TensorFlow is open-source Python library designed by Google to develop Machine Learning models and deep learning neural networks.
batch_jacobian() is used to compute and stack the per example jacobian.
Syntax: batch_jacobian( target, source, unconnected_gradients, parallel_iterations, experimental_use_pfor )
Parameters:
- target: It is a Tensor having minimum rank 2.
- source: It is a Tensor having minimum rank 2.
- unconnected_gradients(optional): It’s value can either be zero or None. Default value is None.
- parallel_iterations(optional): It is used to control parallel iterations and memory usage.
- experimental_use_pfor(optional): It is a boolean with default value True. It uses pfor to calculate jacobian when set to true otherwise tf.while_loop is used.
Returns: It returns a Tensor.
Example 1:
Python3
# Importing the library import tensorflow as tf x = tf.constant([[4, 2],[1, 3]], dtype=tf.dtypes.float32) # Using GradientTape with tf.GradientTape() as gfg: gfg.watch(x) y = x * x * x # Computing jacobian res = gfg.batch_jacobian(y, x) # Printing result print("res: ",res) |
Output:
res: tf.Tensor( [[[48. 0.] [ 0. 12.]] [[ 3. 0.] [ 0. 27.]]], shape=(2, 2, 2), dtype=float32)
Example 2:
Python3
# Importing the library import tensorflow as tf x = tf.constant([[4, 2],[1, 3]], dtype=tf.dtypes.float32) # Using GradientTape with tf.GradientTape() as gfg: gfg.watch(x) # Using nested GradientTape for calculating higher order jacobian with tf.GradientTape() as gg: gg.watch(x) y = x * x * x # Computing first order jacobian first_order = gg.batch_jacobian(y, x) # Computing Second order jacobian second_order = gfg.batch_jacobian(first_order, x) # Printing result print("first_order: ",first_order) print("second_order: ",second_order) |
Output:
first_order: tf.Tensor( [[[48. 0.] [ 0. 12.]] [[ 3. 0.] [ 0. 27.]]], shape=(2, 2, 2), dtype=float32) second_order: tf.Tensor( [[[[24. 0.] [ 0. 0.]] [[ 0. 0.] [ 0. 12.]]] [[[ 6. 0.] [ 0. 0.]] [[ 0. 0.] [ 0. 18.]]]], shape=(2, 2, 2, 2), dtype=float32)
