In [16]:
import tensorflow as tf
hello = tf.constant('Hello, TensorFlow!')
sess = tf.Session()

b'Hello, TensorFlow!'

The Computational Graph

You might think of TensorFlow Core programs as consisting of two discrete sections:

Building the computational graph. Running the computational graph. A computational graph is a series of TensorFlow operations arranged into a graph of nodes. Let's build a simple computational graph. Each node takes zero or more tensors as inputs and produces a tensor as an output. One type of node is a constant. Like all TensorFlow constants, it takes no inputs, and it outputs a value it stores internally. We can create two floating point Tensors node1 and node2 as follows:

In [17]:
node1 = tf.constant(3.0, tf.float32)
node2 = tf.constant(4.0) # also tf.float32 implicitly
print(node1, node2)

Tensor("Const_6:0", shape=(), dtype=float32) Tensor("Const_7:0", shape=(), dtype=float32)

Notice that printing the nodes does not output the values 3.0 and 4.0 as you might expect. Instead, they are nodes that, when evaluated, would produce 3.0 and 4.0, respectively. To actually evaluate the nodes, we must run the computational graph within a session. A session encapsulates the control and state of the TensorFlow runtime.

The following code creates a Session object and then invokes its run method to run enough of the computational graph to evaluate node1 and node2. By running the computational graph in a session as follows:

In [18]:
sess = tf.Session()
print([node1, node2]))

[3.0, 4.0]

We can build more complicated computations by combining Tensor nodes with operations (Operations are also nodes.). For example, we can add our two constant nodes and produce a new graph as follows:

In [19]:
node3 = tf.add(node1, node2)
print("node3: ", node3)
print(" ",

node3:  Tensor("Add_1:0", shape=(), dtype=float32)  7.0

TensorFlow provides a utility called TensorBoard that can display a picture of the computational graph. Here is a screenshot showing how TensorBoard visualizes the graph As it stands, this graph is not especially interesting because it always produces a constant result. A graph can be parameterized to accept external inputs, known as placeholders. A placeholder is a promise to provide a value later.

In [20]:
a = tf.placeholder(tf.float32)
b = tf.placeholder(tf.float32)
adder_node = a + b  # + provides a shortcut for tf.add(a, b)

The preceding three lines are a bit like a function or a lambda in which we define two input parameters (a and b) and then an operation on them. We can evaluate this graph with multiple inputs by using the feed_dict parameter to specify Tensors that provide concrete values to these placeholders:

In [21]:
print(, {a: 3, b:4.5}))
print(, {a: [1,3], b: [2, 4]}))

[ 3.  7.]

In TensorBoard, the graph looks like this: We can make the computational graph more complex by adding another operation. For example,

In [7]:
add_and_triple = adder_node * 3.
print(, {a: 3, b:4.5}))


The preceding computational graph would look as follows in TensorBoard: In machine learning we will typically want a model that can take arbitrary inputs, such as the one above. To make the model trainable, we need to be able to modify the graph to get new outputs with the same input. Variables allow us to add trainable parameters to a graph. They are constructed with a type and initial value:

In [23]:
W = tf.Variable([.3], tf.float32)
b = tf.Variable([-.3], tf.float32)
x = tf.placeholder(tf.float32)
linear_model = W * x + b

Constants are initialized when you call tf.constant, and their value can never change. By contrast, variables are not initialized when you call tf.Variable. To initialize all the variables in a TensorFlow program, you must explicitly call a special operation as follows:

In [24]:
init = tf.global_variables_initializer()

It is important to realize init is a handle to the TensorFlow sub-graph that initializes all the global variables. Until we call, the variables are uninitialized.

Since x is a placeholder, we can evaluate linear_model for several values of x simultaneously as follows:

In [10]:
print(, {x:[1,2,3,4]}))

[ 0.          0.30000001  0.60000002  0.90000004]

We've created a model, but we don't know how good it is yet. To evaluate the model on training data, we need a y placeholder to provide the desired values, and we need to write a loss function.

A loss function measures how far apart the current model is from the provided data. We'll use a standard loss model for linear regression, which sums the squares of the deltas between the current model and the provided data. linear_model - y creates a vector where each element is the corresponding example's error delta. We call tf.square to square that error. Then, we sum all the squared errors to create a single scalar that abstracts the error of all examples using tf.reduce_sum:

In [25]:
y = tf.placeholder(tf.float32)
squared_deltas = tf.square(linear_model - y)
loss = tf.reduce_sum(squared_deltas)
print(, {x:[1,2,3,4], y:[0,-1,-2,-3]}))


We could improve this manually by reassigning the values of W and b to the perfect values of -1 and 1. A variable is initialized to the value provided to tf.Variable but can be changed using operations like tf.assign. For example, W=-1 and b=1 are the optimal parameters for our model. We can change W and b accordingly:

In [13]:
fixW = tf.assign(W, [-1.])
fixb = tf.assign(b, [1.])[fixW, fixb])
print(, {x:[1,2,3,4], y:[0,-1,-2,-3]}))


We guessed the "perfect" values of W and b, but the whole point of machine learning is to find the correct model parameters automatically. We will show how to accomplish this in the next section.

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