Neural Networks
From DmWiki
A neural network is a paradigm for modelling the behaviour of the human brain. By using a simple approximation of how neurons work, neural networks can be used to implement learning behaviour in computer games.
Simple idea of how it works
A neural network is a nothing but a composite (and in most cases) smooth function from Rm to Rn for some positive integers m,n. The dimension of the input space, m, is in the most straightforward cases the dimension of the parameter space.
As an example, say the current weather conditions can be codified into three real parameters: Temparature, Humidity and Strength of wind. Then a neural network deciding whether a given weather condition is suitable for something (for exampel to go sailing) could represent a smooth function N:R3 - > R. In applications, one would feed the neural network with the given input parameters and depending on the outcome value decide whether one should go sailing or stay at home. The decision could be made, for example, by testing if the outcome was positive or not.
In general, a neural net is roughly a way to subdivide the parameter space into cells and label them by the output of the network. In this way, one could differentiate between different input values.
Training a Neural Network
The composite function above is of course not any composite function. A neural network is in its most basic form the composite of several elementary transition functions, each consisting of a linear transformation followed by a smooth step function.
To train a neural network, one applies an algorithm called back tracking which successively adjusts the transistion functions of the composite, starting with the function closest to the output value, and working backwards.
The simple nature of each transition function allows an effective way of doing back tracking.
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