<p>The problem was caused by <code>nan</code> in loss function and weights, as described in <a href="https://stackoverflow.com/q/37448557/41977">this question</a>.</p>

<p>By introducing a different standard deviation for each weights tensor based on its dimensions (as described <a href="https://stackoverflow.com/a/37755443/41977">in this answer</a> and originally in He <em>et al.</em> [1]) I was able to train successfully the network.</p>

<p>[1]: He <em>et al.</em> (2015) <a href="https://arxiv.org/pdf/1502.01852.pdf" rel="nofollow noreferrer">Delving Deep into Rectifiers:
Surpassing Human-Level Performance on ImageNet Classification</a></p>
Low accuracy in Deep Neural Network with Tensorflow
<p>I am following the third Jupyter notebook on <a href="https://github.com/jdwittenauer/ipython-notebooks/blob/master/notebooks/tensorflow/Tensorflow-3-Regularization.ipynb" rel="nofollow noreferrer">Tensorflow examples</a>.</p>

<p>Running problem 4, I tried to implement a function which builds automatically a number of hidden layers, without manually coding the configuration of each layer.</p>

<p>However, the model runs providing very low accuracy (10%) so I thought that maybe such function could not be compatible with the graph builder of Tensorflow.</p>

<p>My code is the following:</p>

<pre><code>def hlayers(n_layers, n_nodes, i_size, a, r=0, keep_p=1):

  for i in range(n_layers):
    if i &gt; 0:
      i_size = n_nodes
    w = tf.Variable(tf.truncated_normal([i_size, n_nodes]), name=f'W{i}')
    b = tf.Variable(tf.zeros([n_nodes]), name=f'b{i}')
    pa = tf.nn.relu(tf.add(tf.matmul(a, w), b))
    a = tf.nn.dropout(pa, keep_prob=keep_p, name=f'a{i}')
    r += tf.nn.l2_loss(w, name=f'r{i}')

  return a, r

batch_size = 128
num_nodes = 1024
beta = 0.01

graph = tf.Graph()
with graph.as_default():

  # Input data. For the training data, we use a placeholder that will be fed
  # at run time with a training minibatch.
  tf_train_dataset = tf.placeholder(
    tf.float32,
    shape=(batch_size, image_size * image_size),
    name='Dataset')
  tf_train_labels = tf.placeholder(
    tf.float32,
    shape=(batch_size, num_labels),
    name='Labels')
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)

  keep_p = tf.placeholder(tf.float32, name='KeepProb')

  # Hidden layers.
  a, r = hlayers(
    n_layers=3,
    n_nodes=num_nodes,
    i_size=image_size * image_size,
    a=tf_train_dataset,
    keep_p=keep_p)

  # Output layer.
  wo = tf.Variable(tf.truncated_normal([num_nodes, num_labels]), name='Wo')
  bo = tf.Variable(tf.zeros([num_labels]), name='bo')
  logits = tf.add(tf.matmul(a, wo), bo, name='Logits')
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(
      labels=tf_train_labels, logits=logits))

  # Regularizer.
  regularizers = tf.add(r, tf.nn.l2_loss(wo))
  loss = tf.reduce_mean(loss + beta * regularizers, name='Loss')

  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)

  a, _ = hlayers(
    n_layers=3,
    n_nodes=num_nodes,
    i_size=image_size * image_size,
    a=tf_valid_dataset)
  valid_prediction = tf.nn.softmax(tf.add(tf.matmul(a, wo), bo))

  a, _ = hlayers(
    n_layers=3,
    n_nodes=num_nodes,
    i_size=image_size * image_size,
    a=tf_test_dataset)
  test_prediction = tf.nn.softmax(tf.add(tf.matmul(a, wo), bo))

num_steps = 3001

with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset[offset:(offset + batch_size), :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {
      tf_train_dataset : batch_data,
      tf_train_labels : batch_labels,
      keep_p : 0.5}
    _, l, predictions = session.run(
      [optimizer, loss, train_prediction], feed_dict=feed_dict)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(
        valid_prediction.eval(), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))
</code></pre>