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Introduction and a historical review

Neural network concepts

Basic models of ANN

Linearly separable functions

Non Linearly separable functions

NN Learning techniques

Associative networks

Mapping networks

Spatiotemporal Network

Stochastic Networks

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- 1. Neural Networks Dr. Randa Elanwar Lecture 2
- 2. Lecture Content • Neural network concepts: – Basic definition. – Connections. – Processing elements. 2Neural Networks Dr. Randa Elanwar
- 3. Artificial Neural Network: Structure • ANN posses a large number of processing elements called nodes/neurons which operate in parallel. • Neurons are connected with others by connection link. • Each link is associated with weights which contain information about the input signal. • Each neuron has an internal state of its own which is a function of the inputs that neuron receives- Activation level 3Neural Networks Dr. Randa Elanwar
- 4. Artificial Neural Network: Neuron Model (dendrite) (axon) (soma) 4Neural Networks Dr. Randa Elanwar f() Y Wa Wb Wc Connection weights Summing function Computation (Activation Function) X1 X3 X2 Input units
- 5. How are neural networks being used in solving problems • From experience: examples / training data • Strength of connection between the neurons is stored as a weight-value for the specific connection. • Learning the solution to a problem = changing the connection weights 5Neural Networks Dr. Randa Elanwar
- 6. How are neural networks being used in solving problems • The problem variables are mainly: inputs, weights and outputs • Examples (training data) represent a solved problem. i.e. Both the inputs and outputs are known • Thus, by certain learning algorithm we can adapt/adjust the NN weights using the known inputs and outputs of training data • For a new problem, we now have the inputs and the weights, therefore, we can easily get the outputs. 6Neural Networks Dr. Randa Elanwar
- 7. How NN learns a task: Issues to be discussed - Initializing the weights. - Use of a learning algorithm. - Set of training examples. - Encode the examples as inputs. -Convert output into meaningful results. 7Neural Networks Dr. Randa Elanwar
- 8. Linear Problems • The simplest type of problems are the linear problems. • Why ‘linear’? Because we can model the problem by a straight line equation (ax+by+c=z) • or • Example: logic linear problems And, OR, NOT problems. We know the truth tables thus we have examples and we can model the operation using a neuron 8Neural Networks Dr. Randa Elanwar bout k i ii inw 1 . outbinwinwinw ...... 332211 bXWOUT .
- 9. Linear Problems • Example: AND (x1,x2), f(net) = 1 if net>1 and 0 otherwise • Check the truth table: y = f(x1+x2) 9Neural Networks Dr. Randa Elanwar x1 x2 y 0 0 0 0 1 0 1 0 0 1 1 1 x1 x2 y 1 1
- 10. Linear Problems • Example: OR(x1,x2), f(net) = 1 if net>1 and 0 otherwise • Check the truth table: y = f(2.x1+2.x2) 10Neural Networks Dr. Randa Elanwar x1 x2 y 0 0 0 0 1 1 1 0 1 1 1 1 x1 x2 y 2 2
- 11. Linear Problems • Example: NOT(x1), f(net) = 1 if net>1 and 0 otherwise • Check the truth table: y = f(-1.x1+2) 11Neural Networks Dr. Randa Elanwar x1 y 0 1 1 0 x1 y -1 2 bias 1
- 12. Linear Problems • Example: AND (x1,NOT(x2)), f(net) = 1 if net>1 and 0 otherwise • Check the truth table: y = f(2.x1-x2) 12Neural Networks Dr. Randa Elanwar x1 x2 y 0 0 0 0 1 0 1 0 1 1 1 0 x1 x2 y 2 -1
- 13. Neural Networks Dr. Randa Elanwar 13 The McCulloch-Pitts Neuron • This vastly simplified model of real neurons is also known as a Threshold Logic Unit – A set of connections brings in activations from other neurons. – A processing unit sums the inputs, and then applies a non-linear activation function (i.e. squashing/transfer/threshold function). – An output line transmits the result to other neurons. ).( 1 bfout n i ii inw f(.) w1 w2 wn b ).( bXWfOUT
- 14. McCulloch-Pitts Neuron Model Neural Networks Dr. Randa Elanwar 14
- 15. Features of McCulloch-Pitts model • Allows binary 0,1 states only • Operates under a discrete-time assumption • Weights and the neurons’ thresholds are fixed in the model and no interaction among network neurons • Just a primitive model Neural Networks Dr. Randa Elanwar 15
- 16. McCulloch-Pitts Neuron Model • When T = 1 and w = 1 • The input passes as is • Thus if input is =1 then o = 1 • Thus if input is =0 then o = 0 (buffer) • Works as ‘1’ detector • When T = 1 and w = -1 • The input is inverted • Thus if input is =0 then o = 0 • Thus if input is =1 then o = 0 • useless 16Neural Networks Dr. Randa Elanwar
- 17. McCulloch-Pitts Neuron Model • When T = 0 and w = 1 • The input passes as is • Thus if input is =0 then o = 1 • Thus if input is =1 then o = 1 • useless • When T = 0 and w = -1 • The input is inverted • Thus if input is =1 then o = 0 • Thus if input is =0 then o = 1 (inverter) • Works as Null detector 17Neural Networks Dr. Randa Elanwar
- 18. McCulloch-Pitts NOR 18Neural Networks Dr. Randa Elanwar •Can be implemented using an OR gate design followed by inverter •We need ‘1’ detector, thus first layer is (T=1) node preceded by +1 weights Zeros stay 0 and Ones stay 1 •We need inverter in the second layer, (T=0) node preceded by -1 weights •Check the truth table
- 19. McCulloch-Pitts NAND 19Neural Networks Dr. Randa Elanwar •Can be implemented using an inverter design followed by OR gate •We need inverter in the first layer is (T=0) node preceded by -1 weights Zeros will be 1 and Ones will be zeros •We need ‘1’ detector, thus first layer is (T=1) node preceded by +1 weights Zeros stay 0 and Ones stay 1
- 20. General symbol of neuron consisting of processing node and synaptic connections Neural Networks Dr. Randa Elanwar 20
- 21. Neuron Modeling for ANN Neural Networks Dr. Randa Elanwar 21 Is referred to activation function. Domain is set of activation values net. (Not a single value fixed threshold) Scalar product of weight and input vector Neuron as a processing node performs the operation of summation of its weighted input.

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