# Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data

arXiv: https://arxiv.org/abs/2011.03474 · HTML: https://mlsanity.com/paper/2011.03474/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2020.

## Built on by (most cited first, 13 of 13)

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- [Machine learning discovery of new phases in programmable quantum simulator snapshots](https://mlsanity.com/paper/2112.10789/) (2021)
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- [Machine learning phase transitions: Connections to the Fisher information](https://mlsanity.com/paper/2311.10710/) (2023)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons](https://mlsanity.com/paper/2111.04881/) (2021)
- [Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients](https://mlsanity.com/paper/2401.04978/) (2024)
- [Fluctuation based interpretable analysis scheme for quantum many-body snapshots](https://mlsanity.com/paper/2304.06029/) (2023)
- [Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets](https://mlsanity.com/paper/2102.01103/) (2021)
- [Machine learning reveals features of spinon Fermi surface](https://mlsanity.com/paper/2306.03143/) (2023)
- [TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data](https://mlsanity.com/paper/2609.20693/) (2026)

## Abstract (arXiv)

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish between snapshots that can not be identified using traditional one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from this approach. Here, using a novel set of nonlinearities we develop a network architecture that discovers features in the data which are directly interpretable in terms of physical observables. In particular, our network can be understood as uncovering high-order correlators which significantly differ between the data studied. We demonstrate this new architecture on sets of simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, which is realized in state-of-the art quantum gas microscopy experiments. From the trained networks, we uncover that the key distinguishing features are fourth-order spin-charge correlators, providing a means to compare experimental data to theoretical predictions. Our approach lends itself well to the construction of simple, end-to-end interpretable architectures and is applicable to arbitrary lattice data, thus paving the way for new physical insights from machine learning studies of experimental as well as numerical data.