====== Neural Networks ======

//Lecture on 15.11.2007//

{{networks:neural_networks.ppt|Presentation}}

===== Neuron Activation =====
  * Many neuron axons are attached to another neuron
  * Neuron “sums” the activation of all inputs
  * If the input is above a threshold, the neuron fires

{{networks:nn_activation1.png|}}

===== Perceptrons =====
  * Sum of inputs*weights, threshold function
  * could learn AND & OR but NOT XOR
  * Only linearly separable functions

===== Multi-layer NNs ====
  * Add a ‘hidden’ layer!
  * Can solve any “reasonable” function (given enough nodes in the hidden layer)
  * But how to train? This stopped research for ~30 years

{{networks:middel_layer.png|}}

==== Back-propagation ====
  * Paul Werbos in 1974, further developed in 1986
  * Requires threshold function to be differentiable
  * Error is ‘propagated’ backwards through the network - units that affected the output the most change more

=== Threshold Function ===
  * Often the logistic sigmoid, but also tanh and others
  * Easily differentiable
{{networks:sigmoid.png|}}
=== Algorithm ===
  - Randomize weights
  - For each example e in training set
    - “Activate” network: O = net(e); T = ‘correct’ output, error = (T - O)
    - Calculate delta for each weight from hidden to output
    - Calculate delta for each weight from input to hidden
  - Update weights by delta
  - Goto 2 unless error low enough

So for each example in your training set you make a **//Forward-Pass//** and let the net calculate the output. As second step you **//determine the error//** for each example. If the errors are under a certain threshold you can stop the training otherwise you continue with step 3. The next step is the **//Backward-Pass//** which is the innovative part. You give the error rate backwards through the neural network and so adjust the threshold-functions to a new level. You do this as long as your error rate is to high. But be careful and do not overtrain your net so it will just recognize specific things.

=== Batch vs. Online Learning ===
When updating the weights after calculating the delta for the entire training set, we call it **//batch learning//**.

If the weights are adjusted after each example this is called //**online learning**//.
== Advantages of online learning ==
  * often faster
  * can be used when there is no fixed training set
  * can be uses in nonstatic environments

== Disadvantages of online learning ==
  * can stuck on local minima and not finding the global minimum
  * no natural plausibility

=== Learning Rate ===
The Question is how fast do we move towards the error minimum?

  * if we move to **slow** we'll never reach the minimum
  * if we move to **fast** we'll bounce around

  * solution: trail and error
    * good first guess: 1 / √(set size)

===== Implementations =====

{{networks:nn.zip|Neural network implementation in C++ by Kennon Ballou}}





===== Links =====
   * [[http://www.neuronalesnetz.de/ | very good German Page about NN]]

   * [[http://www.generation5.org/content/2004/
RealtimeEvolutionAgents.asp | Neuro Invaders]]