# PeTeR: Post-Training Robustification of Probabilistic Circuits

arXiv: https://arxiv.org/abs/2607.07671 · HTML: https://mlsanity.com/paper/2607.07671/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [Distributionally Robust Learning with Stable Adversarial Training](https://mlsanity.com/paper/2106.15791/) (2021)
- [Distributionally Robust Games: f-Divergence and Learning](https://mlsanity.com/paper/1702.05371/) (2017)
- [Discrete Optimal Transport with Independent Marginals is #P-Hard](https://mlsanity.com/paper/2203.01161/) (2022)
- [Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization](https://mlsanity.com/paper/1604.07243/) (2016)
- [Optimal Transport for Probabilistic Circuits](https://mlsanity.com/paper/2410.13061/) (2024)

## Abstract (arXiv)

Probabilistic circuits (PCs) can model complex joint distributions while supporting exact and efficient computation of many inference queries. However, standard likelihood-based PC learning is vulnerable to overfitting and fragile generalization when confronted with data noise, small sample sizes, or distribution shifts. This can be mitigated using distributionally-robust optimization which consider worst-case distributions within a Wasserstein ball of the empirical distribution, but current methods are limited to training a model from scratch in this framework. Instead, we propose PeTeR: a novel, data-free post-training framework designed to robustify pre-trained PCs against distribution shifts without retraining from scratch. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR effectively robustifies baseline models against both random and adversarial perturbations, achieving competitive or superior performance to data-dependent robust learning baselines.