# Discovering quantum phenomena with Interpretable Machine Learning

arXiv: https://arxiv.org/abs/2604.16015 · HTML: https://mlsanity.com/paper/2604.16015/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 17 of 17)

- [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)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [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)
- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator](https://mlsanity.com/paper/2509.13821/) (2025)
- [Machine-Guided Discovery of a Real-World Rogue Wave Model](https://mlsanity.com/paper/2311.12579/) (2023)
- [Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients](https://mlsanity.com/paper/2401.04978/) (2024)
- [Disentanglement by means of action-induced representations](https://mlsanity.com/paper/2602.06741/) (2026)

## Built on by (most cited first, 3 of 3)

- [Towards unsupervised representation learning for quantum data: quantum models with inference and generation](https://mlsanity.com/paper/2609.00372/) (2026)
- [QILP-0: Constructing Observational Declarative Twins of Quantum Circuits](https://mlsanity.com/paper/2609.01049/) (2026)
- [TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data](https://mlsanity.com/paper/2609.20693/) (2026)

## Abstract (arXiv)

Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically meaningful and interpretable representations from a broad class of unlabeled quantum datasets. From raw measurement data alone, the learned representation reveals rich information about the underlying structure of quantum phase spaces. We further augment the learning pipeline with symbolic methods, enabling the discovery of compact analytical descriptors that serve as order parameters for the distinct regimes emerging in the learned representations. We demonstrate the framework on experimental Rydberg-atom snapshots, classical shadows of the cluster Ising model, and hybrid discrete-continuous fermionic data, revealing previously unreported phenomena such as a corner-ordering pattern in the Rydberg arrays. These results establish a general framework for the automated and interpretable discovery of physical laws from diverse quantum datasets. All methods are available through qdisc, an open-source Python library designed to make these tools accessible to the broader community.