In this chapter, we will learn about an interface in MXNet which is termed as Symbol.

Mxnet.ndarray

Apache MXNet’s Symbol API is an interface for symbolic programming. Symbol API features the use of the following −

• Computational graphs

• Reduced memory usage

• Pre-use function optimization

The example given below shows how one can create a simple expression by using MXNet’s Symbol API −

An NDArray by using 1-D and 2-D ‘array’ from a regular Python list −

import mxnet as mx
# Two placeholders namely x and y will be created with mx.sym.variable
x = mx.sym.Variable(''x'')
y = mx.sym.Variable(''y'')
# The symbol here is constructed using the plus ‘+’ operator.
z = x + y

Output

You will see the following output −

<Symbol _plus0>

Example

(x, y, z)

Output

The output is given below −

(<Symbol x>, <Symbol y>, <Symbol _plus0>)

Now let us discuss in detail about the classes, functions, and parameters of ndarray API of MXNet.

Classes

Following table consists of the classes of Symbol API of MXNet −

Functions and their parameters

Following are some of the important functions and their parameters covered by mxnet.Symbol API −

Implementation Examples

In the example below we will be using the function power() which will return element-wise result of base element raised to the powers from exp element:

import mxnet as mx
mx.sym.power(3, 5)

Output

You will see the following output −

243

Example

x = mx.sym.Variable(''x'')
y = mx.sym.Variable(''y'')
z = mx.sym.power(x, 3)
z.eval(x=mx.nd.array([1,2]))[0].asnumpy()

Output

This produces the following output −

array([1., 8.], dtype=float32)

Example

z = mx.sym.power(4, y)
z.eval(y=mx.nd.array([2,3]))[0].asnumpy()

Output

When you execute the above code, you should see the following output −

array([16., 64.], dtype=float32)

Example

z = mx.sym.power(x, y)
z.eval(x=mx.nd.array([4,5]), y=mx.nd.array([2,3]))[0].asnumpy()

Output

The output is mentioned below −

array([ 16., 125.], dtype=float32)

In the example given below, we will be using the function SoftmaxActivation() (or softmax()) which will be applied to input and is intended for internal layers.

input_data = mx.nd.array([[2., 0.9, -0.5, 4., 8.], [4., -.7, 9., 2., 0.9]])
soft_max_act = mx.nd.softmax(input_data)
print (soft_max_act.asnumpy())

Output

You will see the following output −

[[2.4258138e-03 8.0748333e-04 1.9912292e-04 1.7924475e-02 9.7864312e-01]
[6.6843745e-03 6.0796250e-05 9.9204916e-01 9.0463174e-04 3.0112563e-04]]

symbol.contrib

The Contrib NDArray API is defined in the symbol.contrib package. It typically provides many useful experimental APIs for new features. This API works as a place for the community where they can try out the new features. The feature contributor will get the feedback as well.

Functions and their parameters

Following are some of the important functions and their parameters covered by mxnet.symbol.contrib API −

Implementation Examples

In the example below we will be using the function rand_zipfian for drawing random samples from an approximately Zipfian distribution −

import mxnet as mx
true_cls = mx.sym.Variable(''true_cls'')
samples, exp_count_true, exp_count_sample = mx.sym.contrib.rand_zipfian(true_cls, 5, 6)
samples.eval(true_cls=mx.nd.array([3]))[0].asnumpy()

Output

You will see the following output −

array([4, 0, 2, 1, 5], dtype=int64)

Example

exp_count_true.eval(true_cls=mx.nd.array([3]))[0].asnumpy()

Output

The output is mentioned below −

array([0.57336551])

Example

exp_count_sample.eval(true_cls=mx.nd.array([3]))[0].asnumpy()

Output

You will see the following output −

array([1.78103594, 0.46847373, 1.04183923, 0.57336551, 1.04183923])

In the example below we will be using the function while_loop for running a while loop for user-defined computation and loop condition −

cond = lambda i, s: i <= 7
func = lambda i, s: ([i + s], [i + 1, s + i])
loop_vars = (mx.sym.var(''i''), mx.sym.var(''s''))
outputs, states = mx.sym.contrib.while_loop(cond, func, loop_vars, max_iterations=10)
print(outputs)

Output

The output is given below:

[<Symbol _while_loop0>]

Example

Print(States)

Output

This produces the following output −

[<Symbol _while_loop0>, <Symbol _while_loop0>]

In the example below we will be using the function index_copy that copies the elements of new_tensor into the old_tensor.

import mxnet as mx
a = mx.nd.zeros((6,3))
b = mx.nd.array([[1,2,3],[4,5,6],[7,8,9]])
index = mx.nd.array([0,4,2])
mx.nd.contrib.index_copy(a, index, b)

Output

When you execute the above code, you should see the following output −

[[1. 2. 3.]
[0. 0. 0.]
[7. 8. 9.]
[0. 0. 0.]
[4. 5. 6.]
[0. 0. 0.]]
<NDArray 6x3 @cpu(0)>

symbol.image

The Image Symbol API is defined in the symbol.image package. As name implies, it typically used for images and their features.

