Creation and Initialization¶

We can create an NDArray on either CPU or GPU:

>>> import mxnet as mx
>>> a = mx.nd.empty((2, 3)) # create a 2-by-3 matrix on cpu
>>> b = mx.nd.empty((2, 3), mx.gpu()) # create a 2-by-3 matrix on gpu 0
>>> c = mx.nd.empty((2, 3), mx.gpu(2)) # create a 2-by-3 matrix on gpu 2
>>> c.shape # get shape
(2L, 3L)
>>> c.context # get device info
gpu(2)

They can be initialized in various ways:

>>> a = mx.nd.zeros((2, 3)) # create a 2-by-3 matrix filled with 0
>>> b = mx.nd.ones((2, 3))  # create a 2-by-3 matrix filled with 1
>>> b[:] = 2 # set all elements of b to 2

We can copy the value from one NDArray to another, even if they sit on different devices:

>>> a = mx.nd.ones((2, 3))
>>> b = mx.nd.zeros((2, 3), mx.gpu())
>>> a.copyto(b) # copy data from cpu to gpu

We can also convert NDArray to numpy.ndarray:

>>> a = mx.nd.ones((2, 3))
>>> b = a.asnumpy()
>>> type(b)
<type 'numpy.ndarray'>
>>> print b
[[ 1.  1.  1.]
 [ 1.  1.  1.]]

and vice versa:

>>> import numpy as np
>>> a = mx.nd.empty((2, 3))
>>> a[:] = np.random.uniform(-0.1, 0.1, a.shape)
>>> print a.asnumpy()
[[-0.06821112 -0.03704893  0.06688045]
 [ 0.09947646 -0.07700162  0.07681718]]

Basic Operations¶

>>> a = mx.nd.ones((2, 3)) * 2
>>> b = mx.nd.ones((2, 3)) * 4
>>> print b.asnumpy()
[[ 4.  4.  4.]
 [ 4.  4.  4.]]
>>> c = a + b
>>> print c.asnumpy()
[[ 6.  6.  6.]
 [ 6.  6.  6.]]
>>> d = a * b
>>> print d.asnumpy()
[[ 8.  8.  8.]
 [ 8.  8.  8.]]

>>> a = mx.nd.ones((2, 3)) * 2
>>> b = mx.nd.ones((2, 3), mx.gpu()) * 3
>>> c = a.copyto(mx.gpu()) * b
>>> print c.asnumpy()
[[ 6.  6.  6.]
 [ 6.  6.  6.]]

Load and Save¶

There are two ways to save data to (load from) disks easily. The first way uses pickle. NDArray is pickle compatible, which means you can simply pickle the NDArray as you do with numpy.ndarray.

>>> import mxnet as mx
>>> import pickle as pkl

>>> a = mx.nd.ones((2, 3)) * 2
>>> data = pkl.dumps(a)
>>> b = pkl.loads(data)
>>> print b.asnumpy()
[[ 2.  2.  2.]
 [ 2.  2.  2.]]

The second way is to directly dump a list of NDArray to disk in binary format.

>>> a = mx.nd.ones((2,3))*2
>>> b = mx.nd.ones((2,3))*3
>>> mx.nd.save('mydata.bin', [a, b])
>>> c = mx.nd.load('mydata.bin')
>>> print c[0].asnumpy()
[[ 2.  2.  2.]
 [ 2.  2.  2.]]
>>> print c[1].asnumpy()
[[ 3.  3.  3.]
 [ 3.  3.  3.]]

We can also dump a dict:

>>> mx.nd.save('mydata.bin', {'a':a, 'b':b})
>>> c = mx.nd.load('mydata.bin')
>>> print c['a'].asnumpy()
[[ 2.  2.  2.]
 [ 2.  2.  2.]]
>>> print c['b'].asnumpy()
[[ 3.  3.  3.]
 [ 3.  3.  3.]]

In addition, if we have set up distributed filesystems such as S3 and HDFS, we can directly save to and load from them. For example:

>>> mx.nd.save('s3://mybucket/mydata.bin', [a,b])
>>> mx.nd.save('hdfs///users/myname/mydata.bin', [a,b])

Automatic Parallelization¶

NDArray can automatically execute operations in parallel. This is desirable when we use multiple resources such as CPU, GPU cards, and CPU-to-GPU memory bandwidth.

For example, if we write a += 1 followed by b += 1, and a is on CPU while b is on GPU, then we will want to execute them in parallel to improve the efficiency. Furthermore, data copies between CPU and GPU are also expensive, so we hope to run them in parallel with other computations as well.

