解释拓扑量子相变的机器学习

Yi Zhang, P. Ginsparg, Eun-Ah Kim
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引用次数: 26

摘要

利用人工神经网络(ann)对量子多体问题的物理学获得新的理论见解的可能性越来越令人兴奋。“可解释性”仍然是一个问题:我们能否理解人工神经网络决策标准的基础,以便为我们的理论理解提供信息?由于解释非线性人工神经网络的难度更大,迄今为止,量子物质中的“可解释”机器学习仅限于线性模型,如支持向量机。本文考虑了Chern绝缘体、$\mathbb{Z}_2$拓扑绝缘体和$\mathbb{Z}_2$量子自旋液体模型中的拓扑量子相变,每个模型都使用浅全连接前馈神经网络。使用量子环拓扑学,一种“领域知识”引导的特征选择方法,有助于构建忠实的相图。由于人工神经网络的相对简单,它的学习可以在这三种情况下解释。为了识别拓扑阶段,人工神经网络学习物理上有意义的特征,如拓扑不变量和环的定义。在这些情况下的可解释性表明了基于人工神经网络的机器学习在量子多体问题上的未来应用的理论进展的希望。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Interpreting machine learning of topological quantum phase transitions
There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. "Interpretability" remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? "Interpretable" machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $\mathbb{Z}_2$ topological insulator, and $\mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a "domain knowledge"-guided approach to feature selection, facilitates the construction of faithful phase diagrams. Due to the relative simplicity of the ANN, its learning can be interpreted in each of the three cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.
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