# Variational Autoregressive Networks with probability priors

arXiv: https://arxiv.org/abs/2605.16020 · HTML: https://mlsanity.com/paper/2605.16020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 14 of 14)

- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories](https://mlsanity.com/paper/2302.14082/) (2023)
- [Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects](https://mlsanity.com/paper/2410.14466/) (2024)
- [Hierarchical autoregressive neural networks for statistical systems](https://mlsanity.com/paper/2203.10989/) (2022)
- [Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations](https://mlsanity.com/paper/2111.10189/) (2021)
- [The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems](https://mlsanity.com/paper/2302.08347/) (2023)
- [Multilevel Generative Samplers for Investigating Critical Phenomena](https://mlsanity.com/paper/2503.08918/) (2025)
- [Simulating first-order phase transition with hierarchical autoregressive networks](https://mlsanity.com/paper/2212.04955/) (2022)
- [Mutual information of spin systems from autoregressive neural networks](https://mlsanity.com/paper/2304.13412/) (2023)
- [Estimation of the reduced density matrix and entanglement entropies using autoregressive networks](https://mlsanity.com/paper/2506.04170/) (2025)
- [Sampling two-dimensional spin systems with transformers](https://mlsanity.com/paper/2604.27738/) (2026)

## Abstract (arXiv)

Monte Carlo methods are essential across diverse scientific fields, yet their efficiency is frequently hampered by critical slowing down-a sharp increase in autocorrelation times near phase transitions. Although deep learning approaches, such as neural-network-based samplers, have been proposed to alleviate this issue, they face another serious problem: the difficulty of training the models. This difficulty partially stems from the overly general nature of original machine-learning architectures, which often ignore underlying physical symmetries and force networks to relearn them from scratch. In this paper, we demonstrate that incorporating physical priors into the model significantly enhances performance. Building upon existing strategies that integrate spin-spin interactions, we propose a framework that utilizes a prior probability distribution as a starting point for training. Our results for the Ising model, as well as for the Edwards-Anderson spin glass model, suggest that moving away from `blank slate' models in favor of physics-informed priors reduces the training burden and facilitates the simulation of larger system sizes in discrete spin models.