title: Why adding one more layer to the Tensorflow simple neural net example breaks it?
body: <p>Here is <a href="https://www.tensorflow.org/get_started/mnist/beginners" rel="nofollow noreferrer">a basic Tensorflow network example</a> (based on MNIST), complete code, that gives roughly 0.92 accuracy:</p>
  
  <pre><code>import numpy as np
  import tensorflow as tf
  from tensorflow.examples.tutorials.mnist import input_data
  mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
  
  x = tf.placeholder(tf.float32, [None, 784])
  
  W = tf.Variable(tf.zeros([784, 10]))
  b = tf.Variable(tf.zeros([10]))
  y = tf.nn.softmax(tf.matmul(x, W) + b)
  
  y_ = tf.placeholder(tf.float32, [None, 10])
  
  cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_ * tf.log(y), reduction_indices=[1]))
  train_step = tf.train.GradientDescentOptimizer(0.5).minimize(cross_entropy)
  sess = tf.InteractiveSession()
  tf.global_variables_initializer().run() # or 
  tf.initialize_all_variables().run()
  
  for _ in range(1000):
    batch_xs, batch_ys = mnist.train.next_batch(100)
    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})
  
  correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))
  accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
  print(sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels}))
  </code></pre>
  
  <p><strong>Question:</strong> Why adding an extra layer, like in the code below, makes it so much worse that it drops to about 0.11 accuracy?</p>
  
  <pre><code>W = tf.Variable(tf.zeros([784, 100]))
  b = tf.Variable(tf.zeros([100]))
  h0 = tf.nn.relu(tf.matmul(x, W) + b)
  
  W2 = tf.Variable(tf.zeros([100, 10]))
  b2 = tf.Variable(tf.zeros([10]))
  y = tf.nn.softmax(tf.matmul(h0, W2) + b2)
  </code></pre>