i cannot understand what does this “i” mean in this slides. And what does the \theta_1 \theta_2 means in this formular?

In order to implement Gradient Checking, they “unroll” all the parameters (all the W and b values) into a single vector which they call *theta*. Then they step through that vector and perturb each element individually to compute the “finite difference” approximations of the gradients.

Thank you very much! Now i understood how grad check works.

However, as you said, the single \theta, that without any subscript numbers, are the combine of all the parameters that is W and b. But my questions is, if we unroll the single \theta, we should have a lot of W and b of different layers instead of such a lot “\theta_1” “\theta_2” with subscript numbers. So what should “\theta_1” means, that is, for example, **\theta_1 = ?**

In the mean time, i should be what? that is, **the range in the for loop above is from 1 to what ?**

Thank you very much if you could answer my 2 questions above!

The elements of theta are the unrolled elements of all the W and b values for all the layers. So the index steps through those elements in order. The total number will be the sum total of the number of elements in all the W and b values for all the layers of the network. See the routines *dictionary_to_vector* and *gradients_to_vector* and take a look to see how they work if you want to understand this at the next deeper level.

Thanks a lot! And after i finish the exercise i finally got it!