python手写神经网络之Dropout实现

这里写三种实现，一种是vanilla，一种是效率更高的写法，还有一种是作为网络层的实现方法。

虽然dropout的参数叫probability，一般指的不是扔的机率，是keep的机率（因为代码更好解释？）。（但是不固定，注意一致性，自恰即可）

 

vanilla dropout的前向传播网络示意：

作为对照组，给出了predict不乘以p的结果，随着数据量或者数据维度的增大，可以看到最后总输出前两者是接近的，而不乘以p的结果会偏差很大。

""" Vanilla Dropout: Not recommended implementation (see notes below) """
import numpy as np


p = 0.5  # probability of keeping a unit active. higher = less dropout


def train_step(X):
    """ X contains the data """

    # forward pass for example 3-layer neural network
    H1 = np.maximum(0, np.dot(W1, X) + b1)
    U1 = np.random.rand(*H1.shape) < p  # first dropout mask
    H1 *= U1  # drop!
    H2 = np.maximum(0, np.dot(W2, H1) + b2)
    U2 = np.random.rand(*H2.shape) < p  # second dropout mask
    H2 *= U2  # drop!
    out = np.dot(W3, H2) + b3

    return out

    # backward pass: compute gradients... (not shown)
    # perform parameter update... (not shown)


def predict(X):
    # ensembled forward pass
    H1 = np.maximum(0, np.dot(W1, X) + b1) * p  # NOTE: scale the activations
    H2 = np.maximum(0, np.dot(W2, H1) + b2) * p  # NOTE: scale the activations
    out = np.dot(W3, H2) + b3
    return out

def predict_without_multiply_p(X):#作为对比,展示一下忽略scale的结果
    # ensembled forward pass
    H1 = np.maximum(0, np.dot(W1, X) + b1) # NOTE: scale the activations
    H2 = np.maximum(0, np.dot(W2, H1) + b2) # NOTE: scale the activations
    out = np.dot(W3, H2) + b3
    return out
W1 = np.random.randn(4,3)#W1*X=4,1
b1 = np.random.randn(4,1)
W2 = np.random.randn(4,4)#W2*H1=4,1
b2 = np.random.randn(4,1)
W3 = np.random.randn(4,4)#W2*H1=4,1
b3 = np.random.randn(4,1)
if __name__ == '__main__':

    X = np.random.randn(3,1000000)
    y = train_step(X)
    print('in training phase, average value:',y.shape,y.mean())
    predict_y = predict(X)
    print('in predicting phase, average value:',predict_y.shape,predict_y.mean())
    predict_y = predict_without_multiply_p(X)#奇特，不乘以p，反而变小了？？？？#随机的，每一次都不一样，充分说明网络的随机性，每一层的数值大小和最后输出不成绝对比例
    print('in predicting phase(without multiply p), average value:',predict_y.mean())

 

in training phase, average value: (4, 1000000) 0.5332048355924359
in predicting phase, average value: (4, 1000000) 0.4632303379943579
in predicting phase(without multiply p), average value: 2.0510060393300087

上边这个网络逻辑上是没问题的，问题在哪呢？在于运行时性能，因为乘以p的操作在predict时，这就导致运行时开销加大，速度变慢。既然只是要维持train和predict的scale相同，那么把操作移到train时就好了。

 

inverted dropout的前向传播示意网络结构：

注意事项，既然是除法，要注意一下零除的问题（当然，不太可能设置p=0），p的定义，每个课程或者每个人的说法都可能有差异，这里p是keep的概率（感觉keep可能更接近代码的解读，乘以mask），记得李宏毅的课程p好像是drop，那么mask的设置就应该是反向的（>p），除法也是除以1-p而不是p。只要自恰就行了，怎么叫都没关系

import numpy as np
from dropout_vanilla import train_step as vanilla_train
from dropout_vanilla import predict as vanilla_predict
import math
p = 0.5  # probability of keeping a unit active. higher = less dropout
#这里的p是keep，李宏毅的课程，如果p是drop，当然就是除以1-p了，除了绕一点

def train_step(X):
    """ X contains the data """

    # forward pass for example 3-layer neural network
    H1 = np.maximum(0, np.dot(W1, X) + b1)
    U1 = (np.random.rand(*H1.shape) < p) / p  # first dropout mask
    H1 *= U1  # drop!
    H2 = np.maximum(0, np.dot(W2, H1) + b2)
    U2 = (np.random.rand(*H2.shape) < p) / p  # second dropout mask
    H2 *= U2  # drop!
    out = np.dot(W3, H2) + b3

    return out

    # backward pass: compute gradients... (not shown)
    # perform parameter update... (not shown)


def predict(X):
    # ensembled forward pass
    H1 = np.maximum(0, np.dot(W1, X) + b1) # NOTE: scale the activations
    H2 = np.maximum(0, np.dot(W2, H1) + b2) # NOTE: scale the activations
    out = np.dot(W3, H2) + b3
    return out

if __name__ == '__main__':
    np.random.seed(1)

