Neural Networks and Fuzzy Systems

1. M. Raihan
Email: rianku11@gmail.com

2. Multilayer Network

3. Multilayer Network Structure
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A neural network with one or more layers of nodes between the
input and the output nodes is called multilayer network.
The multilayer network structure, or architecture, or topology,
consists of an input layer, two or more hidden layers, and one
output layer.
The input nodes pass values to the first hidden layer, its nodes
to the second and so on till producing outputs.
A network with a layer of input units, a layer of hidden units and a layer of output
units is a two-layer network.
A network with two layers of hidden units is a three layer network, and so on.
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4. Properties of architecture
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No connections within a layer.
No direct connections between input and output
layers.
Fully connected between layers.
Number of output units need not equal number of
input units.
Number of hidden units per layer can be more or
less than input or output units.
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5. Multilayer Perceptron:
Decision Boundaries
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6. Multilayer Perceptron:
Decision Boundaries
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7. Multilayer Perceptron:
Decision Boundaries
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8. XOR
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9. XOR
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10. How to Train MLP
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How we can train the network, so that
The weights are adapted to generate correct (target answer)?
In Perceptron, errors are computed at the output.
In MLP:
Don’t know which weights are wrong
Don’t know the correct activations for the neurons in the hidden layers
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11. Then..
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12. Backpropagation
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13. Backpropagation Algorithm
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 Forward pass phase: Computes ‘functional signal’,
feed forward propagation of input pattern signals
through network.
Backward pass phase: Computes ‘error signal’,
propagates the error backwards through network
starting at output units (where the error is the
difference between actual and desired output
values)
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14. Back Propagation Diagram
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15. Training MLPs
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Forward Pass
Put the input values in the input layer.
Calculate the activations of the hidden nodes.
Calculate the activations of the output nodes.
Calculate the errors using the targets.
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16. Training MLPs
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Backward Pass
From output errors, update last layer of weights.
From these errors, update next layer.
Work backwards through the network.
Error is back propagated through the network.
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17. Error Function
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In Perceptron, E = t – y
Since there is only one set of weights in
the network, it is possible.
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18. Training MLPs
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19. Thank You
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