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Author: Nathan Inkawhich
Introduction¶
This tutorial will give an introduction to DCGANs through an example. Wewill train a generative adversarial network (GAN) to generate newcelebrities after showing it pictures of many real celebrities. Most ofthe code here is from the DCGAN implementation inpytorch/examples, and thisdocument will give a thorough explanation of the implementation and shedlight on how and why this model works. But don’t worry, no priorknowledge of GANs is required, but it may require a first-timer to spendsome time reasoning about what is actually happening under the hood.Also, for the sake of time it will help to have a GPU, or two. Letsstart from the beginning.
Generative Adversarial Networks¶
What is a GAN?¶
GANs are a framework for teaching a deep learning model to capture the trainingdata distribution so we can generate new data from that samedistribution. GANs were invented by Ian Goodfellow in 2014 and firstdescribed in the paper Generative AdversarialNets.They are made of two distinct models, a generator and adiscriminator. The job of the generator is to spawn ‘fake’ images thatlook like the training images. The job of the discriminator is to lookat an image and output whether or not it is a real training image or afake image from the generator. During training, the generator isconstantly trying to outsmart the discriminator by generating better andbetter fakes, while the discriminator is working to become a betterdetective and correctly classify the real and fake images. Theequilibrium of this game is when the generator is generating perfectfakes that look as if they came directly from the training data, and thediscriminator is left to always guess at 50% confidence that thegenerator output is real or fake.
Now, lets define some notation to be used throughout tutorial startingwith the discriminator. Let \(x\) be data representing an image.\(D(x)\) is the discriminator network which outputs the (scalar)probability that \(x\) came from training data rather than thegenerator. Here, since we are dealing with images, the input to\(D(x)\) is an image of CHW size 3x64x64. Intuitively, \(D(x)\)should be HIGH when \(x\) comes from training data and LOW when\(x\) comes from the generator. \(D(x)\) can also be thought ofas a traditional binary classifier.
For the generator’s notation, let \(z\) be a latent space vectorsampled from a standard normal distribution. \(G(z)\) represents thegenerator function which maps the latent vector \(z\) to data-space.The goal of \(G\) is to estimate the distribution that the trainingdata comes from (\(p_{data}\)) so it can generate fake samples fromthat estimated distribution (\(p_g\)).
So, \(D(G(z))\) is the probability (scalar) that the output of thegenerator \(G\) is a real image. As described in Goodfellow’spaper,\(D\) and \(G\) play a minimax game in which \(D\) tries tomaximize the probability it correctly classifies reals and fakes(\(logD(x)\)), and \(G\) tries to minimize the probability that\(D\) will predict its outputs are fake (\(log(1-D(G(z)))\)).From the paper, the GAN loss function is
\[\underset{G}{\text{min}} \underset{D}{\text{max}}V(D,G) = \mathbb{E}_{x\sim p_{data}(x)}\big[logD(x)\big] + \mathbb{E}_{z\sim p_{z}(z)}\big[log(1-D(G(z)))\big]\]
In theory, the solution to this minimax game is where\(p_g = p_{data}\), and the discriminator guesses randomly if theinputs are real or fake. However, the convergence theory of GANs isstill being actively researched and in reality models do not alwaystrain to this point.
What is a DCGAN?¶
A DCGAN is a direct extension of the GAN described above, except that itexplicitly uses convolutional and convolutional-transpose layers in thediscriminator and generator, respectively. It was first described byRadford et. al.in the paper Unsupervised Representation Learning WithDeep Convolutional Generative AdversarialNetworks. The discriminatoris made up of stridedconvolutionlayers, batchnormlayers, andLeakyReLUactivations. The input is a 3x64x64 input image and the output is ascalar probability that the input is from the real data distribution.The generator is comprised ofconvolutional-transposelayers, batch norm layers, andReLU activations. Theinput is a latent vector, \(z\), that is drawn from a standardnormal distribution and the output is a 3x64x64 RGB image. The stridedconv-transpose layers allow the latent vector to be transformed into avolume with the same shape as an image. In the paper, the authors alsogive some tips about how to setup the optimizers, how to calculate theloss functions, and how to initialize the model weights, all of whichwill be explained in the coming sections.
#%matplotlib inlineimport argparseimport osimport randomimport torchimport torch.nn as nnimport torch.nn.parallelimport torch.optim as optimimport torch.utils.dataimport torchvision.datasets as dsetimport torchvision.transforms as transformsimport torchvision.utils as vutilsimport numpy as npimport matplotlib.pyplot as pltimport matplotlib.animation as animationfrom IPython.display import HTML# Set random seed for reproducibilitymanualSeed = 999#manualSeed = random.randint(1, 10000) # use if you want new resultsprint("Random Seed: ", manualSeed)random.seed(manualSeed)torch.manual_seed(manualSeed)torch.use_deterministic_algorithms(True) # Needed for reproducible results
Random Seed: 999
Inputs¶
Let’s define some inputs for the run:
dataroot- the path to the root of the dataset folder. We willtalk more about the dataset in the next section.workers- the number of worker threads for loading the data withtheDataLoader.batch_size- the batch size used in training. The DCGAN paperuses a batch size of 128.image_size- the spatial size of the images used for training.This implementation defaults to 64x64. If another size is desired,the structures of D and G must be changed. Seehere for moredetails.nc- number of color channels in the input images. For colorimages this is 3.nz- length of latent vector.ngf- relates to the depth of feature maps carried through thegenerator.ndf- sets the depth of feature maps propagated through thediscriminator.num_epochs- number of training epochs to run. Training forlonger will probably lead to better results but will also take muchlonger.lr- learning rate for training. As described in the DCGAN paper,this number should be 0.0002.beta1- beta1 hyperparameter for Adam optimizers. As described inpaper, this number should be 0.5.ngpu- number of GPUs available. If this is 0, code will run inCPU mode. If this number is greater than 0 it will run on that numberof GPUs.
