batch normalization代码示例

好的，以下是一个简单的 batch normalization 的代码示例：

import numpy as np

class BatchNorm:
    def __init__(self, gamma, beta, eps=1e-5):
        self.gamma = gamma
        self.beta = beta
        self.eps = eps
        self.mean = None
        self.var = None
        self.batch_size = None
        self.xc = None
        self.std = None

    def forward(self, x):
        self.batch_size = x.shape[0]
        self.mean = np.mean(x, axis=0)
        self.xc = x - self.mean
        self.var = np.var(x, axis=0)
        self.std = np.sqrt(self.var + self.eps)
        x_norm = self.xc / self.std
        out = self.gamma * x_norm + self.beta
        return out

    def backward(self, dout):
        dx_norm = dout * self.gamma
        dxc = dx_norm / self.std
        dstd = -np.sum(dx_norm * self.xc / (self.std * self.std), axis=0)
        dvar = 0.5 * dstd / self.std
        dsq = np.ones_like(dout) / self.batch_size * dvar
        dxc += 2 * self.xc * dsq
        dmu = -np.sum(dxc, axis=0)
        dx = dxc + np.ones_like(dout) / self.batch_size * dmu
        dgamma = np.sum(dout * (self.xc / self.std), axis=0)
        dbeta = np.sum(dout, axis=0)
        return dx, dgamma, dbeta

其中，gamma 和 beta 是可学习的参数，eps 是一个小常数，用于避免除以零的情况。