# Neural Network Approximators for Marginal MAP in Probabilistic Circuits

arXiv: https://arxiv.org/abs/2402.03621 · HTML: https://mlsanity.com/paper/2402.03621/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Inference in Probabilistic Graphical Models by Graph Neural Networks](https://mlsanity.com/paper/1803.07710/) (2018)
- [Solving Marginal MAP Exactly by Probabilistic Circuit Transformations](https://mlsanity.com/paper/2111.04833/) (2021)
- [Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks](https://mlsanity.com/paper/1703.06045/) (2017)
- [Maximum A Posteriori Inference in Sum-Product Networks](https://mlsanity.com/paper/1708.04846/) (2017)
- [Decomposition Bounds for Marginal MAP](https://mlsanity.com/paper/1511.02619/) (2015)

## Built on by (most cited first, 2 of 2)

- [Learning to Condition: A Neural Heuristic for Scalable MPE Inference](https://mlsanity.com/paper/2509.25217/) (2025)
- [ReMAP: Lossless Residual Neural Lifting for Scalable MAP Inference in Arbitrary-Order Markov Random Fields](https://mlsanity.com/paper/2411.18954/) (2024)

## Abstract (arXiv)

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks because PCs can solve marginal inference (MAR) tasks in time that scales linearly in the size of the network. Unfortunately, the maximum-a-posteriori (MAP) and marginal MAP (MMAP) tasks remain NP-hard in these models. Inspired by the recent work on using neural networks for generating near-optimal solutions to optimization problems such as integer linear programming, we propose an approach that uses neural networks to approximate (M)MAP inference in PCs. The key idea in our approach is to approximate the cost of an assignment to the query variables using a continuous multilinear function, and then use the latter as a loss function. The two main benefits of our new method are that it is self-supervised and after the neural network is learned, it requires only linear time to output a solution. We evaluate our new approach on several benchmark datasets and show that it outperforms three competing linear time approximations, max-product inference, max-marginal inference and sequential estimation, which are used in practice to solve MMAP tasks in PCs.