Machine learning meeting the Clauser-Horne-Shimony-Holt scenario

In this work we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterizing the quantum set of correlations. As our main focus is on assessing the usefulness and effectiveness of the ML approach, we focus exclusively on the Clauser-Horne-Shimony-Holt scenario, both the four-dimensional variant, for which an analytical solution is known, and the eight-dimensional variant, for which no analytical solution is known but numerical approaches are relatively well understood. We consider a wide selection of approaches, ranging from simple data science models to dense neural networks. The two classes of models that perform well are support vector machines and dense neural networks, and they are the main focus of this work. We conclude that while it is relatively easy to achieve good performance on average, it is hard to train a model that performs well on the hard cases, i.e., points in the vicinity of the boundary of the quantum set, which are precisely the cases that are interesting from the academic point of view. In order to improve performance on hard cases we must, especially for the eight-dimensional problem, resort to a tailored choice of training data, which means that we are implicitly feeding our intuition and biases into the model. We feel that this is an important and often overlooked aspect of applying ML models to academic problems, where data generation or data selection is performed according to some implicit subjective criteria. In this way, it is possible to unconsciously steer our model so that it exhibits features that we are interested in seeing. Hence, special care must be taken while determining whether ML methods can be considered objective and unbiased in the context of academic problems.