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Neural Networks
Dr. Randa Elanwar
Lecture 2
Lecture Content
• Neural network concepts:
– Basic definition.
– Connections.
– Processing elements.
2Neural Networks Dr. ...
Artificial Neural Network: Structure
• ANN posses a large number of processing elements called
nodes/neurons which operate...
Artificial Neural Network: Neuron Model
(dendrite) (axon)
(soma)
4Neural Networks Dr. Randa Elanwar
 f()
Y
Wa
Wb
Wc
Conn...
How are neural networks being used in
solving problems
• From experience: examples / training data
• Strength of connectio...
How are neural networks being used in
solving problems
• The problem variables are mainly: inputs, weights and
outputs
• E...
How NN learns a task: Issues to be
discussed
- Initializing the weights.
- Use of a learning algorithm.
- Set of training ...
Linear Problems
• The simplest type of problems are the linear problems.
• Why ‘linear’? Because we can model the problem ...
Linear Problems
• Example: AND (x1,x2), f(net) = 1 if net>1 and 0 otherwise
• Check the truth table: y = f(x1+x2)
9Neural ...
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)
10Neur...
Linear Problems
• Example: NOT(x1), f(net) = 1 if net>1 and 0 otherwise
• Check the truth table: y = f(-1.x1+2)
11Neural N...
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)
1...
Neural Networks Dr. Randa Elanwar 13
The McCulloch-Pitts Neuron
• This vastly simplified model of real neurons is also kno...
McCulloch-Pitts Neuron Model
Neural Networks Dr. Randa Elanwar 14
Features of McCulloch-Pitts model
• Allows binary 0,1 states only
• Operates under a discrete-time assumption
• Weights an...
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 in...
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 in...
McCulloch-Pitts NOR
18Neural Networks Dr. Randa Elanwar
•Can be implemented using an OR
gate design followed by inverter
•...
McCulloch-Pitts NAND
19Neural Networks Dr. Randa Elanwar
•Can be implemented using an
inverter design followed by OR gate
...
General symbol of neuron consisting of
processing node and synaptic connections
Neural Networks Dr. Randa Elanwar 20
Neuron Modeling for ANN
Neural Networks Dr. Randa Elanwar 21
Is referred to activation function. Domain is
set of activati...
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Introduction to Neural networks (under graduate course) Lecture 2 of 9

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Undergraduate course content:
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

Published in: Education

Introduction to Neural networks (under graduate course) Lecture 2 of 9

  1. 1. Neural Networks Dr. Randa Elanwar Lecture 2
  2. 2. Lecture Content • Neural network concepts: – Basic definition. – Connections. – Processing elements. 2Neural Networks Dr. Randa Elanwar
  3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 14. McCulloch-Pitts Neuron Model Neural Networks Dr. Randa Elanwar 14
  15. 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. 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. 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. 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. 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. 20. General symbol of neuron consisting of processing node and synaptic connections Neural Networks Dr. Randa Elanwar 20
  21. 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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