如何使用tensorflow逼近hessian矩阵的范数

Question

I wonder is there any method to recompute gradients with updated weights within a graph or if there is any better way to do this. For example, for estimating hessian norm, we need to compute

delta ~ N(0, I)
hessian_norm = 1/M \sum_{1}^{M} gradient(f(x+delta))- gradient(f(x-delta))/(2*delta)

we need to gradient value on x+delta . Currently we will get None type if we use tf.gradient on var+delta directly.

More specifally speaking, if we define

a = tf.Variable
b = some_function(a)
grad = tf.gradients(b, a) 

that's a normal gradient computation but if we do

grad_delta = tf.gradients(b, a+delta) 

it will return None . This feature seems to make it impossible to approximate the hessian norm using the above method.

Answer 1

b is not a function of a+delta , so you get None s. You either need to create new value b2 which depends on a+delta , or just move your a variable by delta and eval again to get second value.

This is similar to how you do line search in TensorFlow .