# Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders

arXiv: https://arxiv.org/abs/2506.11982 · HTML: https://mlsanity.com/paper/2506.11982/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 13 Jun 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Quantum circuit synthesis with diffusion models](https://mlsanity.com/paper/2311.02041/) (2023)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Operationally meaningful representations of physical systems in neural networks](https://mlsanity.com/paper/2001.00593/) (2020)
- [Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data](https://mlsanity.com/paper/2011.03474/) (2020)
- [Machine learning discovery of new phases in programmable quantum simulator snapshots](https://mlsanity.com/paper/2112.10789/) (2021)
- [Explainable Representation Learning of Small Quantum States](https://mlsanity.com/paper/2306.05694/) (2023)
- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
- [Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks](https://mlsanity.com/paper/2205.04051/) (2022)

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

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator](https://mlsanity.com/paper/2509.13821/) (2025)
- [Discovering quantum phenomena with Interpretable Machine Learning](https://mlsanity.com/paper/2604.16015/) (2026)
- [Disentanglement by means of action-induced representations](https://mlsanity.com/paper/2602.06741/) (2026)
- [TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data](https://mlsanity.com/paper/2609.20693/) (2026)
- [Autonomous phase discovery](https://mlsanity.com/paper/2609.33802/) (2026)

## Abstract (arXiv)

Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no supervision nor prior knowledge of the system at study. Yet, the ability of VAEs to create meaningful, interpretable representations relies on their accurate approximation of the underlying probability distribution of their input. When dealing with quantum data, VAEs must hence account for its intrinsic randomness and complex correlations. While VAEs have been previously applied to quantum data, they have often neglected its probabilistic nature, hindering the extraction of meaningful physical descriptors. Here, we demonstrate that two key modifications enable VAEs to learn physically meaningful latent representations: a decoder capable of faithfully reproduce quantum states and a probabilistic loss tailored to this task. Using benchmark quantum spin models, we identify regimes where standard methods fail while the representations learned by our approach remain meaningful and interpretable. Applied to experimental data from Rydberg atom arrays, the model autonomously uncovers the phase structure without access to prior labels, Hamiltonian details, or knowledge of relevant order parameters, highlighting its potential as an unsupervised and interpretable tool for the study of quantum systems.