# Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformations

arXiv: https://arxiv.org/abs/2005.01297 · HTML: https://mlsanity.com/paper/2005.01297/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 3 of 3)

- [Building Expressive and Tractable Probabilistic Generative Models: A Review](https://mlsanity.com/paper/2402.00759/) (2024)
- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [Fitting large mixture models using stochastic component selection](https://mlsanity.com/paper/2110.04776/) (2021)

## Abstract (arXiv)

In this work, we propose Sum-Product-Transform Networks (SPTN), an extension of sum-product networks that uses invertible transformations as additional internal nodes. The type and placement of transformations determine properties of the resulting SPTN with many interesting special cases. Importantly, SPTN with Gaussian leaves and affine transformations pose the same inference task tractable that can be computed efficiently in SPNs. We propose to store affine transformations in their SVD decompositions using an efficient parametrization of unitary matrices by a set of Givens rotations. Last but not least, we demonstrate that G-SPTNs achieve state-of-the-art results on the density estimation task and are competitive with state-of-the-art methods for anomaly detection.