Euclidian Loss (self written)

Hey there, I am trying to implement euclidian loss (from VGG paper). It is not really described there well, but what I am assuming is, that it just measures the euclidian distance between two coordinates and returns it as sort of a loss:
So, my deep CNN wants to predict two coordinates (output tensor of size (batch_size, 1, 2)) lets say out = [[0.3, 0.6]] where batch_size = 1, and my ground_truth = [[0.5, 0.7]] the euclidian loss should be loss = math.sqrt((0.3 - 0.5)**2) + math.sqrt((0.6 - 0.7)**2)

1st question: Do I understand the concept of euclidian loss right?
2nd question: Does the below implementation looks right to you? (first time I create a own loss function)

class EuclidianError(nn.Module):
    """Implements euclidian distance as an error"""
    def forward(self, x_pred, x_ground_truth):
        err = torch.zeros(1)[0]

        for i in range(len(x_ground_truth)):    # i is index of batch
            for j in range(len(x_ground_truth[i])):    # j is index of to predict coordinates within one item of a batch
                for k in range(len(x_ground_truth[i][j])):    # k is index of x, y position in coordinates
                    err += math.sqrt((x_ground_truth[i][j][k] - x_pred[i][j][k])**2)

        return err

Thank you for your help!

Iā€™m not sure why there are 3 nested loops, since your data seems to have only 2 dimensions.
If you want to use it as a criterion without implementing the backward method, you should stick to PyTorch functions. So you should change math.sqrt to torch.sqrt.
Alternatively, you could get rid of the for loops (which can be pretty slow) and use a faster approach:

x = torch.randn(10, 2)
y = torch.randn(10, 2)
loss = torch.sqrt((x - y)**2).sum()

Figuered it out the hard way myself, you are totally right! Thanks!