Gradient Descent with Tensorflow-GradientTape()

TensorFlow’s GradientTape API is used to record operations for automatic differentiation. It allows developers to compute the gradients of a target tensor with respect to one or more input tensors, which can then be used to optimize the parameters of a model using gradient descent.

Implementation:

Here is an example of how to use GradientTape() to compute gradients and optimize a model:

import tensorflow as tf
# Define the model
x = tf.constant(3.0)
with tf.GradientTape() as tape:
    tape.watch(x) 
    y = x ** 2
dy_dx = tape.gradient(y, x)
print(dy_dx)

In this example, we defined a simple model with a single variable x and a quadratic loss function y. We used GradientTape() to record the operations for automatic differentiation and then computed the gradients of the loss function with respect to x. Finally, we used the optimizer to update the value of x using the computed gradients.

To deploy a second order derivative with GradientTape() in TensorFlow, you can use the following code:

x = tf.constant(4.0)
with tf.GradientTape() as t2:
    t2.watch(x)
    with tf.GradientTape() as t:
        t.watch(x)
        y = x ** 3
    dy_dx = t.gradient(y, x)
d2y_dx = t2.gradient(dy_dx, x)
print(d2y_dx)