Welcome back. In this week, you learned to implement a neural network. Before diving into the technical details, I want in this video, to give you a quick overview of what you'll be seeing in this week's videos. So, if you don't follow all the details in this video, don't worry about it, we'll delve into the technical details in the next few videos. But for now, let's give a quick overview of how you implement in your network. Last week, we had talked about logistic regression, and we saw how this model corresponds to the following computation draft, where you didn't put the features x and parameters w and b that allows you to compute z which is then used to computes a, and we were using a interchangeably with this output y hat and then you can compute the loss function, L. A neural network looks like this. As I'd already previously alluded, you can form a neural network by stacking together a lot of little sigmoid units. Whereas previously, this node corresponds to two steps to calculations. The first is compute the z-value, second is it computes this a value. In this neural network, this stack of notes will correspond to a z-like calculation like this, as well as, an a-like calculation like that. Then, that node will correspond to another z and another a like calculation. So the notation which we will introduce later will look like this. First, we'll inputs the features, x, together with some parameters w and b, and this will allow you to compute z one. So, new notation that we'll introduce is that we'll use superscript square bracket one to refer to quantities associated with this stack of nodes, it's called a layer. Then later, we'll use superscript square bracket two to refer to quantities associated with that node. That's called another layer of the neural network. The superscript square brackets, like we have here, are not to be confused with the superscript round brackets which we use to refer to individual training examples. So, whereas x superscript round bracket I refer to the ith training example, superscript square bracket one and two refer to these different layers; layer one and layer two in this neural network. But so going on, after computing z_1 similar to logistic regression, there'll be a computation to compute a_1, and that's just sigmoid of z_1, and then you compute z_2 using another linear equation and then compute a_2. A_2 is the final output of the neural network and will also be used interchangeably with y-hat. So, I know that was a lot of details but the key intuition to take away is that whereas for logistic regression, we had this z followed by a calculation. In this neural network, here we just do it multiple times, as a z followed by a calculation, and a z followed by a calculation, and then you finally compute the loss at the end. You remember that for logistic regression, we had this backward calculation in order to compute derivatives or as you're computing your d a, d z and so on. So, in the same way, a neural network will end up doing a backward calculation that looks like this in which you end up computing da_2, dz_2, that allows you to compute dw_2, db_2, and so on. This right to left backward calculation that is denoting with the red arrows. So, that gives you a quick overview of what a neural network looks like. It's basically taken logistic regression and repeating it twice. I know there was a lot of new notation laws, new details, don't worry about saving them, follow everything, we'll go into the details most probably in the next few videos. So, let's go on to the next video. We'll start to talk about the neural network representation.
