李飞飞CS231n关于hinge loss函数求导的问题

在做CS231 2020 Assignment1的SVM部分时，遇到了关于hinge loss的求梯度（求导）编程实现的问题，故在此记录一下。
首先，给出hinge loss在多分类时的表达式：
$$L_i=\sum _{j\ne y_i}max(0,w_j^T{x}_i-w_{y_i}^T{x}_i+\Delta )$$
其中，$\Delta =1$。通过对$w$求偏导，可以得到最终的求导结果：
$$\frac{\partial L_i}{\partial w_j}=1(w_j^T{x}_i-w_{y_i}^{T}x+\Delta )x_i$$
$$\frac{\partial L_i}{\partial w_{y_i}}=-(\sum _{j\ne y_i}1(w_j^T{x}_i-w_{y_i}^{T}x+\Delta ))x_i$$
最终的代码如下所示：

    dW = np.zeros(W.shape) # initialize the gradient as zero

    # compute the loss and the gradient
    num_classes = W.shape[1]
    num_train = X.shape[0]
    loss = 0.0
    for i in range(num_train):
        scores = X[i].dot(W)
        #print(scores.shape) (10,)
        correct_class_score = scores[y[i]]
        for j in range(num_classes):
            if j == y[i]:
                continue
            margin = scores[j] - correct_class_score + 1 # note delta = 1
            if margin > 0:
                loss += margin
                dW[:,y[i]]-=X[i].T
                dW[:,j]+=X[i].T

    # Right now the loss is a sum over all training examples, but we want it
    # to be an average instead so we divide by num_train.
    loss /= num_train

    # Add regularization to the loss.
    loss += reg * np.sum(W * W)

    #############################################################################
    # TODO:                                                                     #
    # Compute the gradient of the loss function and store it dW.                #
    # Rather than first computing the loss and then computing the derivative,   #
    # it may be simpler to compute the derivative at the same time that the     #
    # loss is being computed. As a result you may need to modify some of the    #
    # code above to compute the gradient.                                       #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    dW/=num_train
	dW+=reg*W
	
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
    
    return loss, dW