heterogenous Neural Network output My neural network (actually it is a CNN) must output the transformation matrix coefficient
it should output tx and ty for translation that lay in the range of [0,200], 2 coefficients for shear [0.7, 1.5] and one angle [-30 60] degrees AND other 10 coefficients/weights to perform the linear combination of predefined vector sets to find first the pixel coordinates at that space and then apply the collected transformation matrix. Those final coordinates will then compared to labels and the model will be optimized based on that comparison criterion
as you may notice the output has different ranges and nature(angles, unitless ones, and pixel)
Is there any way to push the model outputting coefficients in the desired ranges?
 A: Hard constraints are typically enforced by a nonlinearity such as the $\text{tanh}$ function, which squashes the domain $(-\infty, \infty)$ to $(-1,1)$. You can scale this to enforce any desired output interval.
There are also constraints which are soft. For example, if i'm denoising an image, I know every pixel has a value between 0 and 1. However, the loss (L1/L2) doesn't blow up or become nondifferentiable outside of that range -- nothing goes horribly wrong if the model predicts a value outside of that interval. In these cases, it's also possible to keep the output layer perfectly linear, and simply clip the output to the desired range at test time.
Also, as a sidenote, typically it's desireable to normalize the outputs / desired output range to be in the unit interval, or any other reasonable range. This helps avoid any optimization pathologies or weirdness.
A: after thinking about how one can impose an output parameter to lay in a specific range. we can consider this as a regularization problem. my suggestion is when you want an output x to lay in [a, b] we may add a term to the loss function lambda*(max(x-b,0)+min(a-x,0)). lambda should express the importance of x in the ensemble of outputs X
