title: Tensorflow: There is a difference in gradient and loss for the same structure
body: <p>With gradient and loss, I experiment with the learning process of a neural network.</p>
  
  <p>I assumed that learning process(loss function value, gradient value) are same if learning conditions(model structure, initialization, batch input stream) of two models are same.</p>
  
  <p>Under the same initialization, I thought that the gradient and loss calculated for each model would be the same, but the result was not.</p>
  
  <p>The code I have run is the most basic learning code, as shown below.</p>
  
  <p>(to constrained the randomness of dropout, I just deactivated the dropout layer)</p>
  
  <pre><code>import tensorflow as tf
  import numpy as np
  #from pprint import pprint
  from tensorflow.examples.tutorials.mnist import input_data
  
  batch_size = 128
  test_size = 256
  
  def init_weights(shape):
      return tf.Variable(tf.random_normal(shape, stddev=0.01, seed=1))
  
  def model(X, w, w2, w3, w4, w_o, p_keep_conv, p_keep_hidden):
  
      l1a = tf.nn.relu(tf.nn.conv2d(X, w,                       # l1a shape=(?, 28, 28, 32)
                          strides=[1, 1, 1, 1], padding='SAME'))
      l1 = tf.nn.max_pool(l1a, ksize=[1, 2, 2, 1],              # l1 shape=(?, 14, 14, 32)
                          strides=[1, 2, 2, 1], padding='SAME')
      #l1 = tf.nn.dropout(l1, p_keep_conv)
  
      l2a = tf.nn.relu(tf.nn.conv2d(l1, w2,                     # l2a shape=(?, 14, 14, 64)
                          strides=[1, 1, 1, 1], padding='SAME'))
      l2 = tf.nn.max_pool(l2a, ksize=[1, 2, 2, 1],              # l2 shape=(?, 7, 7, 64)
                          strides=[1, 2, 2, 1], padding='SAME')
      #l2 = tf.nn.dropout(l2, p_keep_conv)
  
      l3a = tf.nn.relu(tf.nn.conv2d(l2, w3,                     # l3a shape=(?, 7, 7, 128)
                          strides=[1, 1, 1, 1], padding='SAME'))
      l3 = tf.nn.max_pool(l3a, ksize=[1, 2, 2, 1],              # l3 shape=(?, 4, 4, 128)
                          strides=[1, 2, 2, 1], padding='SAME')
      l3 = tf.reshape(l3, [-1, w4.get_shape().as_list()[0]])    # reshape to (?, 2048)
      #l3 = tf.nn.dropout(l3, p_keep_conv)
  
      l4 = tf.nn.relu(tf.matmul(l3, w4))
      #l4 = tf.nn.dropout(l4, p_keep_hidden)
  
      pyx = tf.matmul(l4, w_o)
      return pyx
  
  
  mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
  trX, trY, teX, teY = mnist.train.images, mnist.train.labels, mnist.test.images, mnist.test.labels
  trX = trX.reshape(-1, 28, 28, 1)  # 28x28x1 input img
  teX = teX.reshape(-1, 28, 28, 1)  # 28x28x1 input img
  
  X0 = tf.placeholder("float", [None, 28, 28, 1], name='input_0')
  X1 = tf.placeholder("float", [None, 28, 28, 1], name='input_1')
  Y  = tf.placeholder("float", [None, 10])
  
  with tf.variable_scope('00'):
      w0_1 = init_weights([3, 3, 1, 32])       # 3x3x1 conv, 32 outputs
      w0_2 = init_weights([3, 3, 32, 64])     # 3x3x32 conv, 64 outputs
      w0_3 = init_weights([3, 3, 64, 128])    # 3x3x32 conv, 128 outputs
      w0_4 = init_weights([128 * 4 * 4, 625]) # FC 128 * 4 * 4 inputs, 625 outputs
      w0_o = init_weights([625, 10])         # FC 625 inputs, 10 outputs (labels)
  
