Neural Network: Remove confusions

I was really in a dillema on how to design an ANN. I know enough theory (at least gained by browsing and everything) but all of them where how it functions and how the structure is done. But none on how can I specifically design a NN for a specific function. At last, I found a quite good post (tutorial) which is written is really simple language and may help you.

http://www.ai-junkie.com/ann/evolved/nnt1.html

Just some confusions that I have removed while reading this tutorial are:

When do we need a hidden layer?
We need a hidden layer whenever out output space is not linear (like the XOR function). Simple, eh!!

Just how many input nodes do I need?
Input nodes depend on the number of different data you have to feed to the neural net. If you have a matrix of 9 cells and need to feed the matrix to the NN then you will need 9 input nodes. But it is also possible to feed the input as binary combinations. If I want to feed a specific locaiton to the NN from a set of 64 locations then probably a input set of 6 nodes will be enough (2^6 = 64).

How can we get the output?
The output is provided by the output layer of neurons. At each neuron there is a activation function, which takes the weighted sum of inputs and produces an output. This output can be binary, in case of a threshold activation function, or it can be continuous, in case of a sigmoid function.

What is a Bias?
As we know, for a simple Neuron the input is the summation of the input values multiplied by the weight and the output depends on whether this summation is greater than the threshold or not. That is:
x1w1 + x2w2 + ...... + xnwn >= t
If we bring the threshold value on the LHS then the equation becomes:
x1w1 + x2w2 + ...... + xnwn - t >= 0
=>x1w1 + x2w2 + ...... + xnwn + (-1)t >= 0
So, as we can see we can treat t also as an input and its weight is always -1. In this way, the threshold value will also evolve with the network and we dont have to think about it. Another advantage is that even if all the inputs are zero, because of the bias value (t) the output will be something, it will not be zero forever.

How does the NN learn or adapt?
The learning is based on the difference between the actual output and the output of the NN. This error is fed to the layers to correct the weight of the input so that the new output of the node is better than the previous one.
Learning can be done by various methods. Two of them are backpropagation and Genetic algorithm. When using backpropagation the error amount is fed back to the layers of the NN so that the weights and the bias of that layer is modified accordingly.

How can we decide on the number of neurons in the layers?
This is what seemed the most perplexing thing while designing a NN. Its natural that the input and output would be directly proportional to the number of input and the number of output we need, but what about the hidden layer? How many hidden layers do we need and how many neurons per hidden layer?
Well, it seems that one hidded layer is what we need. Almost all the jobs can be done using one hidded layer. And in case of number of neurons, I dont know :) They say that you are going to build a feel of it. There are no hard and fast rule of this. Too few neurons will make your result scratchy. And too many will take longer time and rather fune tune to the training data too much. That means, networks with too many neurons will also adapt to the noise data so much that it will be difficul to generalize it. An excellent resource would be:

http://www.dtreg.com/mlfn.htm

ANN with Genetic Algorithm:
If ANN is used with GA then the learning process is done by GA. The initial weight is fed to the GA along with the fitness function of each member of population. The neural network will evaluate the output of the network and increate or decrease the fitness value of the cromosome accordingly. After some time a new generation is created and the GA is called. The GA will then decide according to the fitness value and generate a new generation. The new generation of population with the new weights are then again fed to the neural nework and the loop continues.

For a Good introduction please refer to:
http://www.ai-junkie.com/ann/evolved/nnt1.html