tensorflow - VNET Dice loss higher than 1

Question

I am training a Vnet on a segmentation problem with Keras 2.2.4 and Tensorflow 1.12.0 (I cannot change the tensorflow version). The masks, i.e. y_true, are (1,200,150,100,2) arrays. I want to minimize the dice loss defined as:

'''

def dice_loss_foreground(y_true, y_pred):

    elements_per_class=tf.math.reduce_sum(y_true[:,:,:,:,1])
    predicted_per_class=tf.math.reduce_sum(y_pred[:,:,:,:,1])
    intersection=tf.math.scalar_mul(2.0,tf.math.reduce_sum(tf.math.multiply(y_pred[:,:,:,:,1],y_true[:,:,:,:,1])))
    union=elements_per_class+predicted_per_class
    acc=intersection/(union+0.0001)
    return 1.0-acc

'''

I have tested this definition on mock examples and it goes from 0 to 1 but, during training, the loss reaches a number higher than 1. Can anybody help me in understanding why? Thanks!

Answer 1

The loss function is not merely made by the dice definition but it contains the regularization too. So, even if dice coefficient loss should be in range 0-1, it may be greater than 1 depending on regularization.