A. 对称性与AI的对称性 (Symmetry meets AI)

We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no information on symmetry is provided. We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance. As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.

翻译：我们探索神经网络(NN)能否在学习执行任务时发现对称性的存在。为此,我们根据严格控制的物理模板对数百个NNS进行“ it 诱饵任务” 培训,该模板没有提供对称信息。我们使用所有这些NNS最后隐藏层的输出值,预测其尺寸会更少,作为对称性分类任务的投入,并显示关于对称性的信息确实由原NNN在未经指导的情况下确定。作为这一程序的跨学科应用,我们从不同风格的艺术绘画中,例如Picasso、Pollock和Van Gogh的艺术绘画中,我们发现了对称性的存在和程度。