# Root directory for datasetdataroot = "data/celeba"# Number of workers for dataloaderworkers = 2# Batch size during trainingbatch_size = 128# Spatial size of training images. All images will be resized to this# size using a transformer.image_size = 64# Number of channels in the training images. For color images this is 3nc = 3# Size of z latent vector (i.e. size of generator input)nz = 100# Size of feature maps in generatorngf = 64# Size of feature maps in discriminatorndf = 64# Number of training epochsnum_epochs = 5# Learning rate for optimizerslr = 0.0002# Beta1 hyperparameter for Adam optimizersbeta1 = 0.5# Number of GPUs available. Use 0 for CPU mode.ngpu = 1
Data¶
In this tutorial we will use the Celeb-A Facesdataset which canbe downloaded at the linked site, or in GoogleDrive.The dataset will download as a file named img_align_celeba.zip. Oncedownloaded, create a directory named celeba and extract the zip fileinto that directory. Then, set the dataroot input for this notebook tothe celeba directory you just created. The resulting directorystructure should be:
/path/to/celeba -> img_align_celeba -> 188242.jpg -> 173822.jpg -> 284702.jpg -> 537394.jpg ...
This is an important step because we will be using the ImageFolderdataset class, which requires there to be subdirectories in thedataset root folder. Now, we can create the dataset, create thedataloader, set the device to run on, and finally visualize some of thetraining data.
# We can use an image folder dataset the way we have it setup.# Create the datasetdataset = dset.ImageFolder(root=dataroot, transform=transforms.Compose([ transforms.Resize(image_size), transforms.CenterCrop(image_size), transforms.ToTensor(), transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5)), ]))# Create the dataloaderdataloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=True, num_workers=workers)# Decide which device we want to run ondevice = torch.device("cuda:0" if (torch.cuda.is_available() and ngpu > 0) else "cpu")# Plot some training imagesreal_batch = next(iter(dataloader))plt.figure(figsize=(8,8))plt.axis("off")plt.title("Training Images")plt.imshow(np.transpose(vutils.make_grid(real_batch[0].to(device)[:64], padding=2, normalize=True).cpu(),(1,2,0)))plt.show()
Implementation¶
With our input parameters set and the dataset prepared, we can now getinto the implementation. We will start with the weight initializationstrategy, then talk about the generator, discriminator, loss functions,and training loop in detail.
Weight Initialization¶
From the DCGAN paper, the authors specify that all model weights shallbe randomly initialized from a Normal distribution with mean=0,stdev=0.02. The weights_init function takes an initialized model asinput and reinitializes all convolutional, convolutional-transpose, andbatch normalization layers to meet this criteria. This function isapplied to the models immediately after initialization.
# custom weights initialization called on ``netG`` and ``netD``def weights_init(m): classname = m.__class__.__name__ if classname.find('Conv') != -1: nn.init.normal_(m.weight.data, 0.0, 0.02) elif classname.find('BatchNorm') != -1: nn.init.normal_(m.weight.data, 1.0, 0.02) nn.init.constant_(m.bias.data, 0)
Generator¶
The generator, \(G\), is designed to map the latent space vector(\(z\)) to data-space. Since our data are images, converting\(z\) to data-space means ultimately creating a RGB image with thesame size as the training images (i.e.3x64x64). In practice, this isaccomplished through a series of strided two dimensional convolutionaltranspose layers, each paired with a 2d batch norm layer and a reluactivation. The output of the generator is fed through a tanh functionto return it to the input data range of \([-1,1]\). It is worthnoting the existence of the batch norm functions after theconv-transpose layers, as this is a critical contribution of the DCGANpaper. These layers help with the flow of gradients during training. Animage of the generator from the DCGAN paper is shown below.
Notice, how the inputs we set in the input section (nz, ngf, andnc) influence the generator architecture in code. nz is the lengthof the z input vector, ngf relates to the size of the feature mapsthat are propagated through the generator, and nc is the number ofchannels in the output image (set to 3 for RGB images). Below is thecode for the generator.
# Generator Codeclass Generator(nn.Module): def __init__(self, ngpu): super(Generator, self).__init__() self.ngpu = ngpu self.main = nn.Sequential( # input is Z, going into a convolution nn.ConvTranspose2d( nz, ngf * 8, 4, 1, 0, bias=False), nn.BatchNorm2d(ngf * 8), nn.ReLU(True), # state size. ``(ngf*8) x 4 x 4`` nn.ConvTranspose2d(ngf * 8, ngf * 4, 4, 2, 1, bias=False), nn.BatchNorm2d(ngf * 4), nn.ReLU(True), # state size. ``(ngf*4) x 8 x 8`` nn.ConvTranspose2d( ngf * 4, ngf * 2, 4, 2, 1, bias=False), nn.BatchNorm2d(ngf * 2), nn.ReLU(True), # state size. ``(ngf*2) x 16 x 16`` nn.ConvTranspose2d( ngf * 2, ngf, 4, 2, 1, bias=False), nn.BatchNorm2d(ngf), nn.ReLU(True), # state size. ``(ngf) x 32 x 32`` nn.ConvTranspose2d( ngf, nc, 4, 2, 1, bias=False), nn.Tanh() # state size. ``(nc) x 64 x 64`` ) def forward(self, input): return self.main(input)
Now, we can instantiate the generator and apply the weights_initfunction. Check out the printed model to see how the generator object isstructured.
# Create the generatornetG = Generator(ngpu).to(device)# Handle multi-GPU if desiredif (device.type == 'cuda') and (ngpu > 1): netG = nn.DataParallel(netG, list(range(ngpu)))# Apply the ``weights_init`` function to randomly initialize all weights# to ``mean=0``, ``stdev=0.02``.netG.apply(weights_init)# Print the modelprint(netG)
Generator( (main): Sequential( (0): ConvTranspose2d(100, 512, kernel_size=(4, 4), stride=(1, 1), bias=False) (1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (2): ReLU(inplace=True) (3): ConvTranspose2d(512, 256, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (4): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (5): ReLU(inplace=True) (6): ConvTranspose2d(256, 128, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (7): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (8): ReLU(inplace=True) (9): ConvTranspose2d(128, 64, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (10): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (11): ReLU(inplace=True) (12): ConvTranspose2d(64, 3, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (13): Tanh() ))
Discriminator¶
As mentioned, the discriminator, \(D\), is a binary classificationnetwork that takes an image as input and outputs a scalar probabilitythat the input image is real (as opposed to fake). Here, \(D\) takesa 3x64x64 input image, processes it through a series of Conv2d,BatchNorm2d, and LeakyReLU layers, and outputs the final probabilitythrough a Sigmoid activation function. This architecture can be extendedwith more layers if necessary for the problem, but there is significanceto the use of the strided convolution, BatchNorm, and LeakyReLUs. TheDCGAN paper mentions it is a good practice to use strided convolutionrather than pooling to downsample because it lets the network learn itsown pooling function. Also batch norm and leaky relu functions promotehealthy gradient flow which is critical for the learning process of both\(G\) and \(D\).
