CS231N作业1Softmax

1.完成文件cs231n/classifiers/softmax.py中的softmax_loss_naive方法

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!                                                           #
  #############################################################################
  num_train=X.shape[0]
  num_classes=W.shape[1]
  loss=0.0
  for i in range(num_train):
    f_i=X[i].dot(W)
    f_i-=np.max(f_i)
    sum_j=np.sum(np.exp(f_i))
    p=lambda k:np.exp(f_i[k])/sum_j
    loss+=-np.log(p(y[i]))
    for k in range(num_classes):
      p_k=p(k)
      dW[:,k]+=(p_k-(k==y[i]))*X[i]
  loss/=num_train
  loss+=0.5*reg*np.sum(W*W)
  dW/=num_train
  dW+=reg*W
  #############################################################################
  #                          END OF YOUR CODE                                 #
  #############################################################################

  return loss, dW

2.完成向量版的Softmax损失函数，即softmax_loss_vectorized方法

def softmax_loss_vectorized(W, X, y, reg):
  """
  Softmax loss function, vectorized version.

  Inputs and outputs are the same as softmax_loss_naive.
  """
  # Initialize the loss and gradient to zero.
  loss = 0.0
  dW = np.zeros_like(W)

  #############################################################################
  # TODO: Compute the softmax loss and its gradient using no 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!                                                           #
  #############################################################################
  num_train=X.shape[0]
  f=X.dot(W)
  f-=np.max(f,axis=1,keepdims=True)
  sum_f=np.sum(np.exp(f),axis=1,keepdims=True)
  p=np.exp(f)/sum_f
  loss=np.sum(-np.log(p[np.arange(num_train),y]))
  ind=np.zeros_like(p)
  ind[np.arange(num_train),y]=1
  dW=X.T.dot(p-ind)
  loss/=num_train
  loss+=0.5*reg*np.sum(W*W)
  dW/=num_train
  dW+=reg*W
  #############################################################################
  #                          END OF YOUR CODE                                 #
  #############################################################################

  return loss, dW

3. 超参数调优

from cs231n.classifiers import Softmax
results = {}
best_val = -1
best_softmax = None
learning_rates = [1e-7, 5e-7]
regularization_strengths = [2.5e4, 5e4]

################################################################################
# TODO:                                                                        #
# Use the validation set to set the learning rate and regularization strength. #
# This should be identical to the validation that you did for the SVM; save    #
# the best trained softmax classifer in best_softmax.                          #
################################################################################
iters=100
for lr in learning_rates:
    for rs in regularization_strengths:
        softmax=Softmax()
        softmax.train(X_train,y_train,learning_rate=lr,reg=rs,num_iters=iters)
        y_train_pred=softmax.predict(X_train)
        acc_train=np.mean(y_train_pred==y_train)
        y_val_pred=softmax.predict(X_val)
        acc_val=np.mean(y_val==y_val_pred)
        results[(lr,rs)]=(acc_train,acc_val)
        if best_val<acc_val:
            best_val=acc_val
            best_softmax=softmax
################################################################################
#                              END OF YOUR CODE                                #
################################################################################
    
# Print out results.
for lr, reg in sorted(results):
    train_accuracy, val_accuracy = results[(lr, reg)]
    print('lr %e reg %e train accuracy: %f val accuracy: %f' % (
                lr, reg, train_accuracy, val_accuracy))
    
print('best validation accuracy achieved during cross-validation: %f' % best_val)