Cross Entropy Function (python)

Question

I am learning a neural network and I want to write a function cross_entropyin python. Where is it defined as

where Nis the number of samples, kis the number of classes, logis the natural logarithm, t_i,jis 1 if the sample iis in the class jand 0otherwise and p_i,jis the predicted probability that the sample iis in the class j. To avoid numerical problems with the logarithm, copy the predictions to the range [10^{−12}, 1 − 10^{−12}].

According to the above description, I wrote down the codes by clipping the predictions into a range [epsilon, 1 − epsilon], and then calculated cross_entropy based on the above formula.

def cross_entropy(predictions, targets, epsilon=1e-12):
    """
    Computes cross entropy between targets (encoded as one-hot vectors)
    and predictions. 
    Input: predictions (N, k) ndarray
           targets (N, k) ndarray        
    Returns: scalar
    """
    predictions = np.clip(predictions, epsilon, 1. - epsilon)
    ce = - np.mean(np.log(predictions) * targets) 
    return ce

cross_entropy.

predictions = np.array([[0.25,0.25,0.25,0.25],
                        [0.01,0.01,0.01,0.96]])
targets = np.array([[0,0,0,1],
                  [0,0,0,1]])
ans = 0.71355817782  #Correct answer
x = cross_entropy(predictions, targets)
print(np.isclose(x,ans))

False, , cross_entropy . cross_entropy(predictions, targets). 0.178389544455, ans = 0.71355817782. - , ?

Answer 1

, , N , N = 2 ( ). , :

def cross_entropy(predictions, targets, epsilon=1e-12):
    """
    Computes cross entropy between targets (encoded as one-hot vectors)
    and predictions. 
    Input: predictions (N, k) ndarray
           targets (N, k) ndarray        
    Returns: scalar
    """
    predictions = np.clip(predictions, epsilon, 1. - epsilon)
    N = predictions.shape[0]
    ce = -np.sum(np.sum(targets*np.log(predictions+1e-9)))/N
    return ce

predictions = np.array([[0.25,0.25,0.25,0.25],
                        [0.01,0.01,0.01,0.96]])
targets = np.array([[0,0,0,1],
                   [0,0,0,1]])
ans = 0.71355817782  #Correct answer
x = cross_entropy(predictions, targets)
print(np.isclose(x,ans))

, , , np.sum(). , 1e-9 np.log(), log (0) . , !