这个减法在 python 中是如何工作的？

Question

我的问题只涉及此代码的一小部分，但我将其全部发布以防万一。取自http://neuralnetworksanddeeplearning.com/chap1.html#implementing_our_network_to_classify_digits（从这里向下滚动查看代码解释）

import numpy as np

    class Network(object):

    def __init__(self, sizes):
        """The list ``sizes`` contains the number of neurons in the
        respective layers of the network.  For example, if the list
        was [2, 3, 1] then it would be a three-layer network, with the
        first layer containing 2 neurons, the second layer 3 neurons,
        and the third layer 1 neuron.  The biases and weights for the
        network are initialized randomly, using a Gaussian
        distribution with mean 0, and variance 1.  Note that the first
        layer is assumed to be an input layer, and by convention we
        won't set any biases for those neurons, since biases are only
        ever used in computing the outputs from later layers."""
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        self.weights = [np.random.randn(y, x)
                        for x, y in zip(sizes[:-1], sizes[1:])]

    def feedforward(self, a):
        """Return the output of the network if ``a`` is input."""
        for b, w in zip(self.biases, self.weights):
            a = sigmoid(np.dot(w, a)+b)
        return a

    def SGD(self, training_data, epochs, mini_batch_size, eta,
            test_data=None):
        """Train the neural network using mini-batch stochastic
        gradient descent.  The ``training_data`` is a list of tuples
        ``(x, y)`` representing the training inputs and the desired
        outputs.  The other non-optional parameters are
        self-explanatory.  If ``test_data`` is provided then the
        network will be evaluated against the test data after each
        epoch, and partial progress printed out.  This is useful for
        tracking progress, but slows things down substantially."""
        if test_data: n_test = len(test_data)
        n = len(training_data)
        for j in xrange(epochs):
            random.shuffle(training_data)
            mini_batches = [
                training_data[k:k+mini_batch_size]
                for k in xrange(0, n, mini_batch_size)]
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta)
            if test_data:
                print "Epoch {0}: {1} / {2}".format(
                    j, self.evaluate(test_data), n_test)
            else:
                print "Epoch {0} complete".format(j)

    def update_mini_batch(self, mini_batch, eta):
        """Update the network's weights and biases by applying
        gradient descent using backpropagation to a single mini batch.
        The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
        is the learning rate."""
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        for x, y in mini_batch:
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)
            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
        self.weights = [w-(eta/len(mini_batch))*nw
                        for w, nw in zip(self.weights, nabla_w)]
        self.biases = [b-(eta/len(mini_batch))*nb
                       for b, nb in zip(self.biases, nabla_b)]

    def backprop(self, x, y):
        """Return a tuple ``(nabla_b, nabla_w)`` representing the
        gradient for the cost function C_x.  ``nabla_b`` and
        ``nabla_w`` are layer-by-layer lists of numpy arrays, similar
        to ``self.biases`` and ``self.weights``."""
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        # feedforward
        activation = x
        activations = [x] # list to store all the activations, layer by layer
        zs = [] # list to store all the z vectors, layer by layer
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation)+b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
        # backward pass
        delta = self.cost_derivative(activations[-1], y) * \
            sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        # Note that the variable l in the loop below is used a little
        # differently to the notation in Chapter 2 of the book.  Here,
        # l = 1 means the last layer of neurons, l = 2 is the
        # second-last layer, and so on.  It's a renumbering of the
        # scheme in the book, used here to take advantage of the fact
        # that Python can use negative indices in lists.
        for l in xrange(2, self.num_layers):
            z = zs[-l]
            sp = sigmoid_prime(z)
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
        return (nabla_b, nabla_w)

    def evaluate(self, test_data):
        """Return the number of test inputs for which the neural
        network outputs the correct result. Note that the neural
        network's output is assumed to be the index of whichever
        neuron in the final layer has the highest activation."""
        test_results = [(np.argmax(self.feedforward(x)), y)
                        for (x, y) in test_data]
        return sum(int(x == y) for (x, y) in test_results)

    def cost_derivative(self, output_activations, y):
        """Return the vector of partial derivatives \partial C_x /
        \partial a for the output activations."""
        return (output_activations-y)

#### Miscellaneous functions
def sigmoid(z):
    """The sigmoid function."""
    return 1.0/(1.0+np.exp(-z))

def sigmoid_prime(z):
    """Derivative of the sigmoid function."""
    return sigmoid(z)*(1-sigmoid(z))

忽略大部分代码，除非您需要退后一步了解数据结构。首先，在self.cost_derivative(activations[-1], y) 方法中的一半self.cost_derivative(activations[-1], y) 行中，我们可以看到传递了两个值 - 据我所知，这两个值都是数组（我可以在输出它们时看到这一点，它是也由作者解释）。在cost_derivative 方法中，它所做的只是将两个值相减——但它们是数组，那么它是如何工作的呢？

当我在 python 中执行此操作时，我可以理解地得到一个错误

a = [1,2,4]
b = [5,6,7]
print(a-b)

我相信这可能是因为它们是 numpy 数组？

此外，sigmoid 和 sigmoid_prime 函数也发生了类似的事情，其中​​ z 是一个数组（查看这些函数在哪里以数组形式调用参数）......即使函数将就好像它是一个单一的值......它是如何工作的？我假设它只是对数组中的每个值执行此操作？

从本质上讲，我一直看到我希望仅适用于单个值的功能与数组一起使用。

为任何解释干杯，我发布的链接有更多解释。

Answer 1

当你减去两个列表时：

a = [1,2,4]
b = [5,6,7]
print(a-b)

python 调用一个函数__sub__ 试图减去它们。 Vanilla python的__sub__不能减去list，list对象没有__sub__函数，所以会报错。

当你从一个 numpy 数组中减去一个列表时：

a = [1,2,4]
b = numpy.array([5,6,7])
print(a-b)

Vanilla __sub__ 仍然失败，但 python 查找任何特定于对象的 __sub__ 函数并找到 numpy 的。 Numpy 将所有其他对象包装在 np.asarray() 中，并尝试像 numpy 数组一样减去它们。由于列表映射到一维数组，并且大小相同，因此减法有效，您最终会得到一个数组作为输出。

Answer 2

你说得对，因为 output_activations 和 y 是 numpy 数组。 Numpy 是一个用于快速矩阵运算的python 库，numpy 数组重载- 以执行矩阵减法。

但是，在您的示例中，[1,2,4] 只是一个普通的 python 列表，而不是一个 numpy 数组，并且没有为列表定义 - 运算符。如果你用 numpy 数组替换你的列表，你的输出会更有意义：

import numpy as np

a = np.array([1,2,4])
b = np.array([5,6,7])
print(a-b)
# [-4 -4 -3]

Answer 3

是的，您遇到了错误，因为这些是 numpy 数组而不是标量。 请改用 np.subtract(a, b)。您需要记住您正在尝试减去向量。