Can I get the gradient of a tensor with respect to the input without applying the input?

Question

For example, I need to compute the gradient of the cross_entropy with respect to x, but I need to apply another value to the gradient function.

That is:

f'(x)|x = x_t

I think tf.gradients() function will only give the gradient at x = x. So does tensorflow provide any of this feature?

Answer 1

The result of tf.gradients is a tensor (list of tensors in general), not a float value. In a way, this tensor is a function: it can be evaluated in any point. The client only needs to feed the desired input value.

Example:

features = 3
n_samples = 10
hidden = 1

X = tf.placeholder(dtype=tf.float32, shape=[n_samples, features])
Y = tf.placeholder(dtype=tf.float32, shape=[n_samples])

W = tf.Variable(np.ones([features, hidden]), dtype=tf.float32, name="weight")
b = tf.Variable(np.ones([hidden]), dtype=tf.float32, name="bias")

pred = tf.add(tf.matmul(X, W), b)
cost = tf.reduce_mean(tf.pow(pred - Y, 2))

dc_dw, dc_db = tf.gradients(cost, [W, b])

session.run(tf.global_variables_initializer())

# Let's compute `dc_dw` at `ones` matrix.
print(dc_dw.eval(feed_dict={X: np.ones([n_samples, features]), 
                            Y: np.ones([n_samples])}))