Discriminator Code
class Discriminator(nn.Module): def __init__(self, ngpu): super(Discriminator, self).__init__() self.ngpu = ngpu self.main = nn.Sequential( # input is ``(nc) x 64 x 64`` nn.Conv2d(nc, ndf, 4, 2, 1, bias=False), nn.LeakyReLU(0.2, inplace=True), # state size. ``(ndf) x 32 x 32`` nn.Conv2d(ndf, ndf * 2, 4, 2, 1, bias=False), nn.BatchNorm2d(ndf * 2), nn.LeakyReLU(0.2, inplace=True), # state size. ``(ndf*2) x 16 x 16`` nn.Conv2d(ndf * 2, ndf * 4, 4, 2, 1, bias=False), nn.BatchNorm2d(ndf * 4), nn.LeakyReLU(0.2, inplace=True), # state size. ``(ndf*4) x 8 x 8`` nn.Conv2d(ndf * 4, ndf * 8, 4, 2, 1, bias=False), nn.BatchNorm2d(ndf * 8), nn.LeakyReLU(0.2, inplace=True), # state size. ``(ndf*8) x 4 x 4`` nn.Conv2d(ndf * 8, 1, 4, 1, 0, bias=False), nn.Sigmoid() ) def forward(self, input): return self.main(input)
Now, as with the generator, we can create the discriminator, apply theweights_init function, and print the model’s structure.
# Create the DiscriminatornetD = Discriminator(ngpu).to(device)# Handle multi-GPU if desiredif (device.type == 'cuda') and (ngpu > 1): netD = nn.DataParallel(netD, list(range(ngpu)))# Apply the ``weights_init`` function to randomly initialize all weights# like this: ``to mean=0, stdev=0.2``.netD.apply(weights_init)# Print the modelprint(netD)
Discriminator( (main): Sequential( (0): Conv2d(3, 64, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (1): LeakyReLU(negative_slope=0.2, inplace=True) (2): Conv2d(64, 128, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (3): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (4): LeakyReLU(negative_slope=0.2, inplace=True) (5): Conv2d(128, 256, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (6): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (7): LeakyReLU(negative_slope=0.2, inplace=True) (8): Conv2d(256, 512, kernel_size=(4, 4), stride=(2, 2), padding=(1, 1), bias=False) (9): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True) (10): LeakyReLU(negative_slope=0.2, inplace=True) (11): Conv2d(512, 1, kernel_size=(4, 4), stride=(1, 1), bias=False) (12): Sigmoid() ))
Loss Functions and Optimizers¶
With \(D\) and \(G\) setup, we can specify how they learnthrough the loss functions and optimizers. We will use the Binary CrossEntropy loss(BCELoss)function which is defined in PyTorch as:
\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - \left[ y_n \cdot \log x_n + (1 - y_n) \cdot \log (1 - x_n) \right]\]
Notice how this function provides the calculation of both log componentsin the objective function (i.e. \(log(D(x))\) and\(log(1-D(G(z)))\)). We can specify what part of the BCE equation touse with the \(y\) input. This is accomplished in the training loopwhich is coming up soon, but it is important to understand how we canchoose which component we wish to calculate just by changing \(y\)(i.e.GT labels).
Next, we define our real label as 1 and the fake label as 0. Theselabels will be used when calculating the losses of \(D\) and\(G\), and this is also the convention used in the original GANpaper. Finally, we set up two separate optimizers, one for \(D\) andone for \(G\). As specified in the DCGAN paper, both are Adamoptimizers with learning rate 0.0002 and Beta1 = 0.5. For keeping trackof the generator’s learning progression, we will generate a fixed batchof latent vectors that are drawn from a Gaussian distribution(i.e.fixed_noise) . In the training loop, we will periodically inputthis fixed_noise into \(G\), and over the iterations we will seeimages form out of the noise.
# Initialize the ``BCELoss`` functioncriterion = nn.BCELoss()# Create batch of latent vectors that we will use to visualize# the progression of the generatorfixed_noise = torch.randn(64, nz, 1, 1, device=device)# Establish convention for real and fake labels during trainingreal_label = 1.fake_label = 0.# Setup Adam optimizers for both G and DoptimizerD = optim.Adam(netD.parameters(), lr=lr, betas=(beta1, 0.999))optimizerG = optim.Adam(netG.parameters(), lr=lr, betas=(beta1, 0.999))
Training¶
Finally, now that we have all of the parts of the GAN framework defined,we can train it. Be mindful that training GANs is somewhat of an artform, as incorrect hyperparameter settings lead to mode collapse withlittle explanation of what went wrong. Here, we will closely followAlgorithm 1 from the Goodfellow’s paper,while abiding by some of the bestpractices shown in ganhacks.Namely, we will “construct different mini-batches for real and fake”images, and also adjust G’s objective function to maximize\(log(D(G(z)))\). Training is split up into two main parts. Part 1updates the Discriminator and Part 2 updates the Generator.
Part 1 - Train the Discriminator
Recall, the goal of training the discriminator is to maximize theprobability of correctly classifying a given input as real or fake. Interms of Goodfellow, we wish to “update the discriminator by ascendingits stochastic gradient”. Practically, we want to maximize\(log(D(x)) + log(1-D(G(z)))\). Due to the separate mini-batchsuggestion from ganhacks,we will calculate this in two steps. First, wewill construct a batch of real samples from the training set, forwardpass through \(D\), calculate the loss (\(log(D(x))\)), thencalculate the gradients in a backward pass. Secondly, we will constructa batch of fake samples with the current generator, forward pass thisbatch through \(D\), calculate the loss (\(log(1-D(G(z)))\)),and accumulate the gradients with a backward pass. Now, with thegradients accumulated from both the all-real and all-fake batches, wecall a step of the Discriminator’s optimizer.
