manifold sub manifolds of the high dimensional space okay so let's assume that our data lives not filling up the entire input space but living on some lower dimensional sub manifold or sub manifolds and in this case we can we can look into the manifold learning literature and there's a beautiful paper by Donna Hahn crimes that defines what's called the Hessian eigen map manifold learning technique which is is basically trying to flatten a curvy manifold using the tangent a CN along the manifold so we can just a dot this this same measure