However, finding statements by eye that can be executed in parallel is hard. In the following example, a+=1 and c*=3 can be executed in parallel, but a+=1 and b*=3 have to be sequentially executed.

a = mx.nd.ones((2,3))
b = a
c = a.copyto(mx.cpu())
a += 1
b *= 3
c *= 3

Luckily, MXNet can automatically resolve the dependencies and execute operations in parallel with correctness guaranteed. In other words, we can write a program as if it is using only a single thread, and MXNet will automatically dispatch it to multiple devices such as multiple GPU cards or multiple machines.

This is achieved by lazy evaluation. Any operation we write down is issued to a internal engine, and then returned. For example, if we run a += 1, it returns immediately after pushing the plus operation to the engine. This asynchronicity allows us to push more operations to the engine, so it can determine the read and write dependency and find the best way to execute them in parallel.

The actual computations are finished when we want to copy the results into some other place, such as print a.asnumpy() or mx.nd.save([a]). Therefore, if we want to write highly parallelized code, we only need to postpone asking for the results.

Basic Composition of Symbols¶

The following code creates a two layer perceptron network:

>>> import mxnet as mx
>>> net = mx.symbol.Variable('data')
>>> net = mx.symbol.FullyConnected(data=net, name='fc1', num_hidden=128)
>>> net = mx.symbol.Activation(data=net, name='relu1', act_type="relu")
>>> net = mx.symbol.FullyConnected(data=net, name='fc2', num_hidden=64)
>>> net = mx.symbol.SoftmaxOutput(data=net, name='out')
>>> type(net)
<class 'mxnet.symbol.Symbol'>

Each symbol takes a (unique) string name. Variable often defines the inputs, or free variables. Other symbols take a symbol as their input (data), and may accept other hyperparameters such as the number of hidden neurons (num_hidden) or the activation type (act_type).

The symbol can be viewed simply as a function taking several arguments whose names are automatically generated and can be got by

>>> net.list_arguments()
['data', 'fc1_weight', 'fc1_bias', 'fc2_weight', 'fc2_bias', 'out_label']

As can be seen, these arguments are the parameters needed by each symbol:

• data : input data needed by the variable data
• fc1_weight and fc1_bias : the weight and bias for the first fully connected layer fc1
• fc2_weight and fc2_bias : the weight and bias for the second fully connected layer fc2
• out_label : the label needed by the loss

We can also specify the automatic generated names explicitly:

>>> net = mx.symbol.Variable('data')
>>> w = mx.symbol.Variable('myweight')
>>> net = mx.symbol.FullyConnected(data=net, weight=w, name='fc1', num_hidden=128)
>>> net.list_arguments()
['data', 'myweight', 'fc1_bias']

More Complicated Composition¶

MXNet provides well-optimized symbols (see src/operator) for commonly used layers in deep learning. We can also easily define new operators in python. The following example first performs an elementwise add between two symbols, then feeds them to the fully connected operator.

>>> lhs = mx.symbol.Variable('data1')
>>> rhs = mx.symbol.Variable('data2')
>>> net = mx.symbol.FullyConnected(data=lhs + rhs, name='fc1', num_hidden=128)
>>> net.list_arguments()
['data1', 'data2', 'fc1_weight', 'fc1_bias']

We can also construct a symbol in a more flexible way than the single forward composition exemplified above.

>>> net = mx.symbol.Variable('data')
>>> net = mx.symbol.FullyConnected(data=net, name='fc1', num_hidden=128)
>>> net2 = mx.symbol.Variable('data2')
>>> net2 = mx.symbol.FullyConnected(data=net2, name='net2', num_hidden=128)
>>> composed_net = net(data=net2, name='compose')
>>> composed_net.list_arguments()
['data2', 'net2_weight', 'net2_bias', 'fc1_weight', 'fc1_bias']

In the above example, net is used as a function to apply to an existing symbol net, and the resulting composed_net will replace the original argument data by net2 instead.

Argument Shape Inference¶

Now we know how to define a symbol. Next, we can infer the shapes of all the arguments it needs given the shape of its input data.

>>> net = mx.symbol.Variable('data')
>>> net = mx.symbol.FullyConnected(data=net, name='fc1', num_hidden=10)
>>> arg_shape, out_shape, aux_shape = net.infer_shape(data=(100, 100))
>>> dict(zip(net.list_arguments(), arg_shape))
{'data': (100, 100), 'fc1_weight': (10, 100), 'fc1_bias': (10,)}
>>> out_shape
[(100, 10)]

This shape inference can be used as an early debugging mechanism to detect shape inconsistency.

Bind the Symbols and Run¶

Now we can bind the free variables of the symbol and perform forward and backward operations. The bind function will create a Executor that can be used to carry out the real computations.

