mlsanityData to 14 Oct 2026

Probabilistic Neural Circuits

arXiv 2403.06235 ↗First posted 10 Mar 2024cs.LG cs.AI cs.NEcited by 7

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Abstract (arXiv)

Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions. Nevertheless, tractability comes at a cost: PCs are less expressive than neural networks. In this paper we introduce probabilistic neural circuits (PNCs), which strike a balance between PCs and neural nets in terms of tractability and expressive power. Theoretically, we show that PNCs can be interpreted as deep mixtures of Bayesian networks. Experimentally, we demonstrate that PNCs constitute powerful function approximators.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 19 of its 33 references that are in the map. First posted on arXiv 10 Mar 2024.

Builds on

19 of 33 references.

References · 19

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  3. 2017Decoupled Weight Decay Regularizationcited by 1,831
  4. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
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  6. 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 103
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  10. 2019On the Expressive Power of Deep Polynomial Neural Networkscited by 66
  11. 2022Training and Inference on Any-Order Autoregressive Models the Right Waycited by 64
  12. 2021Tractable Regularization of Probabilistic Circuitscited by 39
7 more
  1. 2016A Unified Approach for Learning the Parameters of Sum-Product Networkscited by 24
  2. 2022Continuous Mixtures of Tractable Probabilistic Modelscited by 19
  3. 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
  4. 2014On the Expressive Efficiency of Sum Product Networkscited by 16
  5. 2021HyperSPNs: Compact and Expressive Probabilistic Circuitscited by 14
  6. 2019Learning Logistic Circuitscited by 12
  7. 2017Sum-Product-Quotient Networkscited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2026Breaking the Factorization Barrier in Diffusion Language Modelscited by 11
  2. 2025Tractable Representation Learning with Probabilistic Circuitscited by 4
  3. 2025Independence Is Not an Issue in Neurosymbolic AIcited by 1
  4. 2025A Quantum Information Theoretic Approach to Tractable Probabilistic Modelscited by 1
  5. 2026Geometry-Aware Probabilistic Circuits via Voronoi Tessellationscited by 1
  6. 2026Hallucination as an Anomaly: Dynamic Intervention via Probabilistic Circuitscited by 1
  7. 2025Learning Tractable Distributions Of Language Model Continuationscited by 0