CS231n 2016 通关 第五、六章 Batch Normalization 作业

BN层在实际中应用广泛。

上一次总结了使得训练变得简单的方法，比如SGD+momentum RMSProp Adam，BN是另外的方法。

cell 1 依旧是初始化设置

cell 2 读取cifar-10数据

cell 3 BN的前传

 # Check the training-time forward pass by checking means and variances
 # of features both before and after batch normalization

 # Simulate the forward pass for a two-layer network
 N, D1, D2, D3 = 200, 50, 60, 3
 X = np.random.randn(N, D1)
 W1 = np.random.randn(D1, D2)
 W2 = np.random.randn(D2, D3)
 a = np.maximum(0, X.dot(W1)).dot(W2)

 print 'Before batch normalization:'
 print '  means: ', a.mean(axis=0)
 print '  stds: ', a.std(axis=0)

 # Means should be close to zero and stds close to one
 print 'After batch normalization (gamma=1, beta=0)'
 a_norm, _ = batchnorm_forward(a, np.ones(D3), np.zeros(D3), {'mode': 'train'})
 print '  mean: ', a_norm.mean(axis=0)
 print '  std: ', a_norm.std(axis=0)

 # Now means should be close to beta and stds close to gamma
 gamma = np.asarray([1.0, 2.0, 3.0])
 beta = np.asarray([11.0, 12.0, 13.0])
 a_norm, _ = batchnorm_forward(a, gamma, beta, {'mode': 'train'})
 print 'After batch normalization (nontrivial gamma, beta)'
 print '  means: ', a_norm.mean(axis=0)
 print '  stds: ', a_norm.std(axis=0)

　　相应的核心代码：

     buf_mean = np.mean(x, axis=0)
     buf_var = np.var(x, axis=0)
     x_hat = x - buf_mean
     x_hat = x_hat / (np.sqrt(buf_var + eps))

     out = gamma * x_hat + beta
     #running_mean = momentum * running_mean + (1 - momentum) * sample_mean
     #running_var = momentum * running_var + (1 - momentum) * sample_var
     running_mean = momentum * running_mean + (1- momentum) * buf_mean
     running_var = momentum * running_var + (1 - momentum) * buf_var   

　　running_mean  running_var 是在test时使用的，test时不再另外计算均值和方差。

　　test 时的前传核心代码：

 x_hat = x - running_mean
 x_hat = x_hat / (np.sqrt(running_var + eps))
 out = gamma * x_hat + beta

cell 5 BN反向传播

　　通过反向传播，计算beta gamma等参数。

　　核心代码：

   dx_hat = dout * cache['gamma']
   dgamma = np.sum(dout * cache['x_hat'], axis=0)
   dbeta = np.sum(dout, axis=0)
   #x_hat = x - buf_mean
   #x_hat = x_hat / (np.sqrt(buf_var + eps))
   t1 = cache['x'] - cache['mean']
   t2 = (-0.5)*((cache['var'] + cache['eps'])**(-1.5))
   t1 = t1 * t2
   d_var = np.sum(dx_hat * t1, axis=0)

   tmean1 = (-1)*((cache['var'] + cache['eps'])**(-0.5))
   d_mean = np.sum(dx_hat * tmean1, axis=0)

   tmean1 = (-1)*tmean1
   tx1 =   dx_hat * tmean1
   tx2 = d_mean * (1.0 / float(N))
   tx3 = d_var * (2 * (cache['x'] - cache['mean']) / N)
   dx = tx1 + tx2 + tx3

cell 9 BN与其他层结合

　　形成的结构：   {affine - [batch norm] - relu - [dropout]} x (L - 1) - affine - softmax

　　原理依旧。

之后是对cell 9 的模型，对cifar-10数据训练。

值得注意的是：

　　使用BN后，正则项与dropout层的需求降低。可以使用较高的学习率加快模型收敛。

附：通关CS231n企鹅群：578975100 validation：DL-CS231n