# Probabilistic Inference in the Era of Tensor Networks and Differential Programming

arXiv: https://arxiv.org/abs/2405.14060 · HTML: https://mlsanity.com/paper/2405.14060/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 50 references that are in the map.
- First posted on arXiv 22 May 2024.

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

- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [An Advance on Variable Elimination with Applications to Tensor-Based Computation](https://mlsanity.com/paper/2002.09320/) (2020)

## Built on by (most cited first, 4 of 4)

- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Fast Trainable Multilinear Bases for Image Compression](https://mlsanity.com/paper/2608.00053/) (2026)
- [EcoNet: Multiagent Planning and Control Of Household Energy Resources Using Active Inference](https://mlsanity.com/paper/2512.21343/) (2025)
- [A Hardware-oriented Approach for Efficient Bayesian Inference Computation and Deployment](https://mlsanity.com/paper/2607.17855/) (2026)

## Abstract (arXiv)

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this work, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (i) computing the partition function, (ii) computing the marginal probability of sets of variables in the model, (iii) determining the most likely assignment to a set of variables, and (iv) the same as (iii) but after having marginalized a different set of variables. We also present a generalized method for generating samples from a learned probability distribution. Our work is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the effectiveness of existing methods for solving probabilistic inference tasks.