# On the Relation of State Space Models and Hidden Markov Models

arXiv: https://arxiv.org/abs/2601.13357 · HTML: https://mlsanity.com/paper/2601.13357/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 4 of 4)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Particle-Filtering-based Latent Diffusion for Inverse Problems](https://mlsanity.com/paper/2408.13868/) (2024)
- [How Many Heads Make an SSM? A Unified Framework for Attention and State Space Models](https://mlsanity.com/paper/2512.15115/) (2025)

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

- [A Taxonomy of Cognitive Capability Gaps in Generative and Agentic AI](https://mlsanity.com/paper/2608.02553/) (2026)
- [How Wrong Can a Good Predictor Be? Diverging Updates with Vanishing Predictive KL](https://mlsanity.com/paper/2609.11132/) (2026)

## Abstract (arXiv)

State Space Models (SSMs) and Hidden Markov Models (HMMs) are foundational frameworks for modeling sequential data with latent variables and are widely used in signal processing, control theory, and machine learning. Despite their shared temporal structure, they differ fundamentally in the nature of their latent states, probabilistic assumptions, inference procedures, and training paradigms. Recently, deterministic state space models have re-emerged in natural language processing through architectures such as S4 and Mamba, raising new questions about the relationship between classical probabilistic SSMs, HMMs, and modern neural sequence models. In this paper, we present a unified and systematic comparison of HMMs, linear Gaussian state space models, Kalman filtering, and contemporary NLP state space models. We analyze their formulations through the lens of probabilistic graphical models, examine their inference algorithms -- including forward-backward inference and Kalman filtering -- and contrast their learning procedures via Expectation-Maximization and gradient-based optimization. By highlighting both structural similarities and semantic differences, we clarify when these models are equivalent, when they fundamentally diverge, and how modern NLP SSMs relate to classical probabilistic models. Our analysis bridges perspectives from control theory, probabilistic modeling, and modern deep learning.