Pytorch实现一个用于学习正态分布的GAN网络

       2014 年，Ian Goodfellow 和他在蒙特利尔大学的同事发表了一篇震撼学界的论文《Generative Adversarial Nets》，这标志着生成对抗网络（GAN）的诞生，而这是通过对计算图和博弈论的创新性结合。研究显示：给定充分的建模能力，两个博弈模型能够通过简单的反向传播（backpropagation）来协同训练。这两个模型的角色定位十分鲜明。给定真实数据集 R，G 是生成器（generator），它的任务是生成能以假乱真的假数据；而 D 是判别器 （discriminator），它从真实数据集或者 G 那里获取数据， 然后做出判别真假的标记。Ian Goodfellow 的比喻是，G 就像一个赝品作坊，想要让做出来的东西尽可能接近真品，蒙混过关。而 D 就是文物鉴定专家，要能区分出真品和高仿（但在这个例子中，造假者 G 看不到原始数据，而只有 D 的鉴定结果——前者是在盲干）。

       理想情况下，D 和 G 都会随着不断训练，做得越来越好——直到 G 基本上成为了一个“赝品制造大师”，而 D 因无法正确区分两种数据分布输给 G。实践中，Ian Goodfellow 展示的GAN在本质上是：G 能够对原始数据集进行一种无监督学习，找到以更低维度的方式（lower-dimensional manner）来表示数据的某种方法。

 下面通过实现一个GAN网络学习正态分布来了解GAN。

 首先导入pytorch依赖的库。

import torch
import torch.nn as nn
import torch.optim as optim
from torch.distributions.normal import Normal

#定义正态分布
#它的均值和标准差如下
data_mean = 3.0 
data_stddev = 0.4
Series_Length = 30

#定义生成网络(Generator)
#接收一些随机输入，按照上面的定义生成正态分布
g_input_size = 20    
g_hidden_size = 150  
g_output_size = Series_Length

#定义对抗网络(Adversarial)
#True(1.0) 如果输入的数据符合定义的正态分布; False(0.0) 如果输入的数据不符合定义的正态分布
d_input_size = Series_Length
d_hidden_size = 75   
d_output_size = 1

#定义数据输入方式
d_minibatch_size = 15 
g_minibatch_size = 10
num_epochs = 5000
print_interval = 1000

#定义学习率(learning rate)
d_learning_rate = 3e-3
g_learning_rate = 8e-3

#以下两个函数一个可以得到真正的分布，一个可以得到噪声。
#真正的分布用来训练 Discriminator，噪声用来作为 Generator的输入

def get_real_sampler(mu, sigma):
    dist = Normal( mu, sigma )
    return lambda m, n: dist.sample( (m, n) ).requires_grad_()  
 
def get_noise_sampler():
    return lambda m, n: torch.rand(m, n).requires_grad_()  # Uniform-dist data into generator, _NOT_ Gaussian
 
actual_data = get_real_sampler( data_mean, data_stddev )
noise_data  = get_noise_sampler()

# 简单的4层网络的生成器用来输出符合我们想要的正态分布的均值。

class Generator(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(Generator, self).__init__()
        self.map1 = nn.Linear(input_size, hidden_size)
        self.map2 = nn.Linear(hidden_size, hidden_size)
        self.map3 = nn.Linear(hidden_size, output_size)
        self.xfer = torch.nn.SELU()
    def forward(self, x):
        x = self.xfer( self.map1(x) )
        x = self.xfer( self.map2(x) )
        return self.xfer( self.map3( x ) )

#鉴别器（Discriminator）简单的Linear模型，返回True或者False 
class Discriminator(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(Discriminator, self).__init__()
        self.map1 = nn.Linear(input_size, hidden_size)
        self.map2 = nn.Linear(hidden_size, hidden_size)
        self.map3 = nn.Linear(hidden_size, output_size)
        self.elu = torch.nn.ELU()
 
    def forward(self, x):
        x = self.elu(self.map1(x))
        x = self.elu(self.map2(x))
        return torch.sigmoid( self.map3(x) )

#搭建网络，使用SGD优化函数和BCE损失函数

G = Generator(input_size=g_input_size, hidden_size=g_hidden_size, output_size=g_output_size)
D = Discriminator(input_size=d_input_size, hidden_size=d_hidden_size, output_size=d_output_size)
 
criterion = nn.BCELoss() 
d_optimizer = optim.SGD(D.parameters(), lr=d_learning_rate ) 
g_optimizer = optim.SGD(G.parameters(), lr=g_learning_rate )

