Hello,
l would like to define a new layer before convolutional layer, which is just a weighted linear combination of my inputs with respect to certain scales.  What l want is to learn the weights of this linear combination.
My inputs are :
X1=0.5X1
X2=1.2X2
X3= 3.6X3
X4=0.002X4
X5=1.75X5
X6=1X6
where X_{i} \in \mathbf{R}^{20 \times 20}
The layer that l would like to add is as follow :
X= \sum_{i} W_{i} X_{i}
Where  X  \in \mathbf{R}^{20 \times 20} and
W \in  \mathbf{R}^{6} the parameters to learn with    0 <= W_{i} <= 1
Then X is fed to convolutional layer.
My question is as follow :
How can l define such layer and do back-propagation on it ?
Thank you