Advanced operations

Introduction to TensorFlow in Python

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

Overview of advanced operations

We have covered basic operations in TensorFlow
- add(), multiply(), matmul(), and reduce_sum()
In this lesson, we explore advanced operations
- gradient(), reshape(), and random()

Overview of advanced operations

Operation	Use
`gradient()`	Computes the slope of a function at a point
`reshape()`	Reshapes a tensor (e.g. 10x10 to 100x1)
`random()`	Populates tensor with entries drawn from a probability distribution

Finding the optimum

In many problems, we will want to find the optimum of a function.
- Minimum: Lowest value of a loss function.
- Maximum: Highest value of objective function.
We can do this using the gradient() operation.
- Optimum: Find a point where gradient = 0.
- Minimum: Change in gradient > 0
- Maximum: Change in gradient < 0

Calculating the gradient

This slide shows a plot of the function y equals x.

Calculating the gradient

This slide shows a plot of the function y equals x squared.

Gradients in TensorFlow

# Import tensorflow under the alias tf
import tensorflow as tf

# Define x
x = tf.Variable(-1.0)

# Define y within instance of GradientTape
with tf.GradientTape() as tape:
    tape.watch(x)
    y = tf.multiply(x, x)

# Evaluate the gradient of y at x = -1
g = tape.gradient(y, x)
print(g.numpy())

-2.0

Images as tensors

The slide shows how an image of two cats can be represented by a 2-dimensional tensor, which can be reshaped into a 1-dimensional vector.

How to reshape a grayscale image

# Import tensorflow as alias tf
import tensorflow as tf

# Generate grayscale image
gray = tf.random.uniform([2, 2], maxval=255, dtype='int32')

# Reshape grayscale image
gray = tf.reshape(gray, [2*2, 1])

The image shows a 2 by 2 grayscale image being reshaped into a 4 by 1 vector.

How to reshape a color image

# Import tensorflow as alias tf
import tensorflow as tf

# Generate color image
color = tf.random.uniform([2, 2, 3], maxval=255, dtype='int32')

# Reshape color image
color = tf.reshape(color, [2*2, 3])

The figure shows a 2 by 2 by 3 color image being reshaped into a 2 by 3 matrix.

Let's practice!

Introduction to TensorFlow in Python