.. _sec_multi_gpu:
Training on Multiple GPUs
=========================
So far we discussed how to train models efficiently on CPUs and GPUs. We
even showed how deep learning frameworks such as MXNet (and TensorFlow)
allow one to parallelize computation and communication automatically
between them in :numref:`sec_auto_para`. Lastly, we showed in
:numref:`sec_use_gpu` how to list all available GPUs on a computer
using ``nvidia-smi``. What we did *not* discuss is how to actually
parallelize deep learning training (we omit any discussion of
*inference* on multiple GPUs here as it’s a rather rarely used and
advanced topic that goes beyond the scope of this book). Instead, we
implied in passing that one would somehow split the data across multiple
devices and make it work. The present section fills in the details and
shows how to train a network in parallel when starting from scratch.
Details on how to take advantage of functionality in Gluon is relegated
to :numref:`sec_multi_gpu_gluon`. We assume that the reader is
familiar with minibatch SGD algorithms such as the ones described in
:numref:`sec_minibatch_sgd`.
Splitting the Problem
---------------------
Let’s start with a simple computer vision problem and a slightly archaic
network, e.g., with multiple layers of convolutions, pooling, and
possibly a few dense layers in the end. That is, let’s start with a
network that looks quite similar to LeNet
:cite:`LeCun.Bottou.Bengio.ea.1998` or AlexNet
:cite:`Krizhevsky.Sutskever.Hinton.2012`. Given multiple GPUs (2 if
it’s a desktop server, 4 on a g4dn.12xlarge, 8 on an AWS p3.16xlarge, or
16 on a p2.16xlarge), we want to partition training in a manner as to
achieve good speedup while simultaneously benefitting from simple and
reproducible design choices. Multiple GPUs, after all, increase both
*memory* and *compute* ability. In a nutshell, we have a number of
choices, given a minibatch of training data that we want to classify.
.. _fig_alexnet_original:
.. figure:: ../img/alexnet-original.svg
Model parallelism in the original AlexNet design due to limited GPU
memory.
- We could partition the network layers across multiple GPUs. That is,
each GPU takes as input the data flowing into a particular layer,
processes data across a number of subsequent layers and then sends
the data to the next GPU.
- This allows us to process data with larger networks when compared
to what a single GPU could handle.
- Memory footprint per GPU can be well controlled (it’s a fraction
of the total network footprint)
- The interface between layers (and thus GPUs) requires tight
synchronization. This can be tricky, in particular if the
computational workloads are not properly matched between layers.
The problem is exacerbated for large numbers of GPUs.
- The interface between layers requires large amounts of data
transfer (activations, gradients). This may overwhelm the
bandwidth of the GPU buses.
- Compute intensive, yet sequential operations are nontrivial to
partition. See e.g., :cite:`Mirhoseini.Pham.Le.ea.2017` for a
best effort in this regard. It remains a difficult problem and it
is unclear whether it is possible to achieve good (linear) scaling
on nontrivial problems. We do not recommend it unless there is
excellent framework / OS support for chaining together multiple
GPUs.
- We could split the work required by individual layers. For instance,
rather than computing 64 channels on a single GPU we could split up
the problem across 4 GPUs, each of which generate data for 16
channels. Likewise, for a dense layer we could split the number of
output neurons. :numref:`fig_alexnet_original` illustrates this
design. The figure is taken from
:cite:`Krizhevsky.Sutskever.Hinton.2012` where this strategy was
used to deal with GPUs that had a very small memory footprint (2GB at
the time).
- This allows for good scaling in terms of computation, provided
that the number of channels (or neurons) is not too small.
- Multiple GPUs can process increasingly larger networks since the
memory available scales linearly.
- We need a *very large* number of synchronization / barrier
operations since each layer depends on the results from all other
layers.
- The amount of data that needs to be transferred is potentially
even larger than when distributing layers across GPUs. We do not
recommend this approach due to its bandwidth cost and complexity.
- Lastly we could partition data across multiple GPUs. This way all
GPUs perform the same type of work, albeit on different observations.
Gradients are aggregated between GPUs after each minibatch.
- This is the simplest approach and it can be applied in any
situation.
