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batchnormalization_answer.py
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batchnormalization_answer.py
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import numpy as np
def batchnorm_forward(x, gamma, beta, bn_param):
mode = bn_param["mode"]
eps = 1e-5
momentum = 0.9
N, D = x.shape
running_mean = bn_param.get("running_mean", np.zeros(D, dtype=x.dtype))
running_var = bn_param.get("running_var", np.zeros(D, dtype=x.dtype))
out, cache = None, None
if mode == 'train':
# TODO: 实现训练过程中batch normalization层的前向传播
# ******请在此段内填写代码(开始)******#
x_mean = np.mean(x, axis=0)
x_sigma = np.var(x, axis=0)
x_hat = (x - x_mean) / np.sqrt(x_sigma + eps)
out = gamma * x_hat + beta
cache = (x, x_hat, gamma, x_mean, x_sigma, eps)
running_mean = momentum * running_mean + (1 - momentum) * x_mean
running_var = momentum * running_var + (1 - momentum) * x_sigma
# ******请在此段内填写代码(结束)******#
elif mode == 'test':
# TODO: 实现测试过程中batch normalization层的前向传播
# ******请在此段内填写代码(开始)******#
x_hat = (x - running_mean) / np.sqrt(running_var + eps)
out = gamma * x_hat + beta
# ******请在此段内填写代码(结束)******#
else:
raise ValueError('ValueError: Batch Normalization mode "%s", only accept for "train" or "test". ' % mode)
bn_param["running_mean"] = running_mean
bn_param["running_var"] = running_var
return out, cache
def batchnorm_backward(dout, cache):
dx, dgamma, dbeta = None, None, None
# TODO: 实现batch normalization层的反向传播,将结果保存在dx, dgamma, dbeta三个变量中
# ******请在此段内填写代码(开始)******#
x, x_hat, gamma, x_mean, x_sigma, eps = cache
N, D = dout.shape
dgamma = np.sum(x_hat * dout, axis=0)
dbeta = np.sum(dout, axis=0)
dx_hat = dout * gamma
dvar = np.sum(dx_hat * (x - x_mean) * (-0.5) * np.power(x_sigma + eps, -1.5), axis=0)
dmean = np.sum(dx_hat * -1 / np.sqrt(x_sigma + eps), axis=0) + dvar * np.mean(-2 * (x - x_mean), axis=0)
dx = 1 / np.sqrt(x_sigma + eps) * dx_hat + dvar * 2.0 / N * (x - x_mean) + 1.0 / N * dmean
# ******请在此段内填写代码(结束)******#
return dx, dgamma, dbeta