Mathematics of neural networks in machine learning: Difference between revisions

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=== Neuron ===
A neuron with label <math>j</math> receiving an input <math>p_j(t)</math> from predecessor neurons consists of the following components:<ref name="Zell1994ch5.2">{{Cite book|url=http://worldcat.org/oclc/249017987|title=Simulation neuronaler Netze|last=Zell|first=Andreas|date=2003|publisher=Addison-Wesley|isbn=978-3-89319-554-1|edition=1st|language=German|trans-title=Simulation of Neural Networks|chapter=chapter 5.2|oclc=249017987}}</ref>
 
* an ''activation'' <math>a_j(t)</math>, the neuron's state, depending on a discrete time parameter,
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=== Propagation function ===
The ''propagation function'' computes the ''input'' <math>p_j(t)</math> to the neuron <math>j</math> from the outputs <math>o_i(t)</math>and typically has the form<ref name="Zell1994ch5.22">{{Cite book|url=http://worldcat.org/oclc/249017987|title=Simulation neuronaler Netze|last=Zell|first=Andreas|date=2003|publisher=Addison-Wesley|isbn=978-3-89319-554-1|edition=1st|language=German|trans-title=Simulation of Neural Networks|chapter=chapter 5.2|oclc=249017987}}</ref>
 
: <math> p_j(t) = \sum_i o_i(t) w_{ij}. </math>