Geometry-Aware Probabilistic Circuits via Voronoi Tessellations
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Abstract (arXiv)
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to incorporate geometric structure directly into the sum nodes of a PC. However, na"ively introducing such structure breaks tractability. We formalize this incompatibility and develop two complementary solutions: (1) an approximate inference framework that provides guaranteed lower and upper bounds for inference, and (2) a structural condition for VT under which exact tractable inference is recovered. Finally, we introduce a differentiable relaxation for VT that enables gradient-based learning and empirically validate the resulting approach on standard density estimation tasks.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 32 of its 45 references that are in the map. First posted on arXiv 12 Mar 2026.
Builds on
32 of 45 references.
References · 32
- 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
- 2017Masked Autoregressive Flow for Density Estimationcited by 684
- 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 103
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- 2021Tractable Regularization of Probabilistic Circuitscited by 39
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- 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
20 more
- 2024Sum of Squares Circuitscited by 21
- 2022Continuous Mixtures of Tractable Probabilistic Modelscited by 19
- 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuitscited by 19
- 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
- 2021HyperSPNs: Compact and Expressive Probabilistic Circuitscited by 14
- 2024Building Expressive and Tractable Probabilistic Generative Models: A Reviewcited by 12
- 2022Semi-Discrete Normalizing Flows through Differentiable Tessellationcited by 11
- 2022VQ-Flows: Vector Quantized Local Normalizing Flowscited by 10
- 2025Scaling Probabilistic Circuits via Monarch Matricescited by 9
- 2023Probabilistic Integral Circuitscited by 8
- 2022Voronoi Density Estimator for High-Dimensional Data: Computation, Compactification and Convergencecited by 7
- 2023Probabilistic Circuits That Know What They Don't Knowcited by 7
- 2024Probabilistic Neural Circuitscited by 7
- 2017Sum-Product-Quotient Networkscited by 5
- 2024Credibility-Aware Multi-Modal Fusion Using Probabilistic Circuitscited by 5
- 2024A Unified Framework for Human-Allied Learning of Probabilistic Circuitscited by 5
- 2025Rethinking Probabilistic Circuit Parameter Learningcited by 4
- 2025Tractable Representation Learning with Probabilistic Circuitscited by 4
- 2022An Efficient and Continuous Voronoi Density Estimatorcited by 3
- 2025Tractable Sharpness-Aware Learning of Probabilistic Circuitscited by 3
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