Part 2 - Train the Generator
As stated in the original paper, we want to train the Generator byminimizing \(log(1-D(G(z)))\) in an effort to generate better fakes.As mentioned, this was shown by Goodfellow to not provide sufficientgradients, especially early in the learning process. As a fix, weinstead wish to maximize \(log(D(G(z)))\). In the code we accomplishthis by: classifying the Generator output from Part 1 with theDiscriminator, computing G’s loss using real labels as GT, computingG’s gradients in a backward pass, and finally updating G’s parameterswith an optimizer step. It may seem counter-intuitive to use the reallabels as GT labels for the loss function, but this allows us to use the\(log(x)\) part of the BCELoss (rather than the \(log(1-x)\)part) which is exactly what we want.
Finally, we will do some statistic reporting and at the end of eachepoch we will push our fixed_noise batch through the generator tovisually track the progress of G’s training. The training statisticsreported are:
Loss_D - discriminator loss calculated as the sum of losses forthe all real and all fake batches (\(log(D(x)) + log(1 - D(G(z)))\)).
Loss_G - generator loss calculated as \(log(D(G(z)))\)
D(x) - the average output (across the batch) of the discriminatorfor the all real batch. This should start close to 1 thentheoretically converge to 0.5 when G gets better. Think about whythis is.
D(G(z)) - average discriminator outputs for the all fake batch.The first number is before D is updated and the second number isafter D is updated. These numbers should start near 0 and converge to0.5 as G gets better. Think about why this is.
Note: This step might take a while, depending on how many epochs yourun and if you removed some data from the dataset.
# Training Loop# Lists to keep track of progressimg_list = []G_losses = []D_losses = []iters = 0print("Starting Training Loop...")# For each epochfor epoch in range(num_epochs): # For each batch in the dataloader for i, data in enumerate(dataloader, 0): ############################ # (1) Update D network: maximize log(D(x)) + log(1 - D(G(z))) ########################### ## Train with all-real batch netD.zero_grad() # Format batch real_cpu = data[0].to(device) b_size = real_cpu.size(0) label = torch.full((b_size,), real_label, dtype=torch.float, device=device) # Forward pass real batch through D output = netD(real_cpu).view(-1) # Calculate loss on all-real batch errD_real = criterion(output, label) # Calculate gradients for D in backward pass errD_real.backward() D_x = output.mean().item() ## Train with all-fake batch # Generate batch of latent vectors noise = torch.randn(b_size, nz, 1, 1, device=device) # Generate fake image batch with G fake = netG(noise) label.fill_(fake_label) # Classify all fake batch with D output = netD(fake.detach()).view(-1) # Calculate D's loss on the all-fake batch errD_fake = criterion(output, label) # Calculate the gradients for this batch, accumulated (summed) with previous gradients errD_fake.backward() D_G_z1 = output.mean().item() # Compute error of D as sum over the fake and the real batches errD = errD_real + errD_fake # Update D optimizerD.step() ############################ # (2) Update G network: maximize log(D(G(z))) ########################### netG.zero_grad() label.fill_(real_label) # fake labels are real for generator cost # Since we just updated D, perform another forward pass of all-fake batch through D output = netD(fake).view(-1) # Calculate G's loss based on this output errG = criterion(output, label) # Calculate gradients for G errG.backward() D_G_z2 = output.mean().item() # Update G optimizerG.step() # Output training stats if i % 50 == 0: print('[%d/%d][%d/%d]\tLoss_D: %.4f\tLoss_G: %.4f\tD(x): %.4f\tD(G(z)): %.4f / %.4f' % (epoch, num_epochs, i, len(dataloader), errD.item(), errG.item(), D_x, D_G_z1, D_G_z2)) # Save Losses for plotting later G_losses.append(errG.item()) D_losses.append(errD.item()) # Check how the generator is doing by saving G's output on fixed_noise if (iters % 500 == 0) or ((epoch == num_epochs-1) and (i == len(dataloader)-1)): with torch.no_grad(): fake = netG(fixed_noise).detach().cpu() img_list.append(vutils.make_grid(fake, padding=2, normalize=True)) iters += 1
Starting Training Loop...