Before revision:  method we are able to leverage proof techniques of SGD and establish a global convergence theory and rates of convergence for SNR . As a special case, our theory also provides a new global convergence theory for the original Newton-Raphson method under strictly weaker assumptions as compared to what is commonly used for global convergence . There are many ways to re-write an optimization problem as nonlinear equations. Each re-write would lead to a distinct method when using SNR. As such, we believe that SNR and its global convergence theorywill open the way to designing and analysing a host of new stochastic second order methods .
After revision:  method we are able to leverage proof techniques of SGD and establish a global convergence theory and rates of convergence for SNR . As a special case, our theory also provides a new global convergence theory for the original Newton-Raphson method under strictly weaker assumptions as compared to the classic monotone convergence theory .