Generalization properties of modular networks: implementing the parity function

The parity function is one of the most used Boolean function for testing learning algorithms because both of its simple definition and its great complexity. We construct a family of modular architectures that implement the parity function in which, every member of the family can be characterized by...

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Veröffentlicht in:IEEE transactions on neural networks Jg. 12; H. 6; S. 1306 - 1313
Hauptverfasser: Franco, L., Cannas, S.A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.11.2001
Schlagworte:
Algorithm design and analysis
Biological neural networks
Boolean functions
Computer architecture
Computer networks
Convergence
Neural networks
Neurons
Numerical simulation
Testing
ISSN:1045-9227
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Zusammenfassung:The parity function is one of the most used Boolean function for testing learning algorithms because both of its simple definition and its great complexity. We construct a family of modular architectures that implement the parity function in which, every member of the family can be characterized by the fan-in max of the network, i.e., the maximum number of connections that a neuron can receive. We analyze the generalization ability of the modular networks first by computing analytically the minimum number of examples needed for perfect generalization and then by numerical simulations. Both results show that the generalization ability of these networks is systematically improved by the degree of modularity of the network. We also analyze the influence of the selection of examples in the emergence of generalization ability, by comparing the learning curves obtained through a random selection of examples to those obtained through examples selected accordingly to a general algorithm we (2000) recently proposed.
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ISSN:1045-9227
DOI:10.1109/72.963767