Is there anything obviously wrong with my very simple vanilla GAN?

Garve: <p>Hello!</p>
<p>I want to train a GAN that is able to output pairs of the form (x, x²), simple as that.</p>
<p>First, In the following, we define the discriminator, the generator and some true samples of the form (x, x²) where x varies from -0.5 to 0.5.</p>
<pre><code class="lang-auto">import torch
import numpy as np
import matplotlib.pyplot as plt

class SampleGenerator:
    def __init__(self, function, value_range):
        self.function = function
        self.range = value_range
    
    def generate(self, n_samples):
        x = (self.range[1] - self.range[0])*np.random.rand(n_samples) + self.range[0]
        x = x.reshape(-1,1)
        return (np.hstack([x, self.function(x)]), np.array(n_samples*[1]).reshape(-1,1))

class Discriminator(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.design = torch.nn.Sequential(
            torch.nn.Linear(2, 10),
            torch.nn.PReLU(),
            torch.nn.Linear(10, 1),
            torch.nn.Sigmoid()
        )
        
    def forward(self, x):
        return self.design(x)

class Generator(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.design = torch.nn.Sequential(
            torch.nn.Linear(5, 20),
            torch.nn.PReLU(),
            torch.nn.Linear(20, 20),
            torch.nn.PReLU(),
            torch.nn.Linear(20, 2),
        )
    
    def forward(self, x):
        return self.design(x)

s = SampleGenerator(lambda x: x**2, (-0.5, 0.5))
X_true, y_true = s.generate(100)

d = Discriminator()
doptimizer = torch.optim.Adam(d.parameters(), lr=0.0002, betas=(0.5, 0.999))

g = Generator()
goptimizer = torch.optim.Adam(g.parameters(), lr=0.0002, betas=(0.5, 0.999))

criterion = torch.nn.BCELoss()

X_true = torch.FloatTensor(X_true)
y_true = torch.FloatTensor(y_true)
y_fake = torch.FloatTensor(len(y_true)*[0]).view(-1,1)

# Now the crucial training step.

for epoch in range(10000):
    d.train()
    g.train()
    
    # Train discriminator
    # ... with real examples
    doptimizer.zero_grad()
    output = d(X_true)
    dloss_real = criterion(output, y_true)
    dloss_real.backward()
    d_x = output.mean().item()

    # ... with fake examples
    seed = torch.randn(100, 5)
    X_fake = g(seed)
    output = d(X_fake)
    dloss_fake = criterion(output, y_fake)
    dloss_fake.backward()
    dloss = dloss_real + dloss_fake
    d_gz = output.mean().item()
    doptimizer.step()

    # Train Generator
    goptimizer.zero_grad()
    output = d(g(seed))
    gloss = criterion(output, y_true)
    gloss.backward()
    goptimizer.step()
    
    if epoch%10==0:
        print(d_x, d_gz)

# I let it run and run and run and in the end, the generated sample output looks quite bad.

seed = torch.rand(100,5)
plt.scatter(g(seed).detach().numpy()[:, 0], g(seed).detach().numpy()[:, 1])
plt.scatter(X_true[:, 0], X_true[:, 1])
</code></pre>
<p><img src="https://discuss.pytorch.org/uploads/default/original/3X/9/4/94519f26df5fff5664d1e47d30fa8e78d53857bb.png" alt="index" data-base62-sha1="la5xr0vvJbSxW5gkkeyTeDKQKaT" width="378" height="251"></p>
<p>Is there anything obviously wrong with what I’ve done? I also noticed, that the errors that I output are always around 0.5. I have understodd it like d_x should start at 1 and decrease towards 0.5, while d_gz should start at 0 and increase towards 0.5 in the training process. But here both start off at the goal. Why?</p>
<p>Thank you very much!</p>
<p>Sincerely<br>
Garve</p>