I've Googled, StackOverflowed, everything, and I cannot seem to find a tutorial I can understand. I understand the concept of genetic algorithms, and how to implement them, (Though I haven't tried) but I cannot grasp the concept of neural networks.
I know vaguely how they work... And that's about it. Could someone give an explanation that can help someone who has not even graduated middle school yet?
Summation is just adding up a bunch of things. So,
Summation(1,2,3,4,5) = 1+2+3+4+5 = 15
(note: it's always adding: if you want to subtract, do a summation with negative numbers)
That was easy, right? ;)
A vector is an ordered tuple, which really just means it's bunch of numbers in a specific order. Most often seen in physics to describe position, force, velocity, etc... it's really nothing special, just some ordered numbers, where the ordering is significant:
v = <1,2,3>
If we are talking about geometry, then this vector represents a point in 3-dimensional space where the x coordinate is 1, the y coordinate is 2, and the z coordinate is 3 (See that was easy too, right)?
In neural nets, the vector is usually the vector of inputs to a neuron, so it's really just a list of numeric values. The summation of the vector would be nothing more than adding up all of the values in the vector and getting a single number as a result (which may be referred to as as "scalar" value).
(this was rushed and simplified - I'm sure someone else will help me refine it ;) )
PS. Kudos to you for diving into this stuff at the middle school level! :)