#Train

def train_D_on_actual():
    real_data = actual_data(d_minibatch_size, d_input_size)
    decision = D(real_data)
    error = criterion(decision, torch.ones(d_minibatch_size, 1))  # ones = true
    error.backward()
    
def train_D_on_generated() :
    noise = noise_data(d_minibatch_size, g_input_size)
    fake_data = G(noise) 
    decision = D(fake_data)
    error = criterion(decision, torch.zeros(d_minibatch_size, 1))  # zeros = fake
    error.backward()


def train_G():
    noise = noise_data(g_minibatch_size, g_input_size)
    fake_data = G(noise)
    fake_decision = D(fake_data)
    error = criterion(fake_decision, torch.ones(g_minibatch_size, 1))  # we want to fool, so pretend it's all genuine

    error.backward()
    return error.item(), fake_data

losses = []

for epoch in range(num_epochs):
    D.zero_grad()
    
    train_D_on_actual()    
    train_D_on_generated()
    d_optimizer.step()
    
    G.zero_grad()
    loss,generated = train_G()
    g_optimizer.step()
    
    losses.append( loss )
    if( epoch % print_interval) == (print_interval-1):
        print( "Epoch %6d. Loss %5.3f" % ( epoch+1, loss ) )
        
print( "Training complete" )

Output:

Epoch   1000. Loss 0.630
Epoch   2000. Loss 0.693
Epoch   3000. Loss 0.699
Epoch   4000. Loss 0.695
Epoch   5000. Loss 0.711
Training complete

结果展示：

import matplotlib.pyplot as plt
def draw( data ) :    
    plt.figure()
    d = data.tolist() if isinstance(data, torch.Tensor ) else data
    plt.plot( d ) 
    plt.show()

d = torch.empty( generated.size(0), 53 ) 
for i in range( 0, d.size(0) ) :
    d[i] = torch.histc( generated[i], min=0, max=5, bins=53 )
draw( d.t() )

 

 