[0/5][0/1583] Loss_D: 1.4640 Loss_G: 6.9360 D(x): 0.7143 D(G(z)): 0.5877 / 0.0017[0/5][50/1583] Loss_D: 0.0174 Loss_G: 23.7368 D(x): 0.9881 D(G(z)): 0.0000 / 0.0000[0/5][100/1583] Loss_D: 0.5983 Loss_G: 9.9471 D(x): 0.9715 D(G(z)): 0.3122 / 0.0003[0/5][150/1583] Loss_D: 0.4940 Loss_G: 5.6772 D(x): 0.7028 D(G(z)): 0.0241 / 0.0091[0/5][200/1583] Loss_D: 0.5931 Loss_G: 7.1186 D(x): 0.9423 D(G(z)): 0.3016 / 0.0018[0/5][250/1583] Loss_D: 0.3846 Loss_G: 3.2697 D(x): 0.7663 D(G(z)): 0.0573 / 0.0739[0/5][300/1583] Loss_D: 1.3306 Loss_G: 8.3204 D(x): 0.8768 D(G(z)): 0.6353 / 0.0009[0/5][350/1583] Loss_D: 0.6451 Loss_G: 6.0499 D(x): 0.9025 D(G(z)): 0.3673 / 0.0060[0/5][400/1583] Loss_D: 0.4211 Loss_G: 3.7316 D(x): 0.8407 D(G(z)): 0.1586 / 0.0392[0/5][450/1583] Loss_D: 0.6569 Loss_G: 2.4818 D(x): 0.6437 D(G(z)): 0.0858 / 0.1129[0/5][500/1583] Loss_D: 1.2208 Loss_G: 2.9943 D(x): 0.4179 D(G(z)): 0.0109 / 0.1133[0/5][550/1583] Loss_D: 0.3400 Loss_G: 4.7669 D(x): 0.9135 D(G(z)): 0.1922 / 0.0145[0/5][600/1583] Loss_D: 0.5756 Loss_G: 4.8500 D(x): 0.9189 D(G(z)): 0.3193 / 0.0187[0/5][650/1583] Loss_D: 0.2470 Loss_G: 4.1606 D(x): 0.9460 D(G(z)): 0.1545 / 0.0250[0/5][700/1583] Loss_D: 0.3887 Loss_G: 4.1884 D(x): 0.8518 D(G(z)): 0.1562 / 0.0297[0/5][750/1583] Loss_D: 0.5353 Loss_G: 4.1742 D(x): 0.8034 D(G(z)): 0.1958 / 0.0302[0/5][800/1583] Loss_D: 0.3213 Loss_G: 5.8919 D(x): 0.9076 D(G(z)): 0.1572 / 0.0065[0/5][850/1583] Loss_D: 0.8850 Loss_G: 7.4333 D(x): 0.9258 D(G(z)): 0.4449 / 0.0017[0/5][900/1583] Loss_D: 1.2624 Loss_G: 10.0392 D(x): 0.9896 D(G(z)): 0.6361 / 0.0002[0/5][950/1583] Loss_D: 0.8802 Loss_G: 6.9221 D(x): 0.5527 D(G(z)): 0.0039 / 0.0045[0/5][1000/1583] Loss_D: 0.5799 Loss_G: 3.1800 D(x): 0.7062 D(G(z)): 0.0762 / 0.0884[0/5][1050/1583] Loss_D: 0.9647 Loss_G: 6.6894 D(x): 0.9429 D(G(z)): 0.5270 / 0.0035[0/5][1100/1583] Loss_D: 0.5624 Loss_G: 3.6715 D(x): 0.7944 D(G(z)): 0.2069 / 0.0445[0/5][1150/1583] Loss_D: 0.6205 Loss_G: 4.8995 D(x): 0.8634 D(G(z)): 0.3046 / 0.0169[0/5][1200/1583] Loss_D: 0.2569 Loss_G: 4.2945 D(x): 0.9455 D(G(z)): 0.1528 / 0.0255[0/5][1250/1583] Loss_D: 0.4921 Loss_G: 3.2500 D(x): 0.8152 D(G(z)): 0.1892 / 0.0753[0/5][1300/1583] Loss_D: 0.4068 Loss_G: 3.7702 D(x): 0.8153 D(G(z)): 0.1335 / 0.0472[0/5][1350/1583] Loss_D: 1.1704 Loss_G: 7.3408 D(x): 0.9443 D(G(z)): 0.5863 / 0.0022[0/5][1400/1583] Loss_D: 0.6111 Loss_G: 2.2676 D(x): 0.6714 D(G(z)): 0.0793 / 0.1510[0/5][1450/1583] Loss_D: 0.7817 Loss_G: 4.0744 D(x): 0.7915 D(G(z)): 0.3573 / 0.0242[0/5][1500/1583] Loss_D: 0.7177 Loss_G: 1.9253 D(x): 0.5770 D(G(z)): 0.0257 / 0.1909[0/5][1550/1583] Loss_D: 0.4518 Loss_G: 2.8314 D(x): 0.7991 D(G(z)): 0.1479 / 0.0885[1/5][0/1583] Loss_D: 0.4267 Loss_G: 4.5150 D(x): 0.8976 D(G(z)): 0.2401 / 0.0196[1/5][50/1583] Loss_D: 0.5106 Loss_G: 2.7800 D(x): 0.7073 D(G(z)): 0.0663 / 0.0932[1/5][100/1583] Loss_D: 0.6300 Loss_G: 1.8648 D(x): 0.6557 D(G(z)): 0.0756 / 0.2118[1/5][150/1583] Loss_D: 1.1727 Loss_G: 5.1536 D(x): 0.8397 D(G(z)): 0.5261 / 0.0125[1/5][200/1583] Loss_D: 0.4675 Loss_G: 2.9615 D(x): 0.7645 D(G(z)): 0.1400 / 0.0780[1/5][250/1583] Loss_D: 0.7938 Loss_G: 3.1614 D(x): 0.6958 D(G(z)): 0.2248 / 0.0678[1/5][300/1583] Loss_D: 0.9869 Loss_G: 5.9243 D(x): 