# Define back-prop on a custom layer by enforcing the sum of its weight to equal 1

#1

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,X2,X3,X4,X5

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}^{5} the parameters to learn with 0 <= W_{i} <= 1 and their sum equals 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 respecting the constraints 0 <= W_{i} <= 1 and their sum equals 1?

Here is what l have tried :

class weighted_linear_combination_layer(nn.module):
'''
I would like to write a new layer (first layer in my CNN before convolutional layer), which is
a  linear combination of K inputs. For the sake of illustration we set here K=5.

X1,X2,X3,X4,X5. each Xi is of dimension 20x20.

The target : learning a weighted linear combination of Xi as follow :

Final_X= W1 X1+ W2 X2+ W3 X3+ W4 X4+ W5 X5 # Final_X is of dimension 20x20

W1, W2,W3, W4,W5 are the scalar parameters of the layer to learn with back-propagation wich are
initialized at random.

I would like to ensure that  Wi =>0 and  sum(W1,W2,W3,W4,W5)=1

'''

def __int__(self):

'''
self.w1=nn.Parameter(torch.randn(1))
self.w2 = nn.Parameter(torch.randn(1))
self.w3 = nn.Parameter(torch.randn(1))
self.w4 = nn.Parameter(torch.randn(1))
self.w5 = nn.Parameter(torch.randn(1))

'''

self.weights=nn.Parameter(nn.functional.softmax(torch.randn(5))) # weights in range [0,1]  where their sum equal 1

def forward(self,x):
# x here is a tensor  5x20x20
# final_x=self.w1*x[0]+self.w2*x[1]+self.w3*x[2]+self.w4*x[3]+self.w5*x[4]
#normalized_weights=nn.functional.softmax(self.weight)
final_x=nn.functional.linear(x,self.weights)

return final_x

module=weighted_linear_combination_layer()
x=Variable(torch.randn(5,20,20))
out=module(x)
'''
l would like to keep the fifth weights W1,W2,W3,W4,W5 between [0,1] and their
sum equals 1.

How can l do that ?

for p in weighted_linear_combination_layer.parameters():
p.clamp_(0, 1)
Does this operation do the job ?
'''
out2=conv_layer1(out)
out3=fc(out2)
loss_train=my_loss(out3,labels)
loss.backward()


Thank you

@rasbt @tom @ptrblck any cue ?

(Clément Pinard) #2

Instead of having the explicit weights W1…W6, maybe you can construct them so that the softmax of them is the weights you want.

def forward(self,x):
normalized_weights = nn.functional.softmax(self.weights)
x = nn.functional.linear(x,normalized_weights)