# Automatic Differentiable Monte Carlo: Theory and Application

arXiv: https://arxiv.org/abs/1911.09117 · HTML: https://mlsanity.com/paper/1911.09117/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 6 of 6)

- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Differentiable Simulations for Enhanced Sampling of Rare Events](https://mlsanity.com/paper/2301.03480/) (2023)
- [Lattice Protein Folding with Variational Annealing](https://mlsanity.com/paper/2502.20632/) (2025)
- [Variational optimization of the amplitude of neural-network quantum many-body ground states](https://mlsanity.com/paper/2308.09664/) (2023)
- [Generalized Lanczos method for systematic optimization of neural-network quantum states](https://mlsanity.com/paper/2502.01264/) (2025)
- [A differentiable programming framework for spin models](https://mlsanity.com/paper/2304.01772/) (2023)

## Abstract (arXiv)

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the general theory enabling infinite-order automatic differentiation on expectations computed by Monte Carlo with unnormalized probability distributions, which we call "automatic differentiable Monte Carlo" (ADMC). By implementing ADMC algorithms on computational graphs, one can also leverage state-of-the-art machine learning frameworks and techniques to traditional Monte Carlo applications in statistics and physics. We illustrate the versatility of ADMC by showing some applications: fast search of phase transitions and accurately finding ground states of interacting many-body models in two dimensions. ADMC paves a promising way to innovate Monte Carlo in various aspects to achieve higher accuracy and efficiency, e.g. easing or solving the sign problem of quantum many-body models through ADMC.