Machine learning meets the CHSH scenario

In this work, we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterising 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 CHSH scenario, both the 4-dimensional variant, for which an analytical solution is known, and the 8-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. Sadly, these are precisely the cases which are interesting from the academic point of view. In order to improve performance on hard cases one must, especially for the 8-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.