We present the Hamilton–Jacobi equation approach to a class of high dimensional statistical inference problems. We start by introducing the model of matrix tensor products, the free energy associated with them, and motivation for studying their high-dimensional limit. Then we sketch the basic setup of the Hamilton–Jacobi equation approach. Lastly, I discuss the application of this approach to models with multiple hidden layers.
This is based on joint work with Hong-Bin Chen, and Jean-Christophe Mourrat.