I am trying to train a machine learning model on product matrices. These product matrices will represent an item (from a finite set) that has been transformed using various matrix transformations (from a finite set). The goal is to use a GAN to generate original product matrices, and then find the closest items and transformations that correspond to that product matrix.
I was originally thinking of using dynamic programming, as this problem can be thought of as a "making change" problem. However, instead of subtracting from the sum to get a smaller value, this application would be multiplying by the inverse of a matrix, so I don't know how dynamic programming would work in this scenario.
Does anyone know of an algorithm or variant that I could use to solve this problem? Any help would be appreciated!