连接二元性和机器学习
Connecting Dualities and Machine Learning
摘要：
对偶性被广泛应用于量子场论和弦论中，以获得高精度的关联函数。在这里，我们给出了一些例子，其中双重数据表示在监督分类中很有用，将机器学习和理论物理中的典型任务联系起来。然后，我们将讨论如何在神经网络的潜在维度中实施这种有益的表示。我们发现，额外的贡献的损失的基础上的功能分离，功能匹配相对于所需的表示，和一个“简单的”关联函数的良好性能可以导致已知和未知的双重表示。这是第一个证明计算机可以找到对偶的概念。我们讨论了我们的例子，离散傅立叶变换和伊辛模型的基础上，连接到理论物理学中的其他对偶，例如塞伯格对偶。
英文摘要：
Dualities are widely used in quantum field theories and string theory to obtain correlation functions at high accuracy. Here we present examples where dual data representations are useful in supervised classification, linking machine learning and typical tasks in theoretical physics. We then discuss how such beneficial representations can be enforced in the latent dimension of neural networks. We find that additional contributions to the loss based on feature separation, feature matching with respect to desired representations, and a good performance on a `simple' correlation function can lead to known and unknown dual representations. This is the first proof of concept that computers can find dualities. We discuss how our examples, based on discrete Fourier transformation and Ising models, connect to other dualities in theoretical physics, for instance Seiberg duality.
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