Hessian-based toolbox for interpretable and reliable machines learning physics"

Identifying phase transitions is one of the key problems in quantum many-body physics. The challenge is the exponential growth of the complexity of quantum systems’ description with the number of studied particles, which quickly renders exact numerical analysis impossible. A promising alternative is to harness the power of machine learning (ML) methods designed to deal with large datasets [1]. However, ML models, and especially neural networks (NNs), are known for their black-box construction, i.e., they usually hinder any insight into the reasoning behind their predictions. As a result, if we apply ML to novel problems, neither we can fully trust their predictions (lack of reliability) nor learn what the ML model learned (lack of interpretability). I will present a set of Hessian-based methods opening the black box of ML models, increasing their interpretability and reliability. We demonstrate how these methods can guide physicists in understanding patterns responsible for the phase transition. We also show that influence functions allow checking that the NN, trained to recognize known quantum phases, can predict new unknown ones. We present this power both for the numerically simulated data from the one-dimensional extended spinless Fermi-Hubbard model [2] and experimental topological data [3]. We also show how we can generate error bars for the NN’s predictions and check whether the NN predicts using extrapolation instead of extracting information from the training data [4]. The presented toolbox is entirely independent of the ML model’s architecture and is thus applicable to various physical problems.

[1] J. Carrasquilla. (2020). Machine learning for quantum matter, Advances in Physics: X, 5:1.

[2] A. Dawid et al. (2020). Phase detection with neural networks: interpreting the black box. New J. Phys. 22, 115001.

[3] N. Käming, A. Dawid, K. Kottmann et al. (2021). Unsupervised machine learning of topological phase transitions from experimental data. Mach. Learn.: Sci. Technol. 2, 035037.

[4] A. Dawid et al. (2022). Hessian-based toolbox for interpretable and reliable machine learning in physics. Mach. Learn.: Sci. Technol. 3, 015002.

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Zoom meeting details

Topic: Quantum Information and Quantum Computing Working Group Seminar
Time: Wednesday, 19.01.2022, 15:15 Warsaw (CET)

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