Intuition behind neural networks

Question

I'm really interested in understanding the intuition behind multilayer perceptrons and neural networks.

I'm following the Caltech video which is excellent https://www.youtube.com/watch?v=Ih5Mr93E-2c

More specifically it goes through an example at 30 mins in where a circle classifier is approximated by intersections of straight lines. More specifically consider the lines

$l1: y-x=1$, $l2: y-x=-1$, $l3: y+x=1$, and $l4: y+x=-1$

Now suppose that i split each space into 2 depending on whether a co-ordinate point is above the line or not call these regions $h_{i}$ and $\overline{h}_{i}$ respectively. Then i know i want to classify positive if i'm in the square intersection of all 4-lines and so if the variable

$\overline{h}_{1}h_{2}\overline{h}_{3}h_{4}$ evaluates to true. They didn't go through this in the lecture but how would i represent this in a neural network like they did at around 27 mins in for the XOR problem?

Any help would be appreciated i really want to try and get a feel for breaking these problems down.

Answer 1

Okay, It's been a long time since I tried to build neural network on paper, but I think it would look something like this: (the red lines have negative weight, the blue ones positive, the threshold-neurons take the inputs and output zero if the sum is 0 or less and 1 if it's positive)