cost function outputs 'nan' in tensorflow

Question

While studying the tensorflow, I faced a problem.
The cost function output 'nan'.

And, if you find any other wrong in source code let me know the links for it.

I am trying to send the cost function value to my trained model, but its not working.

tf.reset_default_graph()

tf.set_random_seed(777)

X = tf.placeholder(tf.float32, [None, 20, 20, 3])
Y = tf.placeholder(tf.float32, [None, 1])

with tf.variable_scope('conv1') as scope:
    W1 = tf.Variable(tf.random_normal([4, 4, 3, 32], stddev=0.01), name='weight1')      
    L1 = tf.nn.conv2d(X, W1, strides=[1, 1, 1, 1], padding='SAME')
    L1 = tf.nn.relu(L1)
    L1 = tf.nn.max_pool(L1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')
    L1 = tf.reshape(L1, [-1, 10 * 10 * 32])

    W1_hist = tf.summary.histogram('conv_weight1', W1)
    L1_hist = tf.summary.histogram('conv_layer1', L1)

with tf.name_scope('fully_connected_layer1') as scope:
    W2 = tf.get_variable('W2', shape=[10 * 10 * 32, 1], initializer=tf.contrib.layers.xavier_initializer())        
    b = tf.Variable(tf.random_normal([1]))
    hypothesis = tf.matmul(L1, W2) + b

    W2_hist = tf.summary.histogram('fully_connected_weight1', W2)
    b_hist = tf.summary.histogram('fully_connected_bias', b)
    hypothesis_hist = tf.summary.histogram('hypothesis', hypothesis)

with tf.name_scope('cost') as scope:
    cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) * tf.log(1 - hypothesis))
    cost_summary = tf.summary.scalar('cost', cost)

with tf.name_scope('train_optimizer') as scope:
    optimizer = tf.train.AdamOptimizer(learning_rate=0.0001).minimize(cost)  

predicted = tf.cast(hypothesis > 0.5, dtype=tf.float32)
accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, Y), dtype=tf.float32))
accuracy_summary = tf.summary.scalar('accuracy', accuracy)

train_data_batch, train_labels_batch = tf.train.batch([train_data, train_labels], enqueue_many=True , batch_size=100, allow_smaller_final_batch=True)

with tf.Session() as sess:
    # tensorboard --logdir=./logs/planesnet2_log
    merged_summary = tf.summary.merge_all()
    writer = tf.summary.FileWriter('./logs/planesnet2_log')   
    writer.add_graph(sess.graph)

    sess.run(tf.global_variables_initializer())
    coord = tf.train.Coordinator()
    threads = tf.train.start_queue_runners(coord=coord)
    total_cost = 0

    for step in range(20):
        x_batch, y_batch = sess.run([train_data_batch, train_labels_batch])
        feed_dict = {X: x_batch, Y: y_batch}
        _, cost_val = sess.run([optimizer, cost], feed_dict = feed_dict)
        total_cost += cost_val
        print('total_cost: ', total_cost, 'cost_val: ', cost_val)
    coord.request_stop()
    coord.join(threads)

Answer 1

As I know,

Cross entropy cost function assumes that the hypothesis which you want to predict is stochastic value. Because cross entropy uses log function and (1-Y_) formula. Therefore, cross entropy loss should be used only for stochastic cases.

So you have to use the softmax function to make the results of the hypothesis probability.

W2 = tf.get_variable('W2', shape=[10 * 10 * 32, 1], 
initializer=tf.contrib.layers.xavier_initializer())        
b = tf.Variable(tf.random_normal([1]))

# hypothesis = tf.matmul(L1, W2) + b
hypothesis = tf.nn.softmax(tf.add(tf.matmul(L1, W2), b))
cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) * tf.log(1 - hypothesis))

Or you can use this code

W2 = tf.get_variable('W2', shape=[10 * 10 * 32, 1], 
initializer=tf.contrib.layers.xavier_initializer())        
b = tf.Variable(tf.random_normal([1]))

hypothesis = tf.matmul(L1, W2) + b
cost = tf.nn.softmax_cross_entropy_with_logits(labels=Y, logits=hypothesis)

Answer 2

You use a cross entropy loss without a sigmoid activation function to hypothesis, thus your values are not bounded in ]0,1]. The log function is not defined for negative values and it most likely get somes. Add a sigmoid and epsilon factor to avoid negative or 0 values and you should be fine.