根据参考资料1训练的正态分布结果如下所示：

Epoch 0: D (0.824586033821106 real_err, 0.5667324066162109 fake_err) G (0.8358850479125977 err); Real Dist ([4.04999169665575, 1.1961469779141327]),  Fake Dist ([-0.7985607595443726, 0.029085312190181612]) 
Epoch 100: D (0.6598804593086243 real_err, 0.650113582611084 fake_err) G (0.7386993169784546 err); Real Dist ([3.992502051591873, 1.2512647908868664]),  Fake Dist ([3.3269334855079653, 0.04917005677031684]) 
Epoch 200: D (0.5211157202720642 real_err, 0.48223015666007996 fake_err) G (0.9489601254463196 err); Real Dist ([4.063567101441324, 1.223350898628472]),  Fake Dist ([4.171090561866761, 0.08437742403922882]) 
Epoch 300: D (0.6931817531585693 real_err, 0.6667982935905457 fake_err) G (0.7198074460029602 err); Real Dist ([3.9114013223052027, 1.1737565311661027]),  Fake Dist ([5.706633312940598, 2.3018437903116187]) 
Epoch 400: D (0.6633034944534302 real_err, 0.6330634951591492 fake_err) G (0.7584028840065002 err); Real Dist ([4.023453078389168, 1.173117767184327]),  Fake Dist ([6.466390012741089, 1.767663960120162]) 
Epoch 500: D (0.6556934118270874 real_err, 0.6795700192451477 fake_err) G (0.6501794457435608 err); Real Dist ([3.973978979229927, 1.2705711235753019]),  Fake Dist ([3.3727304997444154, 1.7591466849210384]) 
Epoch 600: D (0.5973175764083862 real_err, 0.5650959610939026 fake_err) G (0.7776590585708618 err); Real Dist ([3.8488472831845284, 1.1891462464838336]),  Fake Dist ([9.568378679275513, 0.4357023789663153]) 
Epoch 700: D (0.6975439786911011 real_err, 0.7180769443511963 fake_err) G (0.6462653279304504 err); Real Dist ([3.932738121032715, 1.224346374745391]),  Fake Dist ([3.466270624160767, 1.48932632524634]) 
Epoch 800: D (0.6946223378181458 real_err, 0.7050127983093262 fake_err) G (0.680088460445404 err); Real Dist ([4.02625471547246, 1.29204413337018]),  Fake Dist ([4.613226325511932, 0.5539247818601367]) 
Epoch 900: D (0.44320639967918396 real_err, 0.23536285758018494 fake_err) G (1.3666585683822632 err); Real Dist ([3.9780734790563583, 1.1573922540562789]),  Fake Dist ([4.808220813274383, 1.064950020735757]) 
Epoch 1000: D (0.885653555393219 real_err, 0.6489665508270264 fake_err) G (0.7260928153991699 err); Real Dist ([4.0037252243161205, 1.2868414641703296]),  Fake Dist ([4.627316523551941, 1.5317822031475823]) 
Epoch 1100: D (0.6624018549919128 real_err, 0.7288448810577393 fake_err) G (0.6776896119117737 err); Real Dist ([3.9965664629936217, 1.2443392558363737]),  Fake Dist ([4.027970834732056, 1.2487745961745749]) 
Epoch 1200: D (0.7081807851791382 real_err, 0.6922528147697449 fake_err) G (0.694278359413147 err); Real Dist ([3.8926908799931406, 1.2083719715743726]),  Fake Dist ([4.002916200637817, 1.2386345105986898]) 
Epoch 1300: D (0.697959303855896 real_err, 0.6919403076171875 fake_err) G (0.6800123453140259 err); Real Dist ([3.938853431105614, 1.2639616232174713]),  Fake Dist ([4.216027449607849, 1.1380480721612078]) 
Epoch 1400: D (0.6784661412239075 real_err, 0.6617948412895203 fake_err) G (0.6870113611221313 err); Real Dist ([3.975500011086464, 1.2855628816411546]),  Fake Dist ([4.137257863044739, 1.1094145415740049]) 
Epoch 1500: D (0.6794069409370422 real_err, 0.7028912305831909 fake_err) G (0.7014129161834717 err); Real Dist ([4.00296139895916, 1.271967197931525]),  Fake Dist ([3.9285888566970826, 1.1982835178367897]) 
Epoch 1600: D (0.6860584020614624 real_err, 0.7060790657997131 fake_err) G (0.6802226901054382 err); Real Dist ([4.058289145439863, 1.361246466914028]),  Fake Dist ([4.036336513757706, 1.2252188340907701]) 
Epoch 1700: D (0.7053802609443665 real_err, 0.696638822555542 fake_err) G (0.6959577202796936 err); Real Dist ([4.022835171103478, 1.2827733756994895]),  Fake Dist ([4.063137277841568, 1.3042375271806848]) 
Epoch 1800: D (0.6980652213096619 real_err, 0.6925143599510193 fake_err) G (0.694028913974762 err); Real Dist ([3.89647038769722, 1.1976831036253377]),  Fake Dist ([4.048781845808029, 1.2693529337960752]) 
Epoch 1900: D (0.6892062425613403 real_err, 0.6972301006317139 fake_err) G (0.6869157552719116 err); Real Dist ([4.033831748008728, 1.186610768225342]),  Fake Dist ([4.022395441293717, 1.2413968482619808]) 
Epoch 2000: D (0.6959377527236938 real_err, 0.6776554584503174 fake_err) G (0.6982696056365967 err); Real Dist ([4.000252573490143, 1.223225489126993]),  Fake Dist ([3.9199998137950898, 1.3520746107193355]) 
Epoch 2100: D (0.6903250813484192 real_err, 0.6950635313987732 fake_err) G (0.6896666288375854 err); Real Dist ([4.090404322504997, 1.2083467717828416]),  Fake Dist ([3.9939954011440277, 1.2462546765450804]) 
Epoch 2200: D (0.6896629333496094 real_err, 0.6950464248657227 fake_err) G (0.6950165033340454 err); Real Dist ([3.990626331356354, 1.2201043116027737]),  Fake Dist ([4.001183384895325, 1.2655219236978008]) 
Epoch 2300: D (0.6915993690490723 real_err, 0.6974573135375977 fake_err) G (0.6993840336799622 err); Real Dist ([4.023877061843872, 1.321507703580412]),  Fake Dist ([3.9179794733524322, 1.1990433265674747]) 
Epoch 2400: D (0.6870835423469543 real_err, 0.692215621471405 fake_err) G (0.6913619637489319 err); Real Dist ([3.921516800969839, 1.2407385883672248]),  Fake Dist ([4.060535876750946, 1.1816568966425942]) 
Epoch 2500: D (0.6934722065925598 real_err, 0.6907936334609985 fake_err) G (0.6907175779342651 err); Real Dist ([3.9839096758961676, 1.2733894018432854]),  Fake Dist ([3.990558073759079, 1.3400137248202226]) 
Epoch 2600: D (0.6947907209396362 real_err, 0.6915742754936218 fake_err) G (0.6919546127319336 err); Real Dist ([4.0130539444088935, 1.240739679033649]),  Fake Dist ([4.084916990995407, 1.2655242770514346]) 
Epoch 2700: D (0.6968568563461304 real_err, 0.6744566559791565 fake_err) G (0.6968263387680054 err); Real Dist ([3.996440895199776, 1.1986359766448267]),  Fake Dist ([3.9793724551200866, 1.1482623145157824]) 
Epoch 2800: D (0.693473756313324 real_err, 0.697898805141449 fake_err) G (0.7002295255661011 err); Real Dist ([4.00081592977047, 1.2474840907225078]),  Fake Dist ([3.895143656253815, 1.2719435213827661]) 
Epoch 2900: D (0.6950169801712036 real_err, 0.6947277188301086 fake_err) G (0.6900919675827026 err); Real Dist ([4.0483872441053395, 1.232666877408606]),  Fake Dist ([3.9184666118621827, 1.2345984703674788]) 
Epoch 3000: D (0.6994454860687256 real_err, 0.6960627436637878 fake_err) G (0.6918361186981201 err); Real Dist ([4.078680800318718, 1.2215170294711815]),  Fake Dist ([4.022074975967407, 1.1967591283090955]) 
Epoch 3100: D (0.6898576617240906 real_err, 0.6938331127166748 fake_err) G (0.6958847641944885 err); Real Dist ([3.906800366342068, 1.3110840468016158]),  Fake Dist ([3.951125014066696, 1.2253583646427406]) 
Epoch 3200: D (0.694175660610199 real_err, 0.6946524977684021 fake_err) G (0.6921048760414124 err); Real Dist ([3.958098252296448, 1.248056967946781]),  Fake Dist ([4.001224509239197, 1.1983827779563796]) 
Epoch 3300: D (0.6922207474708557 real_err, 0.6947858333587646 fake_err) G (0.6927611231803894 err); Real Dist ([3.8829670441150665, 1.1155963206788106]),  Fake Dist ([4.046220509767532, 1.1753880201920783]) 
Epoch 3400: D (0.6900198459625244 real_err, 0.6953887939453125 fake_err) G (0.6889302134513855 err); Real Dist ([4.065795364975929, 1.213252057901399]),  Fake Dist ([3.9650485837459564, 1.2672685373911108]) 
Epoch 3500: D (0.6929183006286621 real_err, 0.695112943649292 fake_err) G (0.6910595297813416 err); Real Dist ([3.8757613455876707, 1.2584639089844412]),  Fake Dist ([3.9378762912750243, 1.190689370381666]) 
Epoch 3600: D (0.693882942199707 real_err, 0.6944809556007385 fake_err) G (0.6939374804496765 err); Real Dist ([4.123380273818969, 1.2824410770958474]),  Fake Dist ([4.010826068401337, 1.2212849080025636]) 
Epoch 3700: D (0.6974205374717712 real_err, 0.6935890913009644 fake_err) G (0.6917606592178345 err); Real Dist ([4.021837902694941, 1.28027136741628]),  Fake Dist ([4.034767779827118, 1.3234349547715394]) 
Epoch 3800: D (0.6955257654190063 real_err, 0.6945357322692871 fake_err) G (0.6925974488258362 err); Real Dist ([4.12936865234375, 1.2460711614374878]),  Fake Dist ([4.0321874620914455, 1.2769764427346884]) 

