Suppose I have $n$ features as $Y$ = ($y_1 , y_2 ...., y_n$), and a matrix of $J$ of dimension $M$x$N$, one feature of $Y$ is selected randomly to be convolved with one random column of $J$ resulting a new vector called, for example, $X$.
The question, if I have the matrix $J$ and the vector $X$, can I detect the selected feature from $Y$ and selected column from $J$ using any deep learning algorithm? such that CNN or DNN ...... etc. What's about if I don't have the matrix $J$ am I still able to detect the selected feature $y$ and column of $J$ based on $X$ ?
For example, let's $Y = [1,2,3,4]$ and matrix $J$ is any random matrix of dimension $4$x$4$. Hence, one random number of $Y$ either 1 or 2 or 3 or 4 is going to be convolved with one column of matrix $J$, let's say element 2 of vector $Y$ is convolved with with second column of matrix $J$, so the resulted vector is $X$. So the question can we estimate the element selected from $Y$ based on matrix $J$ and resultant vector $X$ using machine or deep learning algorithm? I think yes we can, but what's the most appropriate algorithm to do that?