- Adding more GPUs does not allow us to train larger models.
- We only need to synchronize after each minibatch. That said, it’s
highly desirable to start exchanging gradients parameters already
while others are still being computed.
- Large numbers of GPUs lead to very large minibatch sizes, thus
reducing training efficiency.
.. _fig_splitting:
.. figure:: ../img/splitting.svg
Parallelization on multiple GPUs. From left to right - original
problem, network partitioning, layer partitioning, data parallelism.
By and large, data parallelism is the most convenient way to proceed,
provided that we have access to GPUs with sufficiently large memory. See
also :cite:`Li.Andersen.Park.ea.2014` for a detailed description of
partitioning for distributed training. GPU memory used to be a problem
in the early days of deep learning. By now this issue has been resolved
for all but the most unusual cases. We focus on data parallelism in what
follows.
Data Parallelism
----------------
Assume that there are :math:`k` GPUs on a machine. Given the model to be
trained, each GPU will maintain a complete set of model parameters
independently. Training proceeds as follows (see
:numref:`fig_data_parallel` for details on data parallel training on
two GPUs):
- In any iteration of training, given a random minibatch, we split the
examples in the batch into :math:`k` portions and distribute them
evenly across the GPUs.
- Each GPU calculates loss and gradient of the model parameters based
on the minibatch subset it was assigned and the model parameters it
maintains.
- The local gradients of each of the :math:`k` GPUs are aggregated to
obtain the current minibatch stochastic gradient.
- The aggregate gradient is re-distributed to each GPU.
- Each GPU uses this minibatch stochastic gradient to update the
complete set of model parameters that it maintains.
.. _fig_data_parallel:
.. figure:: ../img/data-parallel.svg
Calculation of minibatch stochastic gradient using data parallelism
and two GPUs.
A comparison of different ways of parallelization on multiple GPUs is
depicted in :numref:`fig_splitting`. Note that in practice we
*increase* the minibatch size :math:`k`-fold when training on :math:`k`
GPUs such that each GPU has the same amount of work to do as if we were
training on a single GPU only. On a 16 GPU server this can increase the
minibatch size considerably and we may have to increase the learning
rate accordingly. Also note that :numref:`sec_batch_norm` needs to be
adjusted (e.g., by keeping a separate batch norm coefficient per GPU).
In what follows we will use :numref:`sec_lenet` as the toy network to
illustrate multi-GPU training. As always we begin by importing the
relevant packages and modules.
.. code:: python
%matplotlib inline
import d2l
from mxnet import autograd, gluon, np, npx
npx.set_np()
A Toy Network
-------------
We use LeNet as introduced in :numref:`sec_lenet`. We define it from
scratch to illustrate parameter exchange and synchronization in detail.
.. code:: python
# Initialize model parameters
scale = 0.01
W1 = np.random.normal(scale=scale, size=(20, 1, 3, 3))
b1 = np.zeros(20)
W2 = np.random.normal(scale=scale, size=(50, 20, 5, 5))
b2 = np.zeros(50)
W3 = np.random.normal(scale=scale, size=(800, 128))
b3 = np.zeros(128)
W4 = np.random.normal(scale=scale, size=(128, 10))
b4 = np.zeros(10)
params = [W1, b1, W2, b2, W3, b3, W4, b4]
# Define the model
def lenet(X, params):
h1_conv = npx.convolution(data=X, weight=params[0], bias=params[1],
kernel=(3, 3), num_filter=20)
h1_activation = npx.relu(h1_conv)
h1 = npx.pooling(data=h1_activation, pool_type='avg', kernel=(2, 2),
stride=(2, 2))
h2_conv = npx.convolution(data=h1, weight=params[2], bias=params[3],
kernel=(5, 5), num_filter=50)
h2_activation = npx.relu(h2_conv)
h2 = npx.pooling(data=h2_activation, pool_type='avg', kernel=(2, 2),
stride=(2, 2))
h2 = h2.reshape(h2.shape[0], -1)
h3_linear = np.dot(h2, params[4]) + params[5]
h3 = npx.relu(h3_linear)
y_hat = np.dot(h3, params[6]) + params[7]
return y_hat
# Cross-entropy loss function
loss = gluon.loss.SoftmaxCrossEntropyLoss()
Data Synchronization
--------------------
For efficient multi-GPU training we need two basic operations: firstly
we need to have the ability to distribute a list of parameters to
multiple devices and to attach gradients (``get_params``). Without
parameters it’s impossible to evaluate the network on a GPU. Secondly,
we need the ability to sum parameters across multiple devices, i.e., we
need an ``allreduce`` function.
