Classifying topological sector via machine learning

We employ a machine learning technique for an estimate of the topological charge $Q$ of gauge configurations in SU(3) Yang-Mills theory in vacuum. As a first trial, we feed the four-dimensional topological charge density with and without smoothing into the convolutional neural network and train it to estimate the value of $Q$. We find that the trained neural network can estimate the value of $Q$ from the topological charge density at small flow time with high accuracy. Next, we perform the dimensional reduction of the input data as a preprocessing and analyze lower dimensional data by the neural network. We find that the accuracy of the neural network does not have statistically-significant dependence on the dimension of the input data. From this result we argue that the neural network does not find characteristic features responsible for the determination of $Q$ in the higher dimensional space.