Conservation law presumption from the manifold structure captured by Deep Neural Networks

It is suggested that Deep Neural Networks (DNN), which continues to develop in recent years, has a function to extract information of data sets necessary to achieve a given task by modeling the distribution as a manifold.
In addition to confirming the usefulness of DNN technology, numerous researchers and engineers are developing various DNN algorithms and tuning parameters.
This situation means that enormous knowledge on the manifold structure for various data sets is being accumulated.
The purpose of this research is to propose a method to extract manifold structure with complex shape extracted in an interpretable form.
Specifically, we propose a method to extract the symmetry of manifold for coordinate transformation.
Applying the proposed method to the time series data of the moving object according to the central force potential, it was confirmed that symmetry according to the conservation law of angular momentum could be extracted.