Hi, thanks for your reply. One example of the relationship between w1,x1 and w,x could be to round each element in w and x to integer first, then expand them to bits expression. For instance, if x = [[1,0], [1,2]], then x1 wuold be [[0,0], [1,0], [0,1], [1,0]]. Then the result y would be w1x1 plus some post processing.
In this case, y is not directly computed from wx, and hence the backpropogation would not flow properly. I wonder if there is a way to tell the neural network to treat y as computed from wx?