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)
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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)
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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)