The sigmoid function, G of

So that's what the sigmoid function looks like.

Lastly, let me show you where the sigmoid function looks like.

E to the negative Z. This called the sigmoid function or the logistic function.

And then this second hidden unit has this activation value computed as sigmoid of this.

And you notice that the sigmoid function, well, it asymptotes at one, and asymptotes at zero as

And, by the way, the terms sigmoid function and logistic function are basically synonyms and mean the same thing.

So here, g as usual is the sigmoid function, and we can include lots of polynomial terms like these.

This first hidden unit here, has its value computed as follows is a a(2)1 is equal to the sigmoid function, or the sigmoid activation function also called the logistic activation function, applied to this sort of linear combination of its inputs.

So, in logistic regression we have our familiar form of the hypotheses there and the sigmoid activation function shown on the right.

Finally, one last bit of terminology when we talk about neural networks, sometimes we'll say that this is a neuron an artificial neuron with a sigmoid or a logistic activation function.

So, I'm going to set that to x and then we're going to compute z(2) equals theta(1) a(1) and a(2) equals g, the sigmoid activation function applied to z(2) and this would give us our activations for the first middle layer.

But many years ago, we took the worst land in Zimbabwe, where I offered a 5 note in a hundred mile drive if somebody could find one grass in a hundred mile drive, and on that, we trebled the stocking rate, the number of animals, in the first year with no feeding, just by the movement, mimicking nature, and using a sigmoid curve, that principle.