Neural Network Basics

Question

I'm a computer science student and for this years project, I need to create and apply a Genetic Algorithm to something. I think Neural Networks would be a good thing to apply it to, but I'm having trouble understanding them. I fully understand the concepts but none of the websites out there really explain the following which is blocking my understanding:

How the decision is made for how many nodes there are. What the nodes actually represent and do. What part the weights and bias actually play in classification.

Could someone please shed some light on this for me?

Also, I'd really appreciate it if you have any similar ideas for what I could apply a GA to.

Thanks very much! :)

Answer 1

Your question is quite complex and I don't think a small answer will fully satisfy you. Let me try, nonetheless.

First of all, there must be at least three layers in your neural network (assuming a simple feedforward one). The first is the input layer and there will be one neuron per input. The third layer is the output one and there will be one neuron per output value (if you are classifying, there might be more than one f you want to assign a "belong to" meaning to each neuron).. The remaining layer is the hidden one, which will stand between the input and output. Determining its size is a complex task as you can see in the following references:

• comp.ai faq
• a post on stack exchange

Nevertheless, the best way to proceed would be for you to state your problem more clearly (as weel as industrial secrecy might allow) and let us think a little more on your context.

Answer 2

The number of input and output nodes is determined by the number of inputs and outputs you have. The number of intermediate nodes is up to you. There is no "right" number.

Imagine a simple network: inputs( age, sex, country, married ) outputs( chance of death this year ). Your network might have a 2 "hidden values", one depending on age and sex, the other depending on country and married. You put weights on each. For example, Hidden1 = age * weight1 + sex * weight2. Hidden2 = country * weight3 + married * weight4. You then make another set of weights, Hidden3 and Hidden4 connecting to the output variable.

Then you get a data from, say the census, and run through your neural network to find out what weights best match the data. You can use genetic algorithms to test different sets of weights. This is useful if you have so many edges you could not try every possible weighting. You need to find good weights without exhaustively trying every possible set of weights, so GA lets you "evolve" a good set of weights.

Then you test your weights on data from a different census to see how well it worked.

Answer 3

The best way to explain an Artificial Neural Network (ANN) is to provide the biological process that it attempts to simulate - a neural network. The best example of one is the human brain. So how does the brain work (highly simplified for CS)?

1. The functional unit (for our purposes) of the brain is the neuron. It is a potential accumulator and "disperser". What that means is that after a certain amount of electric potential (think filling a balloon with air) has been reached, it "fires" (balloon pops). It fires electric signals down any connections it has.

2. How are neurons connected? Synapses. These synapses can have various weights (in real life due to stronger/weaker synapses from thicker/thinner connections). These weights allow a certain amount of a fired signal to pass through.

You thus have a large collection of neurons connected by synapses - the base representation for your ANN. Note that the input/output structures described by the others are an artifact of the type of problem to which ANNs are applied. Theoretically, any neuron can accept input as well. It serves little purpose in computational tasks however.

---

So now on to ANNs.

NEURONS: Neurons in an ANN are very similar to their biological counterpart. They are modeled either as step functions (that signal out "1" after a certain combined input signal, or "0" at all other times), or slightly more sophisticated firing sequences (arctan, sigmoid, etc) that produce a continuous output, though scaled similarly to a step. This is closer to the biological reality.

SYNAPSES: These are extremely simple in ANNs - just weights describing the connections between Neurons. Used simply to weight the neurons that are connected to the current one, but still play a crucial role: synapses are the cause of the network's output. To clarify, the training of an ANN with a set structure and neuron activation function is simply the modification of the synapse weights. That is it. No other change is made in going from a a "dumb" net to one that produces accurate results.

STRUCTURE: There is no "correct" structure for a neural network. The structures are either a) chosen by hand, or b) allowed to grow as a result of learning algorithms (a la Cascade-Correlation Networks).

Assuming the hand-picked structure, these are actually chosen through careful analysis of the problem and expected solution. Too few "hidden" neurons/layers, and you structure is not complex enough to approximate a complex function. Too many, and your training time rapidly grows unwieldy. For this reason, the selection of inputs ("features") and the structure of a neural net are, IMO, 99% of the problem. The training and usage of ANNs is trivial in comparison.

---

To now address your GA concern, it is one of many, many efforts used to train the network by modifying the synapse weights. Why? because in the end, a neural network's output is simply an extremely high-order surface in N dimensions. ANY surface optimization technique can be use to solve the weights, and GA are one such technique. The simple backpropagation method is alikened to a dimension-reduced gradient-based optimization technique.

Answer 4

... my major barrier to understanding this though is understanding how the hidden layer actually works; I don't really understand how a neuron functions and what the weights are for...

Every node in the middle layer is a "feature detector" -- it will (hopefully) "light up" (i.e., be strongly activated) in response to some important feature in the input. The weights are what emphasize an aspect of the previous layer; that is, the set of input weights to a neuron correspond to what nodes in the previous layer are important for that feature.

If a weight connecting myInputNode to myMiddleLayerNode is 0, then you can tell that myInputNode is not important to whatever feature myMiddleLayerNode is detecting. If, though, the weight connecting myInputNode to myMiddleLayerNode is very large (either positive or negative), you know that myInputNode is quite important (if it's very negative it means "No, this feature is almost certainly not there", while if it's very positive it means "Yes, this feature is almost certainly there").

So a corollary of this is that you want the number of your middle-layer nodes to have a correspondence to how many features are needed to classify the input: too few middle-layer nodes and it will be hard to converge during training (since every middle-layer node will have to "double up" on its feature-detection) while too many middle-layer nodes may over-fit your data.

So... a possible use of a genetic algorithm would be to design the architecture of your network! That is, use a GA to set the number of middle-layer nodes and initial weights. Some instances of the population will converge faster and be more robust -- these could be selected for future generations. (Personally, I've never felt this was a great use of GAs since I think it's often faster just to trial-and-error your way into a decent NN architecture, but using GAs this way is not uncommon.)

Answer 5

You might find this wikipedia page on NeuroEvolution of Augmenting Topologies (NEAT) interesting. NEAT is one example of applying genetic algorithms to create the neural network topology.