# On the Relationship Between Probabilistic Circuits and Determinantal Point Processes

arXiv: https://arxiv.org/abs/2006.15233 · HTML: https://mlsanity.com/paper/2006.15233/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [On the Relationship Between Monotone and Squared Probabilistic Circuits](https://mlsanity.com/paper/2408.00876/) (2024)
- [Polynomial Semantics of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2402.09085/) (2024)
- [How to Square Tensor Networks and Circuits Without Squaring Them](https://mlsanity.com/paper/2512.17090/) (2025)
- [Probabilistic Generating Circuits -- Demystified](https://mlsanity.com/paper/2404.02912/) (2024)
- [On the Hardness of Approximating Distributions with Tractable Probabilistic Models](https://mlsanity.com/paper/2506.01281/) (2025)
- [The Limits of Tractable Marginalization](https://mlsanity.com/paper/2506.12020/) (2025)
- [A Quantum Information Theoretic Approach to Tractable Probabilistic Models](https://mlsanity.com/paper/2506.01824/) (2025)

## Abstract (arXiv)

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.