Why do we need layers in artificial neural network?

Question

I am quite new to artificial neural network, and what I cannot understand is why we need the concept of layer. Isn't is enough to connect each neuron to some other neurons creating a kind of web more then a layered based structure?

For example for solving the XOR we usually need at least 3 layers, 1 input with 2 neurons, 1+ hidden layer(s) with some neurons and 1 output layer with 1 neuron.

Couldn't we create a network with 2 input neurons (we need them) and 1 output connected by a web of other neurons?

Example of what I mean

Answer 1

The term 'layer' is different than you might think. There is always a 'web' of neurons. A layer just denotes a group of neurons.

If I want to connect layer X with layer Y, this means I am connecting all neurons from layer X to all neurons from layer Y. But not always! You could also connect each neuron from layer X to just one neuron in layer Y. There are lots of different connection techniques.

But layers aren't required! It just makes the coding (and explanation) process a whole lot easier. Instead of connecting all neurons one by one, you can connect them in layers. It's far easier to say "layer A and B are connected" than "neuron 1,2,3,4,5 are all connected with neurons 6,7,8,9".

If you are interested in 'layerless' networks, please take a look at Liquid State Machines:

(the neurons might look to be layered, but they aren't!)

PS: I develop a Javascript neural network library, and I have created an onlinedemo in which a neural network evolves to an XOR gate - without layers, just starting with input and output. View it here.. Your example picture is exactly what kind of networks you could develop with this library.