new_contents: import tensorflow as tf
  import numpy as np
  
  def average_gradients(tower_grads):
    """Calculate the average gradient for each shared variable across all towers.
  
    Note that this function provides a synchronization point across all towers.
  
    Args:
      tower_grads: List of lists of (gradient, variable) tuples. The outer list
        is over individual gradients. The inner list is over the gradient
        calculation for each tower.
    Returns:
       List of pairs of (gradient, variable) where the gradient has been averaged
       across all towers.
    """
    average_grads = []
    for grad_and_vars in zip(*tower_grads):
      # Note that each grad_and_vars looks like the following:
      #   ((grad0_gpu0, var0_gpu0), ... , (grad0_gpuN, var0_gpuN))
      grads = []
      for g, _ in grad_and_vars:
        # Add 0 dimension to the gradients to represent the tower.
        expanded_g = tf.expand_dims(g, 0)
  
        # Append on a 'tower' dimension which we will average over below.
        grads.append(expanded_g)
  
      # Average over the 'tower' dimension.
      grad = tf.concat(axis=0, values=grads)
      grad = tf.reduce_mean(grad, 0)
  
      # Keep in mind that the Variables are redundant because they are shared
      # across towers. So .. we will just return the first tower's pointer to
      # the Variable.
      v = grad_and_vars[0][1]
      grad_and_var = (grad, v)
      average_grads.append(grad_and_var)
    return average_grads
  
subject: add utils for multi gpus