  with tf.variable_scope('01'):
      w1_1 = init_weights([3, 3, 1, 32])       # 3x3x1 conv, 32 outputs
      w1_2 = init_weights([3, 3, 32, 64])     # 3x3x32 conv, 64 outputs
      w1_3 = init_weights([3, 3, 64, 128])    # 3x3x32 conv, 128 outputs
      w1_4 = init_weights([128 * 4 * 4, 625]) # FC 128 * 4 * 4 inputs, 625 outputs
      w1_o = init_weights([625, 10])         # FC 625 inputs, 10 outputs (labels)
  
  
  p_keep_conv = tf.placeholder("float")
  p_keep_hidden = tf.placeholder("float")
  
  py_x0 = model(X0, w0_1, w0_2, w0_3, w0_4, w0_o, p_keep_conv, p_keep_hidden)
  py_x1 = model(X1, w1_1, w1_2, w1_3, w1_4, w1_o, p_keep_conv, p_keep_hidden)
  
  
  
  cost0 = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=py_x0, labels=Y))
  cost1 = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=py_x1, labels=Y))
  
  
  
  model_0_vars = [tensor for tensor in tf.trainable_variables() if '00/' in tensor.name]
  model_1_vars = [tensor for tensor in tf.trainable_variables() if '01/' in tensor.name]
  
  #pprint(model_0_vars)
  #pprint(model_1_vars)
  
  
  train_op_model_0_grad = tf.train.RMSPropOptimizer(0.001, 0.9).compute_gradients(cost0, var_list = model_0_vars)
  train_op_model_0_apply= tf.train.RMSPropOptimizer(0.001, 0.9).apply_gradients(train_op_model_0_grad)
  
  
  train_op_model_1_grad = tf.train.RMSPropOptimizer(0.001, 0.9).compute_gradients(cost1, var_list = model_1_vars)
  train_op_model_1_apply= tf.train.RMSPropOptimizer(0.001, 0.9).apply_gradients(train_op_model_1_grad)
  
  
  predict_op_0 = tf.argmax(py_x0, 1)
  predict_op_1 = tf.argmax(py_x1, 1)
  
  
  
  # Launch the graph in a session
  with tf.Session() as sess:
      # you need to initialize all variables
      tf.initialize_all_variables().run()
  
  
  
      step = 0
      for i in range(2):
          #check_weight_tmp = sess.run([model_0_vars, model_1_vars])
          #check_weight.append(check_weight_tmp)
  
          training_batch = zip(range(0, len(trX), batch_size),
                               range(batch_size, len(trX)+1, batch_size))
  
  
          for start, end in training_batch:
              step +=1
  
              grad0, grad1 = \
              sess.run([train_op_model_0_grad, train_op_model_1_grad], 
                       feed_dict={X0: trX[start:end], X1: trX[start:end], Y: trY[start:end],
                                  p_keep_conv: 0.8, p_keep_hidden: 0.5})
  
  
              cost0_r, cost1_r = \
              sess.run([cost0, cost1], 
                       feed_dict={X0: trX[start:end], X1: trX[start:end], Y: trY[start:end],
                                  p_keep_conv: 0.8, p_keep_hidden: 0.5})
  
              sess.run([train_op_model_0_apply, train_op_model_1_apply],
                        feed_dict={X0: trX[start:end], X1: trX[start:end], Y: trY[start:end],
                                   p_keep_conv: 0.8, p_keep_hidden: 0.5})
  
  
              print("STEP: {0:5d}, {1:3.6f}, {2:3.6f}, {3:3.6f}".format(step, cost0_r, cost1_r, cost0_r - cost1_r))
  
  
  
          #test_indices = np.arange(len(teX)) # Get A Test Batch
          #np.random.shuffle(test_indices)
          #test_indices = test_indices[0:test_size]
  
          #print(i, np.mean(np.argmax(teY[test_indices], axis=1) ==
          #                 sess.run(predict_op_0,
          #                          feed_dict={X: teX[test_indices],
          #                                     Y: teY[test_indices],
          #                                     p_keep_conv: 1.0,
          #                                     p_keep_hidden: 1.0})))
  </code></pre>
  
  <p>There is a noticeable difference in loss from the 200th epoch.</p>
  
  <p>I think I have missed it, but I can't figure it out even I spend a long time to look at it.</p>
  
  <p>I would appreciate if you could let me know what I am missing.</p>