【python实现卷积神经网络】批量归一化层实现

代码来源：https://github.com/eriklindernoren/ML-From-Scratch

卷积神经网络中卷积层Conv2D（带stride、padding）的具体实现：https://www.cnblogs.com/xiximayou/p/12706576.html

激活函数的实现（sigmoid、softmax、tanh、relu、leakyrelu、elu、selu、softplus）：https://www.cnblogs.com/xiximayou/p/12713081.html

损失函数定义（均方误差、交叉熵损失）：https://www.cnblogs.com/xiximayou/p/12713198.html

优化器的实现（SGD、Nesterov、Adagrad、Adadelta、RMSprop、Adam）：https://www.cnblogs.com/xiximayou/p/12713594.html

卷积层反向传播过程：https://www.cnblogs.com/xiximayou/p/12713930.html

全连接层实现：https://www.cnblogs.com/xiximayou/p/12720017.html

class BatchNormalization(Layer):
    """Batch normalization.
    """
    def __init__(self, momentum=0.99):
        self.momentum = momentum
        self.trainable = True
        self.eps = 0.01
        self.running_mean = None
        self.running_var = None

    def initialize(self, optimizer):
        # Initialize the parameters
        self.gamma  = np.ones(self.input_shape)
        self.beta = np.zeros(self.input_shape)
        # parameter optimizers
        self.gamma_opt  = copy.copy(optimizer)
        self.beta_opt = copy.copy(optimizer)

    def parameters(self):
        return np.prod(self.gamma.shape) + np.prod(self.beta.shape)

    def forward_pass(self, X, training=True):

        # Initialize running mean and variance if first run
        if self.running_mean is None:
            self.running_mean = np.mean(X, axis=0)
            self.running_var = np.var(X, axis=0)

        if training and self.trainable:
            mean = np.mean(X, axis=0)
            var = np.var(X, axis=0)
            self.running_mean = self.momentum * self.running_mean + (1 - self.momentum) * mean
            self.running_var = self.momentum * self.running_var + (1 - self.momentum) * var
        else:
            mean = self.running_mean
            var = self.running_var

        # Statistics saved for backward pass
        self.X_centered = X - mean
        self.stddev_inv = 1 / np.sqrt(var + self.eps)

        X_norm = self.X_centered * self.stddev_inv
        output = self.gamma * X_norm + self.beta

        return output

    def backward_pass(self, accum_grad):

        # Save parameters used during the forward pass
        gamma = self.gamma

        # If the layer is trainable the parameters are updated
        if self.trainable:
            X_norm = self.X_centered * self.stddev_inv
            grad_gamma = np.sum(accum_grad * X_norm, axis=0)
            grad_beta = np.sum(accum_grad, axis=0)

            self.gamma = self.gamma_opt.update(self.gamma, grad_gamma)
            self.beta = self.beta_opt.update(self.beta, grad_beta)

        batch_size = accum_grad.shape[0]

        # The gradient of the loss with respect to the layer inputs (use weights and statistics from forward pass)
        accum_grad = (1 / batch_size) * gamma * self.stddev_inv * (
            batch_size * accum_grad
            - np.sum(accum_grad, axis=0)
            - self.X_centered * self.stddev_inv**2 * np.sum(accum_grad * self.X_centered, axis=0)
            )

        return accum_grad

    def output_shape(self):
        return self.input_shape

批量归一化的过程：

前向传播的时候按照公式进行就可以了。需要关注的是BN层反向传播的过程。

accm_grad是上一层传到本层的梯度。反向传播过程：