We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under infinitesimal symmetry transformations on the input variables. As symmetry transformations are generated post-training, the methodology does not rely on sampling of the full representation space or binning of the dataset, and the possibility of false identification is minimised. We demonstrate our method in the SU(3)-symmetric (non-) linear $\Sigma$ model.

翻译：我们提出一个简单的方法来通过人工神经网络的回归来识别数据集中连续的测代数对称。 我们的建议利用输入变量上极微量对称变体下输出变量的 $\ mathcal{O}(\\ epsilon\ 2) 比例缩放。 当对称变体产生后, 方法并不依赖于对全部代表空间的抽样或数据集的宾客, 并且将虚假识别的可能性降到最低。 我们在 SU(3) 线性对称( 非线性) $\ Sigma$ 模型中展示了我们的方法 。