0
$\begingroup$

I am working through a description of gradient descent and I'm having trouble finding the definition of a couple notations, an arrow and a single quote, v→v′=v−η∇C. I normally express a derivative with a single quote f'(x) but that doesn't appear to be the case here.

The source of this equation is here http://neuralnetworksanddeeplearning.com/chap1.html, about 3/4 of the way down.

Thanks

$\endgroup$
1
$\begingroup$

$$\begin{eqnarray} v \rightarrow v' = v-\eta \nabla C. \tag{15}\end{eqnarray}$$

is a function which maps the velocity to the derivative of the velocity:

This gives us a way of following the gradient to a minimum, even when C is a function of many variables, by repeatedly applying the update rule $$\begin{eqnarray} v \rightarrow v' = v-\eta \nabla C. \tag{15}\end{eqnarray}$$ You can think of this update rule as defining the gradient descent algorithm. It gives us a way of repeatedly changing the position vv in order to find a minimum of the function C.

$\endgroup$
  • $\begingroup$ Could I say the right side of the equation is the function that maps v to v prime with → a notion for mapping? $\endgroup$ – Half_Duplex Jun 10 '16 at 14:52
1
$\begingroup$

It might be read as $v$ tends to $v'$ (v-prime) which is equal to $v$ minus $\eta$ times $\nabla C$.

v-prime, written as $v'$ in the expression is another variable which has something to do with the perturbation $\Delta_{V}$ defined in the link you gave. $\Delta_{V} = v - v'$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.