为什么斯坦福大学的cs231n支持向量机中的点产品是反向的？

Question

我正在观看斯坦福大学cs231n的Youtube视频，并试图把作业作为练习来做。在执行SVM时，我遇到了以下代码：

def svm_loss_naive(W, X, y, reg):
  """
  Structured SVM 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
  """
  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) # This line
    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

这是我遇到麻烦的台词：

scores = X[i].dot(W) 

这是在做xW产品，是不是应该是Wx？我的意思是W.dot(X[i])

Answer 1

由于数组形状分别为(D, C)和(N, D) ( W和X )，所以如果不首先将它们转换，就不能直接取点积(矩阵乘法必须是(C, D)·(D, N) )。

由于X.T.dot(W.T) == W.dot(X)，实现只是反转点积的顺序，而不是接受每个数组的转换。实际上，这只是取决于如何安排输入的决定。在这种情况下，(有些武断的)决定以更直观的方式安排样本和特性，而不是将点积作为x·W。