0.9619 D(G(z)): 0.5349 / 0.0063[1/5][350/1583] Loss_D: 0.5178 Loss_G: 3.0236 D(x): 0.7795 D(G(z)): 0.1769 / 0.0700[1/5][400/1583] Loss_D: 1.4509 Loss_G: 2.7187 D(x): 0.3278 D(G(z)): 0.0133 / 0.1273[1/5][450/1583] Loss_D: 0.5530 Loss_G: 4.8110 D(x): 0.9151 D(G(z)): 0.3237 / 0.0160[1/5][500/1583] Loss_D: 0.4621 Loss_G: 4.1158 D(x): 0.8720 D(G(z)): 0.2278 / 0.0293[1/5][550/1583] Loss_D: 0.4987 Loss_G: 4.0199 D(x): 0.8533 D(G(z)): 0.2367 / 0.0287[1/5][600/1583] Loss_D: 1.0630 Loss_G: 4.6502 D(x): 0.9145 D(G(z)): 0.5018 / 0.0218[1/5][650/1583] Loss_D: 0.6081 Loss_G: 4.3172 D(x): 0.8670 D(G(z)): 0.3312 / 0.0221[1/5][700/1583] Loss_D: 0.4703 Loss_G: 2.4900 D(x): 0.7538 D(G(z)): 0.1245 / 0.1188[1/5][750/1583] Loss_D: 0.4827 Loss_G: 2.2941 D(x): 0.7372 D(G(z)): 0.1105 / 0.1300[1/5][800/1583] Loss_D: 0.4013 Loss_G: 3.8850 D(x): 0.8895 D(G(z)): 0.2179 / 0.0324[1/5][850/1583] Loss_D: 0.7245 Loss_G: 1.9088 D(x): 0.6100 D(G(z)): 0.0950 / 0.1898[1/5][900/1583] Loss_D: 0.8372 Loss_G: 1.2346 D(x): 0.5232 D(G(z)): 0.0332 / 0.3633[1/5][950/1583] Loss_D: 0.5561 Loss_G: 3.2048 D(x): 0.7660 D(G(z)): 0.2035 / 0.0594[1/5][1000/1583] Loss_D: 0.6859 Loss_G: 1.6347 D(x): 0.5764 D(G(z)): 0.0435 / 0.2540[1/5][1050/1583] Loss_D: 0.6785 Loss_G: 4.3244 D(x): 0.9066 D(G(z)): 0.3835 / 0.0203[1/5][1100/1583] Loss_D: 0.4835 Loss_G: 2.4080 D(x): 0.7428 D(G(z)): 0.1073 / 0.1147[1/5][1150/1583] Loss_D: 0.5507 Loss_G: 2.5400 D(x): 0.7857 D(G(z)): 0.2182 / 0.1092[1/5][1200/1583] Loss_D: 0.6054 Loss_G: 3.4802 D(x): 0.8263 D(G(z)): 0.2934 / 0.0441[1/5][1250/1583] Loss_D: 0.4788 Loss_G: 2.3533 D(x): 0.7872 D(G(z)): 0.1698 / 0.1327[1/5][1300/1583] Loss_D: 0.5314 Loss_G: 2.7018 D(x): 0.8273 D(G(z)): 0.2423 / 0.0921[1/5][1350/1583] Loss_D: 0.8579 Loss_G: 4.6214 D(x): 0.9623 D(G(z)): 0.5089 / 0.0159[1/5][1400/1583] Loss_D: 0.4919 Loss_G: 2.7656 D(x): 0.8122 D(G(z)): 0.2147 / 0.0864[1/5][1450/1583] Loss_D: 0.4461 Loss_G: 3.0576 D(x): 0.8042 D(G(z)): 0.1798 / 0.0619[1/5][1500/1583] Loss_D: 0.7182 Loss_G: 3.7270 D(x): 0.8553 D(G(z)): 0.3713 / 0.0382[1/5][1550/1583] Loss_D: 0.6378 Loss_G: 3.7489 D(x): 0.8757 D(G(z)): 0.3523 / 0.0317[2/5][0/1583] Loss_D: 0.3965 Loss_G: 2.6262 D(x): 0.7941 D(G(z)): 0.1247 / 0.0963[2/5][50/1583] Loss_D: 0.6504 Loss_G: 3.9890 D(x): 0.9267 D(G(z)): 0.3865 / 0.0275[2/5][100/1583] Loss_D: 0.6523 Loss_G: 3.8724 D(x): 0.8707 D(G(z)): 0.3613 / 0.0299[2/5][150/1583] Loss_D: 0.7685 Loss_G: 3.9059 D(x): 0.9361 D(G(z)): 0.4534 / 0.0278[2/5][200/1583] Loss_D: 0.6587 Loss_G: 1.9218 D(x): 0.6469 D(G(z)): 0.1291 / 0.1888[2/5][250/1583] Loss_D: 0.6971 Loss_G: 2.2256 D(x): 0.6208 D(G(z)): 0.1226 / 0.1465[2/5][300/1583] Loss_D: 0.5797 Loss_G: 2.4846 D(x): 0.7762 D(G(z)): 0.2434 / 0.1098[2/5][350/1583] Loss_D: 0.4674 Loss_G: 1.8800 D(x): 0.8045 D(G(z)): 0.1903 / 0.1877[2/5][400/1583] Loss_D: 0.6462 Loss_G: 1.9510 D(x): 0.7018 D(G(z)): 0.1935 / 0.1792[2/5][450/1583] Loss_D: 0.9817 Loss_G: 4.2519 D(x): 0.9421 D(G(z)): 0.5381 / 0.0233[2/5][500/1583] Loss_D: 0.7721 Loss_G: 1.0928 D(x): 0.5402 D(G(z)): 0.0316 / 0.3927[2/5][550/1583] Loss_D: 0.6037 Loss_G: 2.6914 D(x): 0.7719 D(G(z)): 0.2504 / 0.0896[2/5][600/1583] Loss_D: 1.4213 Loss_G: 5.4727 D(x): 0.9408 D(G(z)): 0.6792 / 0.0064[2/5][650/1583] Loss_D: 0.7246 Loss_G: 1.7030 D(x): 0.6716 D(G(z)): 0.2184 / 0.2246[2/5][700/1583] Loss_D: 0.6642 Loss_G: 3.3809 D(x): 0.8554 D(G(z)): 0.3438 / 0.0591[2/5][750/1583] Loss_D: 0.6649 Loss_G: 2.0197 D(x): 0.7169 D(G(z)): 0.2333 / 0.1565[2/5][800/1583] Loss_D: 0.4594 Loss_G: 2.6623 D(x): 0.8150 D(G(z)): 0.1930 / 0.0944[2/5][850/1583] Loss_D: 1.1957 Loss_G: 3.1871 D(x): 0.7790 D(G(z)): 0.5576 / 0.0568[2/5][900/1583] Loss_D: 0.6657 Loss_G: 1.5311 D(x): 0.7092 D(G(z)): 0.2122 / 0.2558[2/5][950/1583] Loss_D: 0.6795 Loss_G: 1.4149 