Functions and their parameters

Following are some of the important functions and their parameters covered by mxnet.symbol.image API −

Implementation Examples

In the example below, we will be using the function to_tensor to convert image NDArray of shape (H x W x C) or (N x H x W x C) with the values in the range [0, 255] to a tensor NDArray of shape (C x H x W) or (N x C x H x W) with the values in the range [0, 1].

import numpy as np

img = mx.sym.random.uniform(0, 255, (4, 2, 3)).astype(dtype=np.uint8)

mx.sym.image.to_tensor(img)

Output

The output is stated below −

<Symbol to_tensor4>

Example

img = mx.sym.random.uniform(0, 255, (2, 4, 2, 3)).astype(dtype=np.uint8)

mx.sym.image.to_tensor(img)

Output

The output is mentioned below:

<Symbol to_tensor5>

In the example below, we will be using the function normalize() to normalize an tensor of shape (C x H x W) or (N x C x H x W) with mean and standard deviation(SD).

img = mx.sym.random.uniform(0, 1, (3, 4, 2))

mx.sym.image.normalize(img, mean=(0, 1, 2), std=(3, 2, 1))

Output

Given below is the output of the code −

<Symbol normalize0>

Example

img = mx.sym.random.uniform(0, 1, (2, 3, 4, 2))

mx.sym.image.normalize(img, mean=(0, 1, 2), std=(3, 2, 1))

Output

The output is shown below −

<Symbol normalize1>

symbol.random

The Random Symbol API is defined in the symbol.random package. As name implies, it is random distribution generator Symbol API of MXNet.

Functions and their parameters

Following are some of the important functions and their parameters covered by mxnet.symbol.random API −

Implementation Examples

In the example below, we are going to shuffle the elements randomly using shuffle() function. It will shuffle the array along the first axis.

data = mx.nd.array([[0, 1, 2], [3, 4, 5], [6, 7, 8],[9,10,11]])
x = mx.sym.Variable(''x'')
y = mx.sym.random.shuffle(x)
y.eval(x=data)

Output

You will see the following output:

[
[[ 9. 10. 11.]
[ 0. 1. 2.]
[ 6. 7. 8.]
[ 3. 4. 5.]]
<NDArray 4x3 @cpu(0)>]

Example

y.eval(x=data)

Output

When you execute the above code, you should see the following output −

[
[[ 6. 7. 8.]
[ 0. 1. 2.]
[ 3. 4. 5.]
[ 9. 10. 11.]]
<NDArray 4x3 @cpu(0)>]

In the example below, we are going to draw random samples from a generalized negative binomial distribution. For this will be using the function generalized_negative_binomial().

mx.sym.random.generalized_negative_binomial(10, 0.1)

Output

The output is given below −

<Symbol _random_generalized_negative_binomial0>

symbol.sparse

The Sparse Symbol API is defined in the mxnet.symbol.sparse package. As name implies, it provides sparse neural network graphs and auto-differentiation on CPU.

Functions and their parameters

Following are some of the important functions (includes Symbol creation routines, Symbol Manipulation routines, Mathematical functions, Trigonometric function, Hyberbolic functions, Reduce functions, Rounding, Powers, Neural Network) and their parameters covered by mxnet.symbol.sparse API −

Implementation Example

In the example below, we are going to shuffle the elements randomly using ElementWiseSum() function. It will map integer indices to vector representations i.e. word embeddings.

input_dim = 4
output_dim = 5

Example

/* Here every row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [[ 0., 1., 2., 3., 4.],
[ 5., 6., 7., 8., 9.],
[ 10., 11., 12., 13., 14.],
[ 15., 16., 17., 18., 19.]]
/* Here input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [[ 1., 3.],
[ 0., 2.]]
/* Now, Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.],
[ 15., 16., 17., 18., 19.]],
[[ 0., 1., 2., 3., 4.],
[ 10., 11., 12., 13., 14.]]]