I have a neural network, which produces a single value when excited with input. I need to use this value returned by the network to threshold another array. The result of this threshold operation is used to compute a loss function (the value of threshold is not known before hand and needs to be arrived at by training). Following is an MWE
import torch
x = torch.randn(10, 1) # Say this is the output of the network (10 is my batch size)
data_array = torch.randn(10, 2) # This is the data I need to threshold
ground_truth = torch.randn(10, 2) # This is the ground truth
mse_loss = torch.nn.MSELoss() # Loss function
# Threshold
thresholded_vals = data_array * (data_array >= x) # Returns zero in all places where the value is less than the threshold, the value itself otherwise
# Compute loss and gradients
loss = mse_loss(thresholded_vals, ground_truth)
loss.backward() # Throws error here
Since the operation of thresholding returns a tensor array that is devoid of any gradients the backward() operation throws error.
How does one train a network in such a case?
Your threshold function is not differentiable in the threshold, therefore torch does not calculate the gradient for the threshold which is why your example is not working.
import torch
x = torch.randn(10, 1, requires_grad=True) # Say this is the output of the network (10 is my batch size)
data_array = torch.randn(10, 2, requires_grad=True) # This is the data I need to threshold
ground_truth = torch.randn(10, 2) # This is the ground truth
mse_loss = torch.nn.MSELoss() # Loss function
# Threshold
thresholded_vals = data_array * (data_array >= x) # Returns zero in all places where the value is less than the threshold, the value itself otherwise
# Compute loss and gradients
loss = mse_loss(thresholded_vals, ground_truth)
loss.backward() # Throws error here
print(x.grad)
print(data_array.grad)
Output:
None #<- for the threshold x
tensor([[ 0.1088, -0.0617], #<- for the data_array
[ 0.1011, 0.0000],
[ 0.0000, 0.0000],
[-0.0000, -0.0000],
[ 0.2047, 0.0973],
[-0.0000, 0.2197],
[-0.0000, 0.0929],
[ 0.1106, 0.2579],
[ 0.0743, 0.0880],
[ 0.0000, 0.1112]])