D(x): 0.6134 D(G(z)): 0.1195 / 0.2937[2/5][1000/1583] Loss_D: 0.5995 Loss_G: 2.1744 D(x): 0.7325 D(G(z)): 0.2054 / 0.1484[2/5][1050/1583] Loss_D: 0.6706 Loss_G: 1.6705 D(x): 0.6425 D(G(z)): 0.1414 / 0.2310[2/5][1100/1583] Loss_D: 1.2840 Loss_G: 4.4620 D(x): 0.9736 D(G(z)): 0.6601 / 0.0225[2/5][1150/1583] Loss_D: 0.7568 Loss_G: 3.1238 D(x): 0.8153 D(G(z)): 0.3717 / 0.0581[2/5][1200/1583] Loss_D: 0.6331 Loss_G: 1.9048 D(x): 0.6799 D(G(z)): 0.1604 / 0.1814[2/5][1250/1583] Loss_D: 0.5802 Loss_G: 2.4358 D(x): 0.7561 D(G(z)): 0.2194 / 0.1095[2/5][1300/1583] Loss_D: 0.9613 Loss_G: 2.3290 D(x): 0.7463 D(G(z)): 0.3952 / 0.1349[2/5][1350/1583] Loss_D: 0.5367 Loss_G: 1.7398 D(x): 0.7580 D(G(z)): 0.1898 / 0.2216[2/5][1400/1583] Loss_D: 0.7762 Loss_G: 3.6246 D(x): 0.9006 D(G(z)): 0.4378 / 0.0364[2/5][1450/1583] Loss_D: 0.7183 Loss_G: 4.0442 D(x): 0.8602 D(G(z)): 0.3857 / 0.0254[2/5][1500/1583] Loss_D: 0.5416 Loss_G: 2.0642 D(x): 0.7393 D(G(z)): 0.1758 / 0.1532[2/5][1550/1583] Loss_D: 0.5295 Loss_G: 1.7855 D(x): 0.6768 D(G(z)): 0.0886 / 0.2154[3/5][0/1583] Loss_D: 0.8635 Loss_G: 1.7508 D(x): 0.4918 D(G(z)): 0.0280 / 0.2154[3/5][50/1583] Loss_D: 0.8697 Loss_G: 0.7859 D(x): 0.5216 D(G(z)): 0.1124 / 0.4941[3/5][100/1583] Loss_D: 0.8607 Loss_G: 4.5255 D(x): 0.9197 D(G(z)): 0.4973 / 0.0157[3/5][150/1583] Loss_D: 0.4805 Loss_G: 2.3071 D(x): 0.7743 D(G(z)): 0.1742 / 0.1291[3/5][200/1583] Loss_D: 0.4925 Loss_G: 2.6018 D(x): 0.7907 D(G(z)): 0.1970 / 0.0948[3/5][250/1583] Loss_D: 0.7870 Loss_G: 3.3529 D(x): 0.8408 D(G(z)): 0.4050 / 0.0469[3/5][300/1583] Loss_D: 0.5479 Loss_G: 1.7376 D(x): 0.7216 D(G(z)): 0.1592 / 0.2227[3/5][350/1583] Loss_D: 0.8117 Loss_G: 3.4145 D(x): 0.9076 D(G(z)): 0.4685 / 0.0437[3/5][400/1583] Loss_D: 0.4210 Loss_G: 2.3880 D(x): 0.7543 D(G(z)): 0.1047 / 0.1217[3/5][450/1583] Loss_D: 1.5745 Loss_G: 0.2366 D(x): 0.2747 D(G(z)): 0.0361 / 0.8096[3/5][500/1583] Loss_D: 0.7196 Loss_G: 2.1319 D(x): 0.7332 D(G(z)): 0.2935 / 0.1403[3/5][550/1583] Loss_D: 0.5697 Loss_G: 2.6649 D(x): 0.8816 D(G(z)): 0.3210 / 0.0917[3/5][600/1583] Loss_D: 0.7779 Loss_G: 1.2727 D(x): 0.5540 D(G(z)): 0.0855 / 0.3412[3/5][650/1583] Loss_D: 0.4090 Loss_G: 2.6893 D(x): 0.8334 D(G(z)): 0.1835 / 0.0855[3/5][700/1583] Loss_D: 0.8108 Loss_G: 3.8991 D(x): 0.9241 D(G(z)): 0.4716 / 0.0281[3/5][750/1583] Loss_D: 0.9907 Loss_G: 4.7885 D(x): 0.9111 D(G(z)): 0.5402 / 0.0123[3/5][800/1583] Loss_D: 0.4725 Loss_G: 2.3347 D(x): 0.7577 D(G(z)): 0.1400 / 0.1222[3/5][850/1583] Loss_D: 1.5580 Loss_G: 4.9586 D(x): 0.8954 D(G(z)): 0.7085 / 0.0132[3/5][900/1583] Loss_D: 0.5785 Loss_G: 1.6395 D(x): 0.6581 D(G(z)): 0.1003 / 0.2411[3/5][950/1583] Loss_D: 0.6592 Loss_G: 1.0890 D(x): 0.5893 D(G(z)): 0.0451 / 0.3809[3/5][1000/1583] Loss_D: 0.7280 Loss_G: 3.5368 D(x): 0.8898 D(G(z)): 0.4176 / 0.0409[3/5][1050/1583] Loss_D: 0.7088 Loss_G: 3.4301 D(x): 0.8558 D(G(z)): 0.3845 / 0.0457[3/5][1100/1583] Loss_D: 0.5651 Loss_G: 2.1150 D(x): 0.7602 D(G(z)): 0.2127 / 0.1532[3/5][1150/1583] Loss_D: 0.5412 Loss_G: 1.7790 D(x): 0.6602 D(G(z)): 0.0801 / 0.2088[3/5][1200/1583] Loss_D: 1.2277 Loss_G: 1.1464 D(x): 0.4864 D(G(z)): 0.2915 / 0.3665[3/5][1250/1583] Loss_D: 0.7148 Loss_G: 1.3957 D(x): 0.5948 D(G(z)): 0.1076 / 0.2876[3/5][1300/1583] Loss_D: 1.0675 Loss_G: 1.3018 D(x): 0.4056 D(G(z)): 0.0310 / 0.3355[3/5][1350/1583] Loss_D: 0.8064 Loss_G: 0.7482 D(x): 0.5846 D(G(z)): 0.1453 / 0.5147[3/5][1400/1583] Loss_D: 0.6032 Loss_G: 3.0601 D(x): 0.8474 D(G(z)): 0.3189 / 0.0590[3/5][1450/1583] Loss_D: 0.5329 Loss_G: 2.8172 D(x): 0.8234 D(G(z)): 0.2567 / 0.0795[3/5][1500/1583] Loss_D: 0.9292 Loss_G: 3.5544 D(x): 0.8686 D(G(z)): 0.4887 / 0.0410[3/5][1550/1583] Loss_D: 0.5929 Loss_G: 2.9118 D(x): 0.8614 D(G(z)): 0.3239 / 0.0702[4/5][0/1583] Loss_D: 0.5564 