# Soft Learning Probabilistic Circuits

arXiv: https://arxiv.org/abs/2403.14504 · HTML: https://mlsanity.com/paper/2403.14504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 11 of 11)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [Bayesian Learning of Sum-Product Networks](https://mlsanity.com/paper/1905.10884/) (2019)
- [Joints in Random Forests](https://mlsanity.com/paper/2006.14937/) (2020)
- [TraDE: Transformers for Density Estimation](https://mlsanity.com/paper/2004.02441/) (2020)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [Automatic Bayesian Density Analysis](https://mlsanity.com/paper/1807.09306/) (2018)
- [Online Structure Learning for Sum-Product Networks with Gaussian Leaves](https://mlsanity.com/paper/1701.05265/) (2017)

## Built on by (most cited first, 1 of 1)

- [Tractable Probabilistic Models for Investment Planning](https://mlsanity.com/paper/2511.13888/) (2025)

## Abstract (arXiv)

Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a range of exact inferences. This paper focuses on the main algorithm for training PCs, LearnSPN, a gold standard due to its efficiency, performance, and ease of use, in particular for tabular data. We show that LearnSPN is a greedy likelihood maximizer under mild assumptions. While inferences in PCs may use the entire circuit structure for processing queries, LearnSPN applies a hard method for learning them, propagating at each sum node a data point through one and only one of the children/edges as in a hard clustering process. We propose a new learning procedure named SoftLearn, that induces a PC using a soft clustering process. We investigate the effect of this learning-inference compatibility in PCs. Our experiments show that SoftLearn outperforms LearnSPN in many situations, yielding better likelihoods and arguably better samples. We also analyze comparable tractable models to highlight the differences between soft/hard learning and model querying.