Summary and Contributions: The authors extend the Multi Layer Vector Approximate Message Passing (ML-VAMP) framework, used for inference of signals in multi-layer Generalised Linear Models, to the matrix-valued signal case, and call the algorithm ML-Mat-VAMP. In addition they provide an asymptotic analysis through the demonstration of so-called state evolution equations, that allow to describe the dynamics of the ML-Mat-VAMP through "macroscopic variables" such as mean-square error etc. They also provide numerical experiments to illustrate the validity of the state evolution in order to test error in simple learning model of a shallow neural net. UPDATE POST AUTHOR RESPONSE: My concerns have been mostly answered. About the main concern: the authors mention they will update the numerical part so that their example will not be covered anymore by the existing theory found in ref [1] which is satisfying.