Sometimes, we need to average an array of gradients in deep learning model. Fortunately, Tensorflow divided models into fine-grained tensors and operations, therefore it’s not difficult to implement gradients average by using it.

Let’s see the code from github：

```
with tf.variable_scope(tf.get_variable_scope()):
for i in xrange(FLAGS.num_gpus):
with tf.device('/gpu:%d' % i):
with tf.name_scope('%s_%d' % (cifar10.TOWER_NAME, i)) as scope:
# Dequeues one batch for the GPU
image_batch, label_batch = batch_queue.dequeue()
# Calculate the loss for one tower of the CIFAR model. This function
# constructs the entire CIFAR model but shares the variables across
# all towers.
loss = tower_loss(scope, image_batch, label_batch)
# Reuse variables for the next tower.
tf.get_variable_scope().reuse_variables()
# Retain the summaries from the final tower.
summaries = tf.get_collection(tf.GraphKeys.SUMMARIES, scope)
# Calculate the gradients for the batch of data on this CIFAR tower.
grads = opt.compute_gradients(loss)
# Keep track of the gradients across all towers.
tower_grads.append(grads)
# We must calculate the mean of each gradient. Note that this is the
# synchronization point across all towers.
grads = average_gradients(tower_grads)
......
apply_gradient_op = opt.apply_gradients(grads, global_step=global_step)
```

We should keep in mind that these codes will only build a static graph (the ‘grads; are references rather than values).

```
def average_gradients(tower_grads):
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
```

First, we need to expand dimensions of tensor(gradient) and concatenate them. Then use reduce_mean() to do actually average operation (seems not intuitive).