# TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data

arXiv: https://arxiv.org/abs/2609.20693 · HTML: https://mlsanity.com/paper/2609.20693/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 125 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 30 of 36)

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- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
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- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
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- [Deep Learning is Not So Mysterious or Different](https://mlsanity.com/paper/2503.02113/) (2025)
- [Amazing Things Come From Having Many Good Models](https://mlsanity.com/paper/2407.04846/) (2024)
- [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)
- [What Has a Foundation Model Found? Using Inductive Bias to Probe for World Models](https://mlsanity.com/paper/2507.06952/) (2025)
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- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [From superposition to sparse codes: interpretable representations in neural networks](https://mlsanity.com/paper/2503.01824/) (2025)
- [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)
- [Probing hidden spin order with interpretable machine learning](https://mlsanity.com/paper/1804.08557/) (2018)
- [Why is AI hard and Physics simple?](https://mlsanity.com/paper/2104.00008/) (2021)
- [Machine learning phase transitions: Connections to the Fisher information](https://mlsanity.com/paper/2311.10710/) (2023)
- [Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks](https://mlsanity.com/paper/2205.04051/) (2022)

## Abstract (arXiv)

Detecting phases of matter in general relies on identifying the correct order parameter - a task that remains notoriously difficult for unknown transitions and traditionally is guided by physical intuition and educated guess. Neural networks have recently offered an alternative route by locating phase transitions in known models without any a priori physical knowledge. Yet these approaches remain black boxes and only identify phases without elucidating their properties. Moreover, they often struggle when confronted with realistic, noisy experimental data, which constitute the ultimate testbed for automated methods in physics. Here, we bridge these perspectives by introducing TetrisCNN, a convolutional architecture with parallel branches of differently shaped filters, reminiscent of Tetris blocks, that learns sparse, interpretable latent representations directly in terms of spin correlators. Applied to experimental snapshots of two-dimensional Ising and XY quantum simulators measured in multiple bases, the network not only detects phase transitions and crossovers but also expresses its latent representation and decision boundaries as symbolic formulas built from experimentally measurable spin correlators. This framework opens the way to integrating interpretable neural networks with quantum simulators to uncover and understand new phases of matter.