I was trying to solve the CS 231n assignment 1 and had problems implementing gradient for softmax. Note, I'm not enrolled in the course and just doing it for learning purposes. I calculated the gradient by hand initially and it seems fine to me and I implemented the gradient as below, but when the code is run against numerical gradient the results are not matching, I want to understand where I'm going wrong in this implementation if someone could please help me clarify this clearly.
Thank you.
Code:
def softmax_loss_naive(W, X, y, reg):
"""
Softmax loss function, naive implementation (with loops)
Inputs have dimension D, there are C classes, and we operate on minibatches
of N examples.
Inputs:
- W: A numpy array of shape (D, C) containing weights.
- X: A numpy array of shape (N, D) containing a minibatch of data.
- y: A numpy array of shape (N,) containing training labels; y[i] = c means
that X[i] has label c, where 0 <= c < C.
- reg: (float) regularization strength
Returns a tuple of:
- loss as single float
- gradient with respect to weights W; an array of same shape as W
"""
# Initialize the loss and gradient to zero.
loss = 0.0
dW = np.zeros_like(W)
#############################################################################
# TODO: Compute the softmax loss and its gradient using explicit loops. #
# Store the loss in loss and the gradient in dW. If you are not careful #
# here, it is easy to run into numeric instability. Don't forget the #
# regularization! #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
num_train = X.shape[0]
for i in range(num_train):
score = X[i].dot(W)
correct = y[i]
denom_sum = 0.0
num = 0.0
for j,s in enumerate(score):
denom_sum += np.exp(s)
if j == correct:
num = np.exp(s)
else:
dW[:,j] = X[i].T * np.exp(s)
loss += -np.log(num / denom_sum)
dW[:, correct] += -X[i].T * ( (denom_sum - num) )
dW = dW / (denom_sum)
loss = loss / (num_train)
dW /= num_train
loss += reg * np.sum(W * W)
dW += reg * 2 * W
return loss, dW