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Multi-Valued Neuron with Sigmoid Activation
Function
Shin-Fu Wu 2013/5/10
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Outlines
Multi-Valued Neuron (MVN)
MVN with Sigmoid Activation Function (MVN-sig)
Motivation and Expectation
Multi-Valued Sigmoid Activation Function
Learning using Back-propagation Rule
Simulation Results
Benchmark simulations
Problems and Limitations
Movement of Weighted Sum
Future Works
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MVN
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MVN-sig
Motivation and Expectation
Basic idea: approach the functionality of MVN using sigmoid function
Differentiable
Multi-Valued Logic
Expectation:
Better performance and tolerance
More execution time
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MVN-sig
arg(z)
...
2π 0
1
2
k-1
...
τ 1 τ 2 τ 3 τ k-1 ...
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MVN-sig
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MVN-sig
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MVN-sig
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MVN-sig
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MVN-sig
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Simulation Results
Benchmark Simulations
Wine dataset (5-fold CV, 100% trained)
MVN
Epoch
Sec. acc.
109.2 0.6581
90.17
115.6 0.7072
90.17
91.6 0.5966
90.17
100.4 0.6506
89.69
121.2 0.6927
90.17
107.6 0.6610
90.074
MVN-sig (C=1)
Epoch Sec. Acc.
1228.6 5.9988
70.58
705.2 5.0383
71.53
656 4.2992
70.58
1425.6 6.8748
71.53
1089 8.0087
70.10
1020.88
6.0440
70.86
MVN-sig (C=5)
Epoch Sec. Acc.
1048.6 3.3985
93.50
2022 3.4830
94.02
410.4 2.6888
93.50
3691 9.7389
93.02
299.2 2.0722
92.51
1494.24
4.2763
93.31
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Simulation Results
Glass identification dataset (5-fold CV, 100% trained)
MVN
Epoch
Sec. acc.
108.6 0.6565
91.12
123.8 0.6907
89.21
131.6 0.7178
89.69
103 0.6129
90.60
110 0.6461
90.17
115.4 0.6648
90.158
MVN-sig (C=1)
Epoch
Sec. Acc.
1143.4
4.7687
72.48
1032.6
7.4362
70.62
458.4 2.3950
72.01
388.4 2.0841
71.06
899.8 4.4695
72.05
784.52
4.2307
71.644
MVN-sig (C=5)
Epoch
Sec. Acc.
281.4 3.4416
90.21
207.2 1.9953
93.98
1040.4
5.8584
90.64
1939.2
7.9271
90.60
348.8 3.2267
93.54
763.4 4.4898
91.784
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Simulation Results
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Simulation Results
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Future Works