  We prove that the usual gradient flow in parameter space that underlies many
training algorithms for neural networks in deep learning can be continuously
deformed into an adapted gradient flow which yields (constrained) Euclidean
gradient flow in output space. Moreover, if the Jacobian of the outputs with
respect to the parameters is full rank (for fixed training data), then the time
variable can be reparametrized so that the resulting flow is simply linear
interpolation, and a global minimum can be achieved.
