Computing jacobian matrix in Tensorflow

Question

I want to calculate Jacobian matrix by Tensorflow.

What I have:

def compute_grads(fn, vars, data_num):
    grads = []
    for n in range(0, data_num):
        for v in vars:
            grads.append(tf.gradients(tf.slice(fn, [n, 0], [1, 1]), v)[0])
    return tf.reshape(tf.stack(grads), shape=[data_num, -1])

fn is a loss function, vars are all trainable variables, and data_num is a number of data.

But if we increase the number of data, it takes tremendous time to run the function compute_grads. Any ideas?

Answer 1

Assuming that X and Y are Tensorflow tensors and that Y depends on X:

from tensorflow.python.ops.parallel_for.gradients import jacobian
J=jacobian(Y,X)

The result has the shape Y.shape + X.shape and provides the partial derivative of each element of Y with respect to each element of X.

Answer 2

Assuming you are using Tensorflow 2 or Tensorflow <2 and Eager mode, you can use the GradientTape and the inbuild function:

with tf.GradientTape() as g:
  x  = tf.constant([1.0, 2.0])
  g.watch(x)
  y = x * x
jacobian = g.jacobian(y, x)
# jacobian value is [[2., 0.], [0., 4.]]

Check the official documentation for more