python - 每个 mini-Batch 是否只更新一次权重/偏差？

Question

我正在关注神经网络教程，我对更新权重的函数有疑问。

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]                #Initialize bias matrix with 0's
    nabla_w = [np.zeros(w.shape) for w in self.weights]               #Initialize weights matrix with 0's
    for x, y in mini_batch:                                           #For tuples in one mini_batch
        delta_nabla_b, delta_nabla_w = self.backprop(x, y)            #Calculate partial derivatives of bias/weights with backpropagation, set them to delta_nabla_b
        nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)] #Generate a list with partial derivatives of bias of every neuron
        nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)] #Generate a list with partial derivatives of weights for every neuron
    self.weights = [w-(eta/len(mini_batch))*nw                        #Update weights according to update rule
                    for w, nw in zip(self.weights, nabla_w)]          #What author does is he zips 2 lists with values he needs (Current weights and partial derivatives), then do computations with them.
    self.biases = [b-(eta/len(mini_batch))*nb                         #Update biases according to update rule
                   for b, nb in zip(self.biases, nabla_b)]

我在这里不明白的是使用 for 循环来计算 nabla_b 和 nabla_w （权重/偏差的偏导数）。对小批量中的每个训练示例进行反向传播，但只更新一次权重/偏差。

在我看来，假设我们有一个大小为 10 的小批量，我们计算 nabla_b 和 nabla_w 10 次，然后在 for 循环完成后更新权重和偏差。但是 for 循环不是每次都重置 nabla_b 和 nabla_b 列表吗？为什么我们不更新self.weights并self.biases 在for 循环内？

神经网络工作得很好，所以我认为我在某个地方犯了一个小错误。

仅供参考：我正在关注的教程的相关部分可以在这里找到

标签： pythonneural-networkgradient-descentstochastic-gradient

Answer 1

不，更新发生在批次结束后，依次应用每个训练更新。规范描述说我们计算所有更新的平均值并根据该平均值进行调整；反过来，通过每次更新进行调整在算术上是等效的。

首先，初始化偏差和权重数组。

nabla_b = [np.zeros(b.shape) for b in self.biases]                #Initialize bias matrix with 0's
nabla_w = [np.zeros(w.shape) for w in self.weights]               #Initialize weights matrix with 0's

对于迷你匹配中的每个观察，将训练结果插入到偏差和权重数组中

for x, y in mini_batch:                                           #For tuples in one mini_batch
    delta_nabla_b, delta_nabla_w = self.backprop(x, y)            #Calculate partial derivatives of bias/weights with backpropagation, set them to delta_nabla_b
    nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)] #Generate a list with partial derivatives of bias of every neuron
    nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)] #Generate a list with partial derivatives of weights for every neuron

最后，调整每个权重和偏差，依次调整每个训练结果的值。

self.weights = [w-(eta/len(mini_batch))*nw                        #Update weights according to update rule
                for w, nw in zip(self.weights, nabla_w)]          #What author does is he zips 2 lists with values he needs (Current weights and partial derivatives), then do computations with them.
self.biases = [b-(eta/len(mini_batch))*nb                         #Update biases according to update rule
               for b, nb in zip(self.biases, nabla_b)]