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Artificial Neural Networks

MA4J5 Structures of Complex systems

Michal Tadeusiak

on 3 March 2013

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Transcript of Artificial Neural Networks

Artificial Neural Networks Michał Tadeusiak Introduction: The human brain computes in entirely different way from the conventional digital computers. - the computation is massively distributed and parallel
- learning replaces a priori program development "An artificial neural network is a mathematical model inspired by biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation" The human brain Brain consists of about 10 of neurons, each connected, on average, to 10 others.

Neuron activity is excited or inhibited through connections to other neurons.

The fastest neuron switching times are known to be on the order of 10 seconds
(your laptop: 10 seconds). 4 Artificial neural network key aspects single neuron model receives one or more inputs (dendrites)
sums them to produce an output (axon) topology learning feedforward, multilayered, recurrent Hebbs rule error-correction learning Examples Hopfield network,
Hebbs rule perceptron,
backpropagation highly complex, nonlinear
and parallel computer It has a capability to organize neurons, so as to perform certain computations, e.g. pattern recognition, perception, motor control, many times faster than the fastest digital computers. It requires approximately 0.1 seconds to visually recognize your mothers! 11 -3 Neurons receive signals through dendrites - thin structures that arise from the cell body, often extending for hundreds of micrometres and branching multiple times axon is a special cellular extension that arises from the cell body and travels for a distance, as far as 1 meter. cell body, or soma, when activated by series of action potentials, fires spikes - transmits the information synaptic weights activation function McCulloch-Pitts
neuron model
(1943) Activation function threshold function picewise-linear sigmoid "Learning is a process by which the free parameters of a neural network are adapted through a process of stimulation by the environment in which the network is embedded. The type of learning is determined by the manner in which the parameter changes take place." backpropagation: http://galaxy.agh.edu.pl/~vlsi/AI/backp_t_en/backprop.html Hebb's rule is the oldest (1949) and most famous of all learning rules If two neurons on either side of a synapse (connection) are activated simultaneously, then the strength of that synapse is selectively increased.
If they are activated asynchronously, then that synapse is selectively weakened an example: Hopfield network energy function: learning: patterns: Now we check if pattern
is learned the same signs!
pattern is remembered References: Tom Mitchell "Machine Learning"
Simon Haykin "Neural Networks: a Comprehensive Foundation"
Robert J. Schalkoff "Artificial Neural Networks"
Robert Kosiński "Sztuczne Sieci Neuronowe – Dynamika Nieliniowa i Chaos" ("Artificial neural networks – nonlinear dynamics and chaos") Thank you for your attention! i ≠ j = 0 i = j -11 Recognizing b&w digits
of size 16 x 16 pixels Hopfield network of 256 neurons 256
neurons 16
neurons 10
neurons http://www.codeproject.com/Articles/13582/Back-propagation-Neural-Net based on C++ code by Tejpal Singh Chhabra: S = {-1,1} i
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