/paper/2602.12087/) (2026)
- [Belief-State RWKV for Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2604.09671/) (2026)
- [How Wrong Can a Good Predictor Be? Diverging Updates with Vanishing Predictive KL](https://mlsanity.com/paper/2609.11132/) (2026)

## Abstract (arXiv)

Probabilistic State Space Models (SSMs) are essential for Reinforcement Learning (RL) from high-dimensional, partial information as they provide concise representations for control. Yet, they lack the computational efficiency of their recent deterministic counterparts such as S4 or Mamba. We propose KalMamba, an efficient architecture to learn representations for RL that combines the strengths of probabilistic SSMs with the scalability of deterministic SSMs. KalMamba leverages Mamba to learn the dynamics parameters of a linear Gaussian SSM in a latent space. Inference in this latent space amounts to standard Kalman filtering and smoothing. We realize these operations using parallel associative scanning, similar to Mamba, to obtain a principled, highly efficient, and scalable probabilistic SSM. Our experiments show that KalMamba competes with state-of-the-art SSM approaches in RL while significantly improving computational efficiency, especially on longer interaction sequences.