# Functional Tensors for Probabilistic Programming

arXiv: https://arxiv.org/abs/1910.10775 · HTML: https://mlsanity.com/paper/1910.10775/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [Automatically Marginalized MCMC in Probabilistic Programming](https://mlsanity.com/paper/2302.00564/) (2023)
- [Probabilistic Programming with Programmable Variational Inference](https://mlsanity.com/paper/2406.15742/) (2024)
- [Marginalized particle Gibbs for multiple state-space models coupled through shared parameters](https://mlsanity.com/paper/2210.07379/) (2022)
- [Inference Plans for Hybrid Particle Filtering](https://mlsanity.com/paper/2408.11283/) (2024)

## Abstract (arXiv)

It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software abstraction for integration --functional tensors-- that captures many of the benefits of tensors, while also being able to describe continuous probability distributions. Moreover, functional tensors are a natural candidate for generalized variable elimination and parallel-scan filtering algorithms that enable parallel exact inference for a large family of tractable modeling motifs. We demonstrate the versatility of functional tensors by integrating them into the modeling frontend and inference backend of the Pyro programming language. In experiments we show that the resulting framework enables a large variety of inference strategies, including those that mix exact and approximate inference.