As an aside, you might not want to use an exponential loss.
Now to your specific question: Your label values are 0 and 1.
Is there a simple way to implement my own exponential function.
Anyway, I think of it as being: exp mismatch between prediction and actual , where exp mismatch is used to strongly amplify being wrong.
Although the first and last predictions are right, they are only mildly right, while the second prediction is strongly wrong, making the predictions overall more wrong than right.
Your known class labels are 0 and 1, where 1 indicates that the image is a picture of a bird, and 0 indicates that it is not a bird.