Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed probability distribution can be reproduced using only classical resources. This causal inference task is challenging even for simple networks, both analytically and using standard numerical techniques. We propose to use neural networks as numerical tools to overcome these challenges, by learning the classical strategies required to reproduce a distribution. As such, a neural network acts as an oracle for an observed behavior, demonstrating that it is classical if it can be learned. We apply our method to several examples in the triangle configuration. After demonstrating that the method is consistent with previously known results, we give solid evidence that a quantum distribution recently proposed by Gisin is indeed nonlocal as conjectured. Finally we examine the genuinely nonlocal distribution recently presented by Renou et al., and, guided by the findings of the neural network, conjecture nonlocality in a new range of parameters in these distributions. The method allows us to get an estimate on the noise robustness of all examined distributions.

表征网络中的量子非局部性是一个具有挑战性但重要的问题。使用量子源，可以实现传统上无法达到的分布。研究的关键点是决定是否只能使用经典资源来重现观察到的概率分布。即使对于简单网络，无论是在分析上还是在使用标准数值技术时，这种因果推理任务都具有挑战性。我们建议通过学习再现分布所需的经典策略，使用神经网络作为数值工具来克服这些挑战。因此，神经网络充当了观察到的行为的预言，表明如果可以学习，它就是经典的。我们将我们的方法应用于三角形配置中的几个示例。在证明该方法与先前已知的结果一致之后，我们提供了有力的证据，证明了Gisin最近提出的量子分布确实是非局部的。最后，我们检查了Renou等人最近提出的真正的非局部分布，并在神经网络的发现指导下，在这些分布的新参数范围内推​​测了非局部性。该方法允许我们获得所有检查分布的噪声鲁棒性的估计。