.. code:: python
def get_params(params, ctx):
new_params = [p.copyto(ctx) for p in params]
for p in new_params:
p.attach_grad()
return new_params
Let’s try it out by copying the model parameters of lenet to gpu(0).
.. code:: python
new_params = get_params(params, d2l.try_gpu(0))
print('b1 weight:', new_params[1])
print('b1 grad:', new_params[1].grad)
.. parsed-literal::
:class: output
b1 weight: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] @gpu(0)
b1 grad: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] @gpu(0)
Since we didn’t perform any computation yet, the gradient with regard to
the bias weights is still :math:`0`. Now let’s assume that we have a
vector distributed across multiple GPUs. The following allreduce
function adds up all vectors and broadcasts the result back to all GPUs.
Note that for this to work we need to copy the data to the device
accumulating the results.
.. code:: python
def allreduce(data):
for i in range(1, len(data)):
data[0][:] += data[i].copyto(data[0].context)
for i in range(1, len(data)):
data[0].copyto(data[i])
Let’s test this by creating vectors with different values on different
devices and aggregate them.
.. code:: python
data = [np.ones((1, 2), ctx=d2l.try_gpu(i)) * (i + 1) for i in range(2)]
print('before allreduce:\n', data[0], '\n', data[1])
allreduce(data)
print('after allreduce:\n', data[0], '\n', data[1])
.. parsed-literal::
:class: output
before allreduce:
[[1. 1.]] @gpu(0)
[[2. 2.]] @gpu(1)
after allreduce:
[[3. 3.]] @gpu(0)
[[3. 3.]] @gpu(1)
Distributing Data
-----------------
We need a simple utility function to distribute a minibatch evenly
across multiple GPUs. For instance, on 2 GPUs we’d like to have half of
the data to be copied to each of the GPUs. Since it’s more convenient
and more concise, we use the built-in split and load function in Gluon
(to try it out on a :math:`4 \times 5` matrix).
.. code:: python
data = np.arange(20).reshape(4, 5)
ctx = [npx.gpu(0), npx.gpu(1)]
split = gluon.utils.split_and_load(data, ctx)
print('input :', data)
print('load into', ctx)
print('output:', split)
.. parsed-literal::
:class: output
input : [[ 0. 1. 2. 3. 4.]
[ 5. 6. 7. 8. 9.]
[10. 11. 12. 13. 14.]
[15. 16. 17. 18. 19.]]
load into [gpu(0), gpu(1)]
output: [array([[0., 1., 2., 3., 4.],
[5., 6., 7., 8., 9.]], ctx=gpu(0)), array([[10., 11., 12., 13., 14.],
[15., 16., 17., 18., 19.]], ctx=gpu(1))]
For later reuse we define a ``split_batch`` function which splits both
data and labels.
.. code:: python
# Saved in the d2l package for later use
def split_batch(X, y, ctx_list):
"""Split X and y into multiple devices specified by ctx."""
assert X.shape[0] == y.shape[0]
return (gluon.utils.split_and_load(X, ctx_list),
gluon.utils.split_and_load(y, ctx_list))
Training
--------
Now we can implement multi-GPU training on a single minibatch. Its
implementation is primarily based on the data parallelism approach
described in this section. We will use the auxiliary functions we just
discussed, ``allreduce`` and ``split_and_load``, to synchronize the data
among multiple GPUs. Note that we don’t need to write any specific code
to achieve parallelism. Since the compute graph doesn’t have any
dependencies across devices within a minibatch, it is executed in
parallel *automatically*.
