dimensional manifold in high dimensional space where points on that manifold were translates and rotations of each other then the it's very convenient that these augmented data points that are generated from just your raw initial training data will live on the same data manifold okay so there's a in this particular setting you can you can prove a result that says that just starting with date writing out the the cost of say cross-entropy cost function with data augmentation terms you can actually develop that those data