Why is topology hard to learn?
This work addresses challenges in learning topological invariants for condensed matter physics, representing an incremental step towards more accurate and generalizable machine learning representations.
The paper tackled the problem of learning topological invariants in physics using machine learning, by constructing a hybrid tensor-neural network that exactly expresses a real-space topological invariant and benchmarking it against other neural networks, showing differences in trainability and representational power.
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.