I am now learning the stanford cs231n course. When completing the softmax_loss function, I found it is not easy to write in a full-vectorized type, especially dealing with the dw term. Below is my code. Can somebody optimize the code. Would be appreciated.
def softmax_loss_vectorized(W, X, y, reg):
loss = 0.0
dW = np.zeros_like(W)
num_train = X.shape[0]
num_classes = W.shape[1]
scores = X.dot(W)
scores -= np.max(scores, axis = 1)[:, np.newaxis]
exp_scores = np.exp(scores)
sum_exp_scores = np.sum(exp_scores, axis = 1)
correct_class_score = scores[range(num_train), y]
loss = np.sum(np.log(sum_exp_scores)) - np.sum(correct_class_score)
exp_scores = exp_scores / sum_exp_scores[:,np.newaxis]
# **maybe here can be rewroten into matrix operations**
for i in xrange(num_train):
dW += exp_scores[i] * X[i][:,np.newaxis]
dW[:, y[i]] -= X[i]
loss /= num_train
loss += 0.5 * reg * np.sum( W*W )
dW /= num_train
dW += reg * W
return loss, dW
Here's a vectorized implementation below. But I suggest you try to spend a little bit more time and get to the solution yourself. The idea is to construct a matrix with all softmax values and subtract -1 from the correct elements.
def softmax_loss_vectorized(W, X, y, reg):
num_train = X.shape[0]
scores = X.dot(W)
scores -= np.max(scores)
correct_scores = scores[np.arange(num_train), y]
# Compute the softmax per correct scores in bulk, and sum over its logs.
exponents = np.exp(scores)
sums_per_row = np.sum(exponents, axis=1)
softmax_array = np.exp(correct_scores) / sums_per_row
information_array = -np.log(softmax_array)
loss = np.mean(information_array)
# Compute the softmax per whole scores matrix, which gives the matrix for X rows coefficients.
# Their linear combination is algebraically dot product X transpose.
all_softmax_matrix = (exponents.T / sums_per_row).T
grad_coeff = np.zeros_like(scores)
grad_coeff[np.arange(num_train), y] = -1
grad_coeff += all_softmax_matrix
dW = np.dot(X.T, grad_coeff) / num_train
# Regularization
loss += 0.5 * reg * np.sum(W * W)
dW += reg * W
return loss, dW