Gauge invariant input to neural network for path optimization method

Understand

We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method.

• While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple gauge theory, the optimization does not work well when the gauge degrees of freedom remain.
• We propose to employ a gauge invariant input, such as plaquette, to overcome this problem.
• The efficiency of the gauge invariant input to the neural network is evaluated for the 2-dimensional $U(1)$ gauge theory with a complex coupling.