# Autonomous phase discovery

arXiv: https://arxiv.org/abs/2609.33802 · HTML: https://mlsanity.com/paper/2609.33802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 86 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients](https://mlsanity.com/paper/2010.01709/) (2020)
- [Machine learning discovery of new phases in programmable quantum simulator snapshots](https://mlsanity.com/paper/2112.10789/) (2021)
- [Probing hidden spin order with interpretable machine learning](https://mlsanity.com/paper/1804.08557/) (2018)
- [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)
- [Neural network based order parameter for phase transitions and its applications in high-entropy alloys](https://mlsanity.com/paper/2109.05598/) (2021)
- [Discovering and decoding latent mean-field structure with variational autoencoders](https://mlsanity.com/paper/2606.08694/) (2026)

## Abstract (arXiv)

Understanding quantum phases of matter has long relied on physicists' intuition and mathematical tools such as symmetry and topology. Remarkably successful as these approaches have been, they provide no universal way to explore a Hamiltonian space whose organizing principle is not known in advance. In this work, we introduce a fully autonomous system combining differentiable programming and unsupervised learning for quantum phase discovery. The search evaluates ground-state data along an adaptive trajectory rather than on a predetermined parameter grid. We demonstrate the system with three different solvers and benchmark it against random sampling at equal ground-state-evaluation budgets. On a generalized cluster chain hosting up to 200 distinct phases, the search finds up to 25 more phases at the same budget, and matches random sampling given thirty times its budget. On a 50-parameter Chern insulator, it reaches sectors not obtained by the simple harmonic constructions considered here, in a family whose inverse problem remains open, while recovering all sectors found by sampling. Our results establish autonomous, gradient-driven exploration of Hamiltonian space as a practical route to discovering quantum phases without phase labels or a prescribed target phase.