使用TensorFlow改变梯度

Question

I am new to TensorFlow, and I am struggling a bit with the following: Given and , I would like to compute .

I understand how to compute the gradient without the shift, and how I can numerically evaluate the gradient with the shift, but I do not see how to compute symbolically.

import tensorflow as tf

x = tf.placeholder(tf.float32)
f = (x + 1.0)**2
s = tf.constant(1.0, tf.float32)

# Gradient of f(.)
grad_f = tf.gradients(f, x)[0]

# Gradient of f(. + s)
grad_f_shifted = ?

Note that I do not know the definition of , so I cannot simply define

f_shifted = (x + s + 1.0)**2

or at least I do not know how.

Answer 1

I think I found a solution: My goal was to compute the term , and I tried to compute it symbolically and then evaluate . However, after looking at my problem again, I realized that I only need the value of for a specific and not as a function of . Hence, I can compute in the following way:

x = tf.Variable(0.0, tf.float32)
f = (x + 1.0)**2.0
grad_f = tf.gradients(f, x)[0]
y = tf.Variable(0.0, tf.float32)
x0 = tf.constant(1.0, tf.float32)
s = tf.constant(1.0, tf.float32)

tensors = []
tensors.append(tf.assign(x, x0))
tensors.append(tf.assign(y, -grad_f))
tensors.append(tf.assign(x, x0 + s))
# Coming from a numerical background, the line below confused me a bit,
# because the dependency of grad_f on x is not "visible" in the code.
tensors.append(tf.assign_add(y, grad_f))

with tf.Session():
  for t in tensors:
    t.eval()