Epoch 3900: D (0.6915967464447021 real_err, 0.6909477114677429 fake_err) G (0.6927705407142639 err); Real Dist ([4.0268408809900285, 1.2063883800130077]),  Fake Dist ([4.052658556222916, 1.2281464364273882]) 
Epoch 4000: D (0.6922350525856018 real_err, 0.6925557255744934 fake_err) G (0.6929080486297607 err); Real Dist ([4.021845901966095, 1.2925729163376942]),  Fake Dist ([4.025567240476608, 1.1972493940735556]) 
Epoch 4100: D (0.6933664679527283 real_err, 0.6933354139328003 fake_err) G (0.6938549280166626 err); Real Dist ([3.989677229881287, 1.2065878529125207]),  Fake Dist ([4.0539454262256625, 1.2933863721439718]) 
Epoch 4200: D (0.6897806525230408 real_err, 0.6932942867279053 fake_err) G (0.6924738883972168 err); Real Dist ([3.9900609830617904, 1.271517711087724]),  Fake Dist ([3.9614700605869295, 1.2921971453653849]) 
Epoch 4300: D (0.6924872398376465 real_err, 0.6926604509353638 fake_err) G (0.6937258839607239 err); Real Dist ([4.0992556612789635, 1.2569412389872303]),  Fake Dist ([4.127795008897781, 1.2884594395504811]) 
Epoch 4400: D (0.6946849822998047 real_err, 0.6911969184875488 fake_err) G (0.6942746639251709 err); Real Dist ([4.076893085479736, 1.2744374182411338]),  Fake Dist ([3.969561124563217, 1.2501441583969877]) 
Epoch 4500: D (0.6914315819740295 real_err, 0.6935481429100037 fake_err) G (0.6912876963615417 err); Real Dist ([3.94799566257, 1.2232376272767607]),  Fake Dist ([4.002278556823731, 1.2505587333284056]) 
Epoch 4600: D (0.7037312388420105 real_err, 0.6909893155097961 fake_err) G (0.6984265446662903 err); Real Dist ([3.9354238008633255, 1.2836771049555928]),  Fake Dist ([3.9731800141334532, 1.2964666046336777]) 
Epoch 4700: D (0.6944875121116638 real_err, 0.6940887570381165 fake_err) G (0.6929762363433838 err); Real Dist ([4.047859039783478, 1.190815309623828]),  Fake Dist ([3.990305748939514, 1.2529010827404359]) 
Epoch 4800: D (0.6942726373672485 real_err, 0.692735493183136 fake_err) G (0.6925361752510071 err); Real Dist ([3.9683418440818787, 1.2123594456412528]),  Fake Dist ([4.032746832132339, 1.213276069713684]) 
Epoch 4900: D (0.6940117478370667 real_err, 0.6929702758789062 fake_err) G (0.6935417652130127 err); Real Dist ([3.947842192411423, 1.2553405683297756]),  Fake Dist ([4.038874376773834, 1.2395540432380345]) 
Plotting the generated distribution...

