探究机器学习为何难学拓扑相变，揭示其训练与泛化瓶颈。
Why is topology hard to learn?
- 构建张量-神经网络混合模型精确表达实空间拓扑不变量。
- 对比多种网络结构，发现拓扑学习在训练精度与泛化上存在显著差异。
- 为凝聚态物理中的可解释性机器学习提供关键实验依据。
机器学习在近似物理概念方面受到广泛关注，但其可解释性问题使得模型究竟学到了什么仍不明确。本文聚焦神经网络在物理中的原始应用——拓扑相分类，构建一种混合张量-神经网络，精确表达实空间拓扑不变量，并严格评估其可训练性与泛化能力。我们对张量-神经网络与多种神经网络进行基准测试，揭示其在训练表现和表征能力上的差异。研究凸显了学习拓扑不变量的挑战，为凝聚态物理中更准确、更具泛化能力的机器学习表示提供了重要基础。
原文摘要 · Abstract (English)
Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here we bridge the concept a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses real space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone towards more accurate and better generalizable machine learning representations in condensed matter physics.
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