.. code:: python
def train_batch(X, y, gpu_params, ctx_list, lr):
gpu_Xs, gpu_ys = split_batch(X, y, ctx_list)
with autograd.record(): # Loss is calculated separately on each GPU
losses = [loss(lenet(gpu_X, gpu_W), gpu_y)
for gpu_X, gpu_y, gpu_W in zip(gpu_Xs, gpu_ys, gpu_params)]
for l in losses: # Back Propagation is performed separately on each GPU
l.backward()
# Sum all gradients from each GPU and broadcast them to all GPUs
for i in range(len(gpu_params[0])):
allreduce([gpu_params[c][i].grad for c in range(len(ctx_list))])
# The model parameters are updated separately on each GPU
for param in gpu_params:
d2l.sgd(param, lr, X.shape[0]) # Here, we use a full-size batch
Now, we can define the training function. It is slightly different from
the ones used in the previous chapters: we need to allocate the GPUs and
copy all the model parameters to all devices. Obviously each batch is
processed using ``train_batch`` to deal with multiple GPUs. For
convenience (and conciseness of code) we compute the accuracy on a
single GPU (this is *inefficient* since the other GPUs are idle).
.. code:: python
def train(num_gpus, batch_size, lr):
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
ctx_list = [d2l.try_gpu(i) for i in range(num_gpus)]
# Copy model parameters to num_gpus GPUs
gpu_params = [get_params(params, c) for c in ctx_list]
# num_epochs, times, acces = 10, [], []
num_epochs = 10
animator = d2l.Animator('epoch', 'test acc', xlim=[1, num_epochs])
timer = d2l.Timer()
for epoch in range(num_epochs):
timer.start()
for X, y in train_iter:
# Perform multi-GPU training for a single minibatch
train_batch(X, y, gpu_params, ctx_list, lr)
npx.waitall()
timer.stop()
# Verify the model on GPU 0
animator.add(epoch+1, (d2l.evaluate_accuracy_gpu(
lambda x: lenet(x, gpu_params[0]), test_iter, ctx[0]),))
print('test acc: %.2f, %.1f sec/epoch on %s' % (
animator.Y[0][-1], timer.avg(), ctx_list))
Experiment
----------
Let’s see how well this works on a single GPU. We use a batch size of
256 and a learning rate of 0.2.
.. code:: python
train(num_gpus=1, batch_size=256, lr=0.2)
.. parsed-literal::
:class: output
test acc: 0.86, 2.2 sec/epoch on [gpu(0)]
.. figure:: output_multiple-gpus_c746cb_21_1.svg
By keeping the batch size and learning rate unchanged and changing the
number of GPUs to 2, we can see that the improvement in test accuracy is
roughly the same as in the results from the previous experiment. In
terms of the optimization algorithms, they are identical. Unfortunately
there’s no meaningful speedup to be gained here: the model is simply too
small; moreover we only have a small dataset, where our slightly
unsophisticated approach to implementing multi-GPU training suffered
from significant Python overhead. We will encounter more complex models
and more sophisticated ways of parallelization going forward. Let’s see
what happens nonetheless for MNIST.
.. code:: python
train(num_gpus=2, batch_size=256, lr=0.2)
.. parsed-literal::
:class: output
test acc: 0.83, 4.0 sec/epoch on [gpu(0), gpu(1)]
.. figure:: output_multiple-gpus_c746cb_23_1.svg
Summary
-------
- There are multiple ways to split deep network training over multiple
GPUs. We could split them between layers, across layers, or across
data. The former two require tightly choreographed data transfers.
Data parallelism is the simplest strategy.
- Data parallel training is straightforward. However, it increases the
effective minibatch size to be efficient.
- Data is split across multiple GPUs, each GPU executes its own forward
and backward operation and subsequently gradients are aggregated and
results broadcast back to the GPUs.
- Large minibatches may require a slightly increased learning rate.
Exercises
---------
1. When training on multiple GPUs, change the minibatch size from
:math:`b` to :math:`k \cdot b`, i.e., scale it up by the number of
GPUs.
2. Compare accuracy for different learning rates. How does it scale with
the number of GPUs.
3. Implement a more efficient allreduce that aggregates different
parameters on different GPUs (why is this more efficient in the first
place).
4. Implement multi-GPU test accuracy computation.
`Discussions `__
-------------------------------------------------
|image0|
.. |image0| image:: ../img/qr_multiple-gpus.svg