XOR is considered as
the 'Hello World' of Neural Networks. It seems like the best problem
to try your first TensorFlow program.

Tensorflow makes it
easy to build a neural network with few tweaks. All you have to do is
make a graph and you have a neural network that learns the XOR
function.

Why XOR? Well, XOR
is the reason why backpropogation was invented in the first place. A
single layer perceptron although quite successful in learning the AND
and OR functions, can't learn XOR (Table 1) as it is just a linear
classifier, and XOR is a linearly inseparable pattern (Figure 1).
Thus the single layer perceptron goes into a panic mode while
learning XOR – it can't just do that.

Deep Propogation
algorithm comes for the rescue. It learns an XOR by adding two lines
L1 and L2 (Figure 2). This post assumes you know how the
backpropogation algorithm works.

Following are the
steps to implement the neural network in Figure 3 for XOR in Tensorflow:

1. Import necessary libraries

import
tensorflow as tf

import
math

import
numpy as np

2. Declare the
number of input, hidden and output layer nodes.

INPUT_COUNT
= 2

OUTPUT_COUNT
= 2

HIDDEN_COUNT
= 2

LEARNING_RATE
= 0.4

MAX_STEPS
= 5000

3. Nodes are created
in Tensorflow using placeholders. Placeholders are values that we
will input when we ask Tensorflow to run a computation.

Create inputs x
consisting of a 2d tensor of floating point numbers

```
inputs_placeholder
= tf.placeholder(
```*"float"*,
shape=[None, INPUT_COUNT])

` `

`4. Define weights and biases from input layer to hidden layer`

WEIGHT_HIDDEN
= tf.Variable(tf.truncated_normal([INPUT_COUNT, HIDDEN_COUNT]))

BIAS_HIDDEN
= tf.Variable(tf.zeros([HIDDEN_COUNT]))

A
variable is a value that lives in a Tensorflow's computation graph
that can be

```
modified
by the computation.
```

5.
Define an activation function for the
hidden layer. Here we are using the Sigmoid function, but you can use
other activation functions offered by Tensorflow.

AF_HIDDEN
= tf.nn.sigmoid(tf.matmul(inputs_placeholder, WEIGHT_HIDDEN) +
BIAS_HIDDEN)

6.

```
Define
weights and biases from
```

`hidden`

```
layer to output layer.
```

```
The
biases are initialized with tf.zeros to make sure
```

`they`

```
start with zero values.
```

WEIGHT_OUTPUT
= tf.Variable(tf.truncated_normal([HIDDEN_COUNT, OUTPUT_COUNT]))

BIAS_OUTPUT
= tf.Variable(tf.zeros([OUTPUT_COUNT]))

`7`

```
.
With one line of code we can calculate t
```

```
he
logits tensor that will contain the output that is returned
```

logits
= tf.matmul(AF_HIDDEN, WEIGHT_OUTPUT) + BIAS_OUTPUT

We
then compute the softmax probabilities that are assigned to each
class

y
= tf.nn.softmax(logits)

8.
```
The
```

tf.nn.softmax_cross_entropy_with_logits
op is added to compare the output logits to expected output
cross_entropy
= tf.nn.softmax_cross_entropy_with_logits(logits, y_)

It
then uses tf.reduce_mean to average the cross entropy values across
the batch dimension as the total loss

loss
= tf.reduce_mean(cross_entropy)

The
tensor that will contain the loss value will be returned

9.
Next, we instantiate a tf.train.GradientDescentOptimizer that applies
gradients with the requested learning rate.
Since Tensorflow has access to the
entire computation graph, it can find the gradients of the cost of
all the variables.

train_step
= tf.train.GradientDescentOptimizer(LEARNING_RATE).minimize(loss)

The tensor
containing the outputs of the training step is returned.

10. Next we create
a tf.Session () to run the graph

with
tf.Session() as sess:

We
initialize all the variables before we use them

init
= tf.initialize_all_variables()

Then
we run the session

sess.run(init)

For
every training loop we are going to provide the same input and
expected output data

INPUT_TRAIN
= np.array([[0, 0], [0, 1], [1, 0], [1, 1]])

OUTPUT_TRAIN
= np.array([[1, 0], [0, 1], [0, 1], [1, 0]])

We need to create
a python dictionary object with placeholders as keys and feed
tensors as values

feed_dict
= {
inputs_placeholder: INPUT_TRAIN,

labels_placeholder: OUTPUT_TRAIN,

}

This is passed into the

The following code fetch two values [train_step, loss] in its run
call. Because there are two values to fetch, `sess.run()`

function's `feed_dict`

parameter to
provide the input examples for this step of training.`sess.run()`

returns a tuple with two items. We also print the loss and outputs
every 100 steps.
for
step in xrange(MAX_STEPS)

loss_val
= sess.run([train_step,
loss], feed_dict)

if
step % 100 == 0:

print

*"Step:"*, step,*"loss: "*, loss_val
for input_value in INPUT_TRAIN:

print
input_value, sess.run(y,

feed_dict={inputs_placeholder:
[input_value]})

11. When you run Tensorflow, on the
4900th step you will get a similar output as shown

[0
1] [[ 0.99858057 0.00141946]]

[0
1] [[ 0.00187515 0.9981249]]

[1
0] [[ 0.00128779 0.99871218]]

[1
1] [[ 0.99883229 0.00116773]]

12. The following points should be
noted:

- You will need to experiment with Tensorflow to create an optimized code. Play around with HIDDEN_COUNT, LEARNING_RATE AND MAX_STEPS
- You can use variety of activation functions and increase the number of hidden nodes to make your program efficient and faster.

Wonderful post. Thanks for taking time to share this information with us.

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