>>> # define computation graphs
>>> A = mx.symbol.Variable('A')
>>> B = mx.symbol.Variable('B')
>>> C = A * B
>>> a = mx.nd.ones(3) * 4
>>> b = mx.nd.ones(3) * 2
>>> # bind the symbol with real arguments
>>> c_exec = C.bind(ctx=mx.cpu(), args={'A' : a, 'B': b})
>>> # do forward pass calclation.
>>> c_exec.forward()
>>> c_exec.outputs[0].asnumpy()
[ 8.  8.  8.]

For neural nets, a more commonly used pattern is simple_bind, which will create all the argument arrays for you. Then you can call forward, and backward (if gradient is needed) to get the gradient.

>>> # define computation graphs
>>> net = some symbol
>>> texec = net.simple_bind(data=input_shape)
>>> texec.forward()
>>> texec.backward()

The model API is a thin wrapper around the symbolic executors to support neural net training.

You are also strongly encouraged to read Symbolic Configuration and Execution in Pictures, which provides a detailed explanation of the concepts in pictures.

How Efficient is the Symbolic API?¶

In short, it is designed to be very efficient in both memory and runtime.

The major reason for us to introduce the Symbolic API is to bring the efficient C++ operations in powerful toolkits such as cxxnet and caffe together with the flexible dynamic NDArray operations. All the memory and computation resources are allocated statically during Bind, to maximize the runtime performance and memory utilization.

The coarse grained operators are equivalent to cxxnet layers, which are extremely efficient. We also provide fine grained operators for more flexible composition. Because we are also doing more inplace memory allocation, mxnet can be more memory efficient than cxxnet, and achieves the same runtime, with greater flexiblity.

Initialization¶

Let’s first consider a simple example: initialize a (int, NDAarray) pair into the store, and then pull the value out.

>>> kv = mx.kv.create('local') # create a local kv store.
>>> shape = (2,3)
>>> kv.init(3, mx.nd.ones(shape)*2)
>>> a = mx.nd.zeros(shape)
>>> kv.pull(3, out = a)
>>> print a.asnumpy()
[[ 2.  2.  2.]
 [ 2.  2.  2.]]

Push, Aggregation, and Updater¶

For any key has been initialized, we can push a new value with the same shape to the key.

>>> kv.push(3, mx.nd.ones(shape)*8)
>>> kv.pull(3, out = a) # pull out the value
>>> print a.asnumpy()
[[ 8.  8.  8.]
 [ 8.  8.  8.]]

The data for pushing can be on any device. Furthermore, we can push multiple values into the same key, where KVStore will first sum all these values and then push the aggregated value.

>>> gpus = [mx.gpu(i) for i in range(4)]
>>> b = [mx.nd.ones(shape, gpu) for gpu in gpus]
>>> kv.push(3, b)
>>> kv.pull(3, out = a)
>>> print a.asnumpy()
[[ 4.  4.  4.]
 [ 4.  4.  4.]]

For each push, KVStore combines the pushed value with the value stored using an updater. The default updater is ASSIGN; we can replace the default to control how data is merged.

>>> def update(key, input, stored):
>>>     print "update on key: %d" % key
>>>     stored += input * 2
>>> kv._set_updater(update)
>>> kv.pull(3, out=a)
>>> print a.asnumpy()
[[ 4.  4.  4.]
 [ 4.  4.  4.]]
>>> kv.push(3, mx.nd.ones(shape))
update on key: 3
>>> kv.pull(3, out=a)
>>> print a.asnumpy()
[[ 6.  6.  6.]
 [ 6.  6.  6.]]

Pull¶

We have already seen how to pull a single key-value pair. Similarly to push, we can also pull the value into several devices by a single call.

>>> b = [mx.nd.ones(shape, gpu) for gpu in gpus]
>>> kv.pull(3, out = b)
>>> print b[1].asnumpy()
[[ 6.  6.  6.]
 [ 6.  6.  6.]]

Handle a list of key-value pairs¶

All operations introduced so far involve a single key. KVStore also provides an interface for a list of key-value pairs. For a single device:

>>> keys = [5, 7, 9]
>>> kv.init(keys, [mx.nd.ones(shape)]*len(keys))
>>> kv.push(keys, [mx.nd.ones(shape)]*len(keys))
update on key: 5
update on key: 7
update on key: 9
>>> b = [mx.nd.zeros(shape)]*len(keys)
>>> kv.pull(keys, out = b)
>>> print b[1].asnumpy()
[[ 3.  3.  3.]
 [ 3.  3.  3.]]

For multiple devices:

>>> b = [[mx.nd.ones(shape, gpu) for gpu in gpus]] * len(keys)
>>> kv.push(keys, b)
update on key: 5
update on key: 7
update on key: 9
>>> kv.pull(keys, out = b)
>>> print b[1][1].asnumpy()
[[ 11.  11.  11.]
 [ 11.  11.  11.]]

Multiple machines¶

Base on parameter server. The updater will runs on the server nodes. This section will be updated when the distributed version is ready.