    W1 = np.random.randn(4,3)#W1*X=4,1
    b1 = np.random.randn(4,1)
    W2 = np.random.randn(4,4)#W2*H1=4,1
    b2 = np.random.randn(4,1)
    W3 = np.random.randn(4,4)#W2*H1=4,1
    b3 = np.random.randn(4,1)
    X = np.random.randn(3,1000000)
    y = train_step(X)
    print(y.shape)
    print('inverted train,average value:',y.mean())
    predict_y = predict(X)
    print('inverted predict,average value:',predict_y.mean())

    #想对比两者的期望，但是想了一下，本来激活之后的数据就是杂乱的，没法比,简单示意,两个从量级上都保持了相对稳定
    y = vanilla_train(X)
    predict_y = vanilla_predict(X)
    print('vanilla train,average value:',y.mean())
    print('vanilla predict,average value:',predict_y.mean())

inverted train,average value: -0.19223531434253763
inverted predict,average value: -0.24786749397781124
vanilla train,average value: 0.0815151269153607
vanilla predict,average value: 0.13525566404177755

当然，上边都是裸露的网络，下面实现一个网络层。

 

dropout网络层实现：

相对于其他网络层（尤其BNhttps://blog.csdn.net/huqinweI987/article/details/103229158），这个可以说是非常简单。

 

class Dropout:
    def __init__(self,dropout_ratio=0.5):#这里的是扔的概率
        self.dropout_ratio = dropout_ratio
        self.mask = None
    def forward(self,x,is_train):
        if is_train:
            self.mask = np.random.rand(*x.shape) > self.dropout_ratio
            return x * self.mask
        else:
            return x * (1 - self.dropout_ratio)
    def backward(self,dout):
        return dout * self.mask

 第一段参考代码就是属于vanilla的那种实现，并且p是drop的概率，等下我优化一下，两个版本都看一下。

class Dropout:
    def __init__(self,keep_probability=0.5):#这里的是保留的概率
        self.keep_probability = keep_probability
        self.mask = None
    def forward(self,x,is_train):
        if is_train:
            self.mask = np.random.rand(*x.shape) < self.keep_probability
            return x * self.mask
        else:
            return x * self.keep_probability
    def backward(self,dout):
        return dout * self.mask

然后是测试性能优化：

class Dropout:
    def __init__(self,keep_probability=0.5):#这里的是保留的概率
        self.keep_probability = keep_probability
        self.mask = None
    def forward(self,x,is_train):
        if is_train:
            self.mask = np.random.rand(*x.shape) < self.keep_probability
            return x * self.mask / self.keep_probability
        else:
            return x
    def backward(self,dout):
        return dout * self.mask

然后就把这个层丢进网络结构就可以了。

        # 生成层
        activation_layer = {'sigmoid': Sigmoid, 'relu': Relu}
        self.layers = OrderedDict()
        for idx in range(1, self.hidden_layer_num+1):
            self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)],
                                                      self.params['b' + str(idx)])
            if self.use_batchnorm:
                self.params['gamma' + str(idx)] = np.ones(hidden_size_list[idx-1])
                self.params['beta' + str(idx)] = np.zeros(hidden_size_list[idx-1])
                self.layers['BatchNorm' + str(idx)] = BatchNormalization(self.params['gamma' + str(idx)], self.params['beta' + str(idx)])
                
            self.layers['Activation_function' + str(idx)] = activation_layer[activation]()
            
            if self.use_dropout:
                self.layers['Dropout' + str(idx)] = Dropout(dropout_ration)

        idx = self.hidden_layer_num + 1
        self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)], self.params['b' + str(idx)])

        self.last_layer = SoftmaxWithLoss()

提到丢进网络结构，因为简化的网络前向传播迭代都是如下形式：

for layer in self.layers:

x = layer.forward(x)

这样输入参数是不方便的，所以要给is_train加一个默认参数True，就可以了，这样只要测试时自己手动加上False就可以了

class Dropout:
    def __init__(self,keep_probability=0.5):#这里的是保留的概率
        self.keep_probability = keep_probability
        self.mask = None
    def forward(self,x,is_train=True):
        if is_train:
            self.mask = np.random.rand(*x.shape) < self.keep_probability
            return x * self.mask / self.keep_probability
        else:
            return x
    def backward(self,dout):
        return dout * self.mask

 

不使用dropout结果：300次基本train set过拟合和test set停滞

 

使用dropout结果（drop概率0.2，即，keep概率0.8）：仍然在上涨

3000次