『cs231n』作业2选讲_通过代码理解Dropout
Dropout
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def dropout_forward(x, dropout_param): p, mode = dropout_param['p'], dropout_param['mode'] if 'seed' in dropout_param: np.random.seed(dropout_param['seed']) mask = None out = None if mode == 'train': #训练环节开启 mask = (np.random.rand(*x.shape) < p) / p out = x * mask elif mode == 'test': #测试环节关闭 out = x cache = (dropout_param, mask) out = out.astype(x.dtype, copy=False) return out, cachedef dropout_backward(dout, cache): dropout_param, mask = cache mode = dropout_param['mode'] dx = None if mode == 'train': dx = dout * mask elif mode == 'test': dx = dout return dx |
Batch Normalization
Batch Normalization就是在每一层的wx+b和f(wx+b)之间加一个归一化（将wx+b归一化成：均值为0，方差为1
通常：Means should be close to zero and stds close to one
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gamma, beta = np.ones(C), np.zeros(C) |
先给出Batch Normalization的算法和反向求导公式：
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import numpy as npdef batchnorm_forward(x, gamma, beta, bn_param): mode = bn_param['mode'] eps = bn_param.get('eps', 1e-5) momentum = bn_param.get('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': sample_mean = np.mean(x, axis=0, keepdims=True) # [1,D] sample_var = np.var(x, axis=0, keepdims=True) # [1,D] x_normalized = (x - sample_mean) / np.sqrt(sample_var + eps) # [N,D] out = gamma * x_normalized + beta cache = (x_normalized, gamma, beta, sample_mean, sample_var, x, eps) running_mean = momentum * running_mean + (1 - momentum) * sample_mean running_var = momentum * running_var + (1 - momentum) * sample_var elif mode == 'test': x_normalized = (x - running_mean) / np.sqrt(running_var + eps) out = gamma * x_normalized + beta else: raise ValueError('Invalid forward batchnorm mode "%s"' % mode) # Store the updated running means back into bn_param bn_param['running_mean'] = running_mean bn_param['running_var'] = running_var return out, cachedef batchnorm_backward(dout, cache): dx, dgamma, dbeta = None, None, None x_normalized, gamma, beta, sample_mean, sample_var, x, eps = cache N, D = x.shape dx_normalized = dout * gamma # [N,D] x_mu = x - sample_mean # [N,D] sample_std_inv = 1.0 / np.sqrt(sample_var + eps) # [1,D] dsample_var = -0.5 * np.sum(dx_normalized * x_mu, axis=0, keepdims=True) * sample_std_inv**3 dsample_mean = -1.0 * np.sum(dx_normalized * sample_std_inv, axis=0, keepdims=True) - 2.0 * dsample_var * np.mean(x_mu, axis=0, keepdims=True) dx1 = dx_normalized * sample_std_inv dx2 = 2.0/N * dsample_var * x_mu dx = dx1 + dx2 + 1.0/N * dsample_mean dgamma = np.sum(dout * x_normalized, axis=0, keepdims=True) dbeta = np.sum(dout, axis=0, keepdims=True) return dx, dgamma, dbeta |
批量归一化（spatia Batch Normalization）
我们已经看到，批量归一化是训练深度完全连接网络的非常有用的技术。批量归一化也可以用于卷积网络，但我们需要调整它一点;该修改将被称为“空间批量归一化”。
通常，批量归一化接受形状（N，D）的输入并产生形状（N，D）的输出，其中我们在小批量维度N上归一化。对于来自卷积层的数据，批归一化需要接受形状（N,C，H，W），并且产生形状（N，C，H，W）的输出，其中N维给出小容器大小，（H，W）维给出特征图的空间大小。
如果使用卷积产生特征图，则我们期望每个特征通道的统计在相同图像内的不同图像和不同位置之间相对一致。因此，空间批量归一化通过计算小批量维度N和空间维度H和W上的统计量来计算C个特征通道中的每一个的平均值和方差。
同样的：#Means should be close to zero and stds close to one
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gamma, beta = np.ones(C), np.zeros(C) |
代码如下，
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def spatial_batchnorm_forward(x, gamma, beta, bn_param): N, C, H, W = x.shape x_new = x.transpose(0, 2, 3, 1).reshape(N*H*W, C) out, cache = batchnorm_forward(x_new, gamma, beta, bn_param) out = out.reshape(N, H, W, C).transpose(0, 3, 1, 2) return out, cachedef spatial_batchnorm_backward(dout, cache): N, C, H, W = dout.shape dout_new = dout.transpose(0, 2, 3, 1).reshape(N*H*W, C) dx, dgamma, dbeta = batchnorm_backward(dout_new, cache) dx = dx.reshape(N, H, W, C).transpose(0, 3, 1, 2) return dx, dgamma, dbeta |