Where to use tf.GradientTape?

For compute Jacobian Matrix:

tf.GradientTape can compute the Jacobian matrix, which is the matrix of partial derivatives of a vector-valued function. The Jacobian matrix can be used for vector-Jacobian products, which are useful for reverse-mode autodiff. To compute the Jacobian matrix, we can use the tape.jacobian() method. The tape.jacobian() method takes two arguments: the output tensor and the input tensor. It returns the Jacobian tensor, which has the shape of the output tensor concatenated with the shape of the input tensor

For batch Jacobian Matrix:

tf.GradientTape can also compute the batch Jacobian matrix, which is the Jacobian matrix for a batch of outputs and inputs. The batch Jacobian matrix can be used for batch vector-Jacobian products, which are useful for parallelizing autodiff. To compute the batch Jacobian matrix, we can use the tape.batch_jacobian() method. The tape.batch_jacobian() method takes two arguments: the output tensor and the input tensor. It returns the batch Jacobian tensor, which has the shape of the output tensor without the first dimension concatenated with the shape of the input tensor.

For higher-order derivatives:

tf.GradientTape can be nested to compute higher-order derivatives.

For example, we are going to compute the first and second order derivative of the function [Tex]y = x^3[/Tex] with respect ot the input x.

The constant is defined with the value ‘5.0’.
We create a nested with block for two instances of tf.GradientTape. The outer tape is responsible for computing the second-order derivative, while the inner tape computes the first-order derivative. The inner tape block defines the function, and the watch method ensures that the tape tracks the variable ‘x’.
We will compute the first order derivative of y w.r.t. x using the gradient method of inner_tape.
We will exit the inner tape block and move to outer tape block. inside the outer tape, compute the second order derivative of y w.r.t x by again calling gradient method.

Python

import tensorflow as tf
 
x = tf.constant(5.0)
 
with tf.GradientTape() as outer_tape:
    outer_tape.watch(x)
     
    with tf.GradientTape() as inner_tape:
        inner_tape.watch(x)
        y = x **3 #the function is x cube 
     
    dy_dx = inner_tape.gradient(y, x)  # First-order derivative of y with respect to x (dy_dx = 2 * x)
 
d2y_dx2 = outer_tape.gradient(dy_dx, x)  # Second-order derivative of y with respect to x (d2y_dx2 = 2)
 
print("First-order derivative (dy_dx):", dy_dx)
print("Second-order derivative (d2y_dx2):", d2y_dx2)

Output:

First-order derivative (dy_dx): tf.Tensor(75.0, shape=(), dtype=float32)
Second-order derivative (d2y_dx2): tf.Tensor(30.0, shape=(), dtype=float32)

The output of the code is two tensors: dy_dx and d2y_dx2. The values of these tensors depend on the function f(x) and the initial value of x. For f(x) = x**3 and x = 5.0 the output is:

For custom training loops, gradients and layers:

tf.GradientTape can be used for custom training loops, custom gradients, and custom layers. Custom training loops are more flexible and transparent than the built-in tf.keras methods. Custom gradients are useful for modifying or overriding the default gradients of an operation. Custom layers are user-defined layers that can be reused and combined with other layers

Basically, “tf.GradientTape” is a TensorFlow API for automatic differentiation, which means computing the gradient of a computation with respect to some inputs, usually tf.Variable. It is useful for implementing gradient-based optimization algorithms, such as gradient descent or backpropagation.

tf.GradientTape in TensorFlow

TensorFlow is an open-source library for data science and machine learning. It provides various tools and APIs for building, training, and deploying models. One of the core features of TensorFlow is automatic differentiation (autodiff). Autodiff is the process of computing the gradients of a function with respect to its inputs. Gradients are the slopes or rates of change of a function. They are useful for optimizing the parameters of a model, such as weights and biases. TensorFlow provides the tf.GradientTape API for autodiff.