Loss_G: 2.7516 D(x): 0.8716 D(G(z)): 0.3145 / 0.0799[4/5][50/1583] Loss_D: 1.0485 Loss_G: 0.6751 D(x): 0.4332 D(G(z)): 0.0675 / 0.5568[4/5][100/1583] Loss_D: 0.6753 Loss_G: 1.4046 D(x): 0.6028 D(G(z)): 0.0882 / 0.2901[4/5][150/1583] Loss_D: 0.5946 Loss_G: 1.7618 D(x): 0.6862 D(G(z)): 0.1488 / 0.2016[4/5][200/1583] Loss_D: 0.4866 Loss_G: 2.2638 D(x): 0.7628 D(G(z)): 0.1633 / 0.1321[4/5][250/1583] Loss_D: 0.7493 Loss_G: 1.0999 D(x): 0.5541 D(G(z)): 0.0659 / 0.3787[4/5][300/1583] Loss_D: 1.0886 Loss_G: 4.6532 D(x): 0.9370 D(G(z)): 0.5811 / 0.0149[4/5][350/1583] Loss_D: 0.6106 Loss_G: 1.9212 D(x): 0.6594 D(G(z)): 0.1322 / 0.1825[4/5][400/1583] Loss_D: 0.5226 Loss_G: 2.9611 D(x): 0.8178 D(G(z)): 0.2378 / 0.0731[4/5][450/1583] Loss_D: 1.0068 Loss_G: 1.3267 D(x): 0.4310 D(G(z)): 0.0375 / 0.3179[4/5][500/1583] Loss_D: 3.1088 Loss_G: 0.1269 D(x): 0.0706 D(G(z)): 0.0061 / 0.8897[4/5][550/1583] Loss_D: 1.7889 Loss_G: 0.4800 D(x): 0.2175 D(G(z)): 0.0143 / 0.6479[4/5][600/1583] Loss_D: 0.6732 Loss_G: 3.5685 D(x): 0.8775 D(G(z)): 0.3879 / 0.0362[4/5][650/1583] Loss_D: 0.5169 Loss_G: 2.1943 D(x): 0.7222 D(G(z)): 0.1349 / 0.1416[4/5][700/1583] Loss_D: 0.4567 Loss_G: 2.4442 D(x): 0.7666 D(G(z)): 0.1410 / 0.1204[4/5][750/1583] Loss_D: 0.5972 Loss_G: 2.2992 D(x): 0.6286 D(G(z)): 0.0670 / 0.1283[4/5][800/1583] Loss_D: 0.5461 Loss_G: 1.9777 D(x): 0.7013 D(G(z)): 0.1318 / 0.1795[4/5][850/1583] Loss_D: 0.6317 Loss_G: 2.2345 D(x): 0.6962 D(G(z)): 0.1854 / 0.1385[4/5][900/1583] Loss_D: 0.6034 Loss_G: 3.2300 D(x): 0.8781 D(G(z)): 0.3448 / 0.0517[4/5][950/1583] Loss_D: 0.6371 Loss_G: 2.7755 D(x): 0.8595 D(G(z)): 0.3357 / 0.0826[4/5][1000/1583] Loss_D: 0.6077 Loss_G: 3.3958 D(x): 0.9026 D(G(z)): 0.3604 / 0.0458[4/5][1050/1583] Loss_D: 0.5057 Loss_G: 3.2545 D(x): 0.8705 D(G(z)): 0.2691 / 0.0546[4/5][1100/1583] Loss_D: 0.4552 Loss_G: 2.0632 D(x): 0.7887 D(G(z)): 0.1704 / 0.1524[4/5][1150/1583] Loss_D: 0.9933 Loss_G: 1.0264 D(x): 0.4507 D(G(z)): 0.0636 / 0.4182[4/5][1200/1583] Loss_D: 0.5037 Loss_G: 1.9940 D(x): 0.6967 D(G(z)): 0.0959 / 0.1698[4/5][1250/1583] Loss_D: 0.4760 Loss_G: 2.5973 D(x): 0.8192 D(G(z)): 0.2164 / 0.0945[4/5][1300/1583] Loss_D: 1.0137 Loss_G: 3.8782 D(x): 0.9330 D(G(z)): 0.5405 / 0.0309[4/5][1350/1583] Loss_D: 0.9084 Loss_G: 3.1406 D(x): 0.7540 D(G(z)): 0.3980 / 0.0648[4/5][1400/1583] Loss_D: 0.6724 Loss_G: 4.1269 D(x): 0.9536 D(G(z)): 0.4234 / 0.0236[4/5][1450/1583] Loss_D: 0.6452 Loss_G: 3.5163 D(x): 0.8730 D(G(z)): 0.3555 / 0.0412[4/5][1500/1583] Loss_D: 0.8843 Loss_G: 1.4950 D(x): 0.5314 D(G(z)): 0.1035 / 0.2835[4/5][1550/1583] Loss_D: 2.3345 Loss_G: 1.0675 D(x): 0.1448 D(G(z)): 0.0228 / 0.4177
Results¶
Finally, lets check out how we did. Here, we will look at threedifferent results. First, we will see how D and G’s losses changedduring training. Second, we will visualize G’s output on the fixed_noisebatch for every epoch. And third, we will look at a batch of real datanext to a batch of fake data from G.
Loss versus training iteration
Below is a plot of D & G’s losses versus training iterations.
plt.figure(figsize=(10,5))plt.title("Generator and Discriminator Loss During Training")plt.plot(G_losses,label="G")plt.plot(D_losses,label="D")plt.xlabel("iterations")plt.ylabel("Loss")plt.legend()plt.show()
Visualization of G’s progression
Remember how we saved the generator’s output on the fixed_noise batchafter every epoch of training. Now, we can visualize the trainingprogression of G with an animation. Press the play button to start theanimation.
fig = plt.figure(figsize=(8,8))plt.axis("off")ims = [[plt.imshow(np.transpose(i,(1,2,0)), animated=True)] for i in img_list]ani = animation.ArtistAnimation(fig, ims, interval=1000, repeat_delay=1000, blit=True)HTML(ani.to_jshtml())
