Machine Learning of Chiral Symmetric Topological Insulator with Transformer-based Geometric Tomography

Machine learning is emerging as an important tool in the study of topological states of matter, whose existence is intrinsically linked to the geometric structure of quantum states. While many machine learning methods can efficiently predict topological invariants of band insulators, they often act like “black boxes”, failing to simultaneously reveal the underlying geometric features of the band structure. In this work, we design a neural network based on the Transformer architecture to characterize the topological properties of one-dimensional chiral symmetric topological insulators in the AIII symmetry class. After suitable training, the network not only accurately predicts topological invariants, but its attention map also autonomously highlights band regions with the maximal phase gradient as being topologically relevant. Remarkably, the network achieves this simultaneous identification even for the Hamiltonians whose topological numbers are not included in the training set. Moreover, we investigate how the number of sampling points and the choice of loss function affect the network training efficiency. This work provides an efficient and partially interpretable approach for characterizing topological states of matter.