Backpropagation in python: cannot understand a line of code

Question

I am trying to read the following code for back propagation in python

probs = exp_scores /np.sum(exp_scores, axis=1, keepdims=True) 
#Backpropagation
delta3 = probs
delta3[range(num_examples), y] -= 1
dW2 = (a1.T).dot(delta3)
....

but I cannot understand the following line of the code:

delta3[range(num_examples), y] -= 1

could you please tell me what does this do?

Thank you very much for your help!

Answer 1

There are two things here. First it is using numpy slicing to select only a fraction of delta3. Secondly it is removing 1 to every element of this fraction of the matrix.

More precisely, delta3[range(num_example), y] is selecting lines of the matrix delta3 ranging from 0 to num_examples but only selecting column y.