KII Models: Simplification of the KII with identical parameters

1
KII Models Simplification of the KII with
identical parameters

• Computer Science
• Comp 7991
• John P. Oliver

2
Definition of Problem

• Simplify the KII model by reducing the K0
• nodes from four K0 nodes to two K0
• Nodes. Expand the number of KII units in
• layer from 1 to 1,000. Determine lateral
• connection weights We1 and Wi1 which
• will produce identical parameters thus
• showing the model can be simplified.

3
Methodology

• To reduce K0 units from four to two, the
• Weights Wee and Wii must be set to zero.
• To increase the number of KII units in the
• Layer, the KII sample code needed to be
• Modified by setting NN1,000 and by
• Changing the dimensions of the A0 matrix
• From a 1 x 4 to a 1 x 4000.

4
Code Modification

• KII Connection Weights, there are four weights,
  but they need to be
• organized in a 4 by 4 matrix
• Kee 0 Kei 1.6 Kie 1.5 Kii 0
• W 0 Kee -Kie -Kie Kee 0 -Kie 0
  Kei Kei 0 -Kii Kei 0 -Kii 0

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Code Modification (contd)

• Number of Units in layer
• NN 1000
• Initial Conditions
• A0 -0.5 0 0 0 B0 initial
  activations A0 and derivatives
• of initial activations B0
• if NN gt 1
• A0 repmat(A0,1,NN)
• end

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Determine Lateral Weights

• The lateral connection weights We1 and
• Wi1 were determined using trial and error
• for the original KII model having four K0
• nodes. The resulting weight values that
• produced a graph with limit cycle
• oscillations were We1.02 and Wi1-.03.

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Lateral connection weights simplified model

• The lateral connection weights for the
• simplified model have not yet been
• determined. The trial and error method
• has produced limit cycle oscillations,
• however the frequencies and amplitudes
• do not match the original KII model.

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(contd)

• The trial and error method is too tedious
• and time consuming. The code needed
• to be modified to generate multiple figures with
• many combinations of lateral weights
• We1 and Wi1, so I have automated the
• procedure to generate multiple figures by
• changing the KII code as follows.

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(contd)

• for p 0-.002-.02
• for s 0.002.02
• we1 s wi1 p
• By varying the start, increments and end
• values in the for loops, any number of
• figures can be generated for comparison
• to the original KII output graph.

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Code to display figure for all combinations in
range

• display output, if necessary
• r r'
• c c'
• if c r
• f figure
• n m size(r)
• plot(0dTdT(m-1), r(,))
• end
• end
• end

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Identical comparison

• After a range has been identified to
• produce similar results, the output can
• be directly compared with the output
• of the original KII by saving the output
• layer from the original KII and only
• generating the figure if it is an identical
• match. Modified code follows.

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Code to compare outputs for identical match

• load the results from the file and process if
  needed
• r load(fname)
• c load('good.m')
• r load(fname)
• display output, if necessary
• r r'
• c c'
• if c r
• f figure
• n m size(r)
• plot(0dTdT(m-1), r(,))
• end
• end
• end

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Work in progress

• The comparable range of values for
• the simplified lateral weight values are
• still being determined. Once I have
• found the comparable range, I can use
• modified code to determine the exact
• weights for the simplified KII model.

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Conclusion

• Although I have not found the exact
• weights to simplify the KII model, I
• do believe I am on the right track for
• determining the values that will generate
• identical output which will prove the KII
• model can be simplified.