GAN not converging. Discriminator loss keeps increasing

Question

I am making a simple generative adverserial network on mnist dataset.

This is my implementation :

import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np
from tensorflow.examples.tutorials.mnist import input_data

mnist = input_data.read_data_sets("MNIST_data/",one_hot=True)

def noise(batch_size):
    return np.random.uniform(-1, 1, (batch_size, 100))

learning_rate = 0.001
batch_size = 128

input = tf.placeholder('float', [None, 100])
real_data = tf.placeholder('float', [None, 784])

def generator(x):
    weights = {
        'hl1' : tf.Variable(tf.random_normal([100, 200])),
        'ol'  : tf.Variable(tf.random_normal([200, 784]))
    }
    biases = {
        'hl1' : tf.Variable(tf.random_normal([200])),
        'ol'  : tf.Variable(tf.random_normal([784]))
    }

    hl1 = tf.add(tf.matmul(x, weights['hl1']), biases['hl1'])
    ol = tf.nn.sigmoid(tf.add(tf.matmul(hl1, weights['ol']), biases['ol']))

    return ol


def discriminator(x):
    weights = {
        'hl1' : tf.Variable(tf.random_normal([784, 200])),
        'ol'  : tf.Variable(tf.random_normal([200, 1]))
    }
    biases = {
        'hl1' : tf.Variable(tf.random_normal([200])),
        'ol'  : tf.Variable(tf.random_normal([1]))
    }

    hl1 = tf.add(tf.matmul(x, weights['hl1']), biases['hl1'])
    ol = tf.nn.sigmoid(tf.add(tf.matmul(hl1, weights['ol']), biases['ol']))

    return ol

with tf.variable_scope("G"):
    G = generator(input)

with tf.variable_scope("D"):
    D_real = discriminator(real_data)

with tf.variable_scope("D", reuse = True):
    D_gen = discriminator(G)

generator_parameters = [x for x in tf.trainable_variables() if x.name.startswith('G/')]
discriminator_parameters = [x for x in tf.trainable_variables() if x.name.startswith('D/')]

G_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=D_gen, labels=tf.ones_like(D_gen)))
D_real_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=D_real, labels=tf.ones_like(D_real)))
D_fake_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=D_gen, labels=tf.zeros_like(D_gen)))
D_total_loss = tf.add(D_fake_loss, D_real_loss)

G_train = tf.train.AdamOptimizer(learning_rate).minimize(G_loss,var_list=generator_parameters)
D_train = tf.train.AdamOptimizer(learning_rate).minimize(D_total_loss,var_list=discriminator_parameters)

sess = tf.Session()
init = tf.global_variables_initializer()

sess.run(init)

loss_g_function = []
loss_d_function = []

for epoch in range(200):
    for iteratiion in range(int(len(mnist.train.images)/batch_size)):
        real_batch, _ = mnist.train.next_batch(batch_size)

        _, d_err = sess.run([D_train, D_total_loss], feed_dict = {real_data : real_batch, input : noise(batch_size)})
        _, g_err = sess.run([G_train, G_loss], feed_dict = {input : noise(batch_size)})

    print("Epoch = ", epoch)
    print("D_loss = ", d_err)
    print("G_loss = ", g_err)
    loss_g_function.append(g_err)
    loss_d_function.append(d_err)

# Visualizing
import matplotlib.pyplot as plt

test_noise = noise(1)

plt.subplot(2, 2, 1)
plt.plot(test_noise[0])
plt.title("Noise")
plt.subplot(2, 2, 2)
plt.imshow(np.reshape(sess.run(G, feed_dict = {input : test_noise})[0], [28, 28]))
plt.title("Generated Image")
plt.subplot(2, 2, 3)
plt.plot(loss_d_function, 'r')
plt.xlabel("Epochs")
plt.ylabel("Discriminator Loss")
plt.title("D-Loss")
plt.subplot(2, 2, 4)
plt.plot(loss_g_function, 'b')
plt.xlabel("Epochs")
plt.ylabel("Generator Loss")
plt.title("G_Loss")
plt.show()

I have tried lr = 0.001 lr = 0.0001 and lr = 0.00003.

These are my results : https://i.sstatic.net/NXA0H.jpg

What could be the reason? My weights initialization are randomly drawn from the normal distribution. Also, please check the loss function, are they correct?

Answer 1

Issues:

---

It has just a single layer:

hl1 = tf.add(tf.matmul(x, weights['hl1']), biases['hl1'])    
ol = tf.nn.sigmoid(tf.add(tf.matmul(hl1, weights['ol']), biases['ol']))

Above network defined for both discriminator and generator has no activation defined for the first layer. This literally means the network is just one layer: y = act(w2(x*w1+b1)+b2) = act(x*w+b)

---

Sigmoid applied twice:

ol = tf.nn.sigmoid(tf.add(tf.matmul(hl1, weights['ol']) ...
D_real_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(...)

As mentioned in the comments, activation is applied twice.

---

Weight initializations:

tf.Variable(tf.random_normal([784, 200]))

In case of sigmoid activation if the weights are large, the gradients will be small, which means the weights are effectively not changing values. (Bigger w + very small delta(w)). May be the reason why when i run the above code, the loss seems to not change much. Its better to adopt industry best practices and use something like: xavier_initializer().

---

Dynamic range inconsistencies: The input to the generator is in the dynamic range of [-1, 1], it gets multipled by a weight of [-1, 1] but gets outputed to a [ 0 1] range. There is nothing wrong with this, a bias can learn to map the output range. But its better to use a activation layer, that outputs [-1, 1] like a tanh, so the network can learn faster. If tanh is used as activation for the generator, then the input images feed to the descriminator need to be scaled to [-1 1] for training consistency.

---

With the above changes, you can get something similar to:

The above network is a really simple one and the output quality is not great. I have deliberately not changed the complexity to find out what kind of output one can get out of a simple network.

You can build a bigger network (that includes CNN) and as well try out recent GAN models to obtain better quality results.

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Code for reproducing the above can be obtained from here.