 Values: [4.539769649505615, 1.63444983959198, 4.4557600021362305, 5.5528364181518555, 4.340044021606445, 2.198087453842163, 2.9329943656921387, 2.3880555629730225, 1.5384184122085571, 4.269472122192383, 4.8173933029174805, 4.85664176940918, 1.6450153589248657, 3.9355251789093018, 5.932168960571289, 1.3862096071243286, 3.9333181381225586, 3.1726975440979004, 3.696260452270508, 3.052525520324707, 3.3560595512390137, 3.0390870571136475, 2.6469674110412598, 4.103339195251465, 4.503757476806641, 4.599853038787842, 4.138694763183594, 4.259690284729004, 4.146164417266846, 1.6029934883117676, 5.843445777893066, 2.2497828006744385, 3.3378164768218994, 1.9207507371902466, 2.179079532623291, 4.690481185913086, 4.0812296867370605, 4.095373630523682, 3.8689160346984863, 6.373284816741943, 4.976202964782715, 2.3788414001464844, 4.4080915451049805, 4.072725772857666, 3.577080726623535, 1.4012407064437866, 3.4651074409484863, 1.9623477458953857, 2.1658592224121094, 4.821807861328125, 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​

 

 

 

参考资料：

1. https://github.com/devnag/pytorch-generative-adversarial-networks/blob/master/gan_pytorch.py

2. https://github.com/rcorbish/pytorch-notebooks/blob/master/gan-basic.ipynb

3. https://www.pytorchtutorial.com/pytorch-sample-gan/