• implement a fully-vectorized loss function for the Softmax classifier

• implement the fully-vectorized expression for its analytic gradient

• check your implementation with numerical gradient

• use a validation set to tune the learning rate and regularization strength

• optimize the loss function with SGD

• visualize the final learned weights

• Setting

• Load CIFAR-10

Implement the naive softmax loss function

# First implement the naive softmax loss function with nested loops.
# Open the file cs231n/classifiers/softmax.py and implement the
# softmax_loss_naive function.

from cs231n.classifiers.softmax import softmax_loss_naive
import time

# Generate a random softmax weight matrix and use it to compute the loss.
W = np.random.randn(3073, 10) * 0.0001
loss, grad = softmax_loss_naive(W, X_dev, y_dev, 0.0)

# As a rough sanity check, our loss should be something close to -log(0.1).
print('loss: %f' % loss)
print('sanity check: %f' % (-np.log(0.1)))

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)*****
    score = []    

    for i in range(X.shape[0]):
      score = X[i].dot(W)
      score -= np.max(score)  # for numeric stability
      n_score = np.exp(score)/np.sum(np.exp(score))

      loss += -np.log(np.exp(score[y[i]])/np.sum(np.exp(score)))

      for j in range(W.shape[1]):
        if j == y[i]:
          dW[:,y[i]] -= X[i]
        else :
          dW[:,j] += X[i]*n_score[j]
    
    loss /= X.shape[0]
    dW /= W.shape[1]

    loss += reg*np.sum(W*W)
    dW += reg*2*W
    
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW

loss: 2.425888
sanity check: 2.302585

Complete the implementation of softmax_loss_naive