Title: Machine Learning Topological Invariants with Neural Networks,
Abstract: In this Letter we supervisedly train neural networks to distinguish different
topological phases in the context of topological band insulators. After
training with Hamiltonians of one-dimensional insulators with chiral symmetry,
the neural network can predict their topological winding numbers with nearly
100% accuracy, even for Hamiltonians with larger winding numbers that are not
included in the training data. These results show a remarkable success that the
neural network can capture the global and nonlinear topological features of
quantum phases from local inputs. By opening up the neural network, we confirm
that the network does learn the discrete version of the winding number formula.
We also make a couple of remarks regarding the role of the symmetry and the
opposite effect of regularization techniques when applying machine learning to
physical systems.