Computing with Nonmonotone Multivalued Neurons
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Abstract:
Although most of the neural network studies use analog neurons with continuous monotone increasing transfer functions, the reasons for using them are not very well founded. The objective of this paper is to study computational ability of more general neural networks whose transfer functions are not necessarily monotone. A nonmonotone multivalued neural network is proposed as a model for reasoning about certain aspects of the behavior of limited precision analog neural networks with arbitrary continuous transfer functions. The nonmonotone multivalued model is compared to previously studied monotone multivalued and to nonmonotone binary neural networks and it is shown that the models are essentially equivalent. However, the savings in time and hardware arising from using a nonmonotone network rather than monotone can be quite significant as demonstrated on the example of computing symmetric functions and of summing two natural numbers. 1
Citations
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| 40 | The Complexity of Boolean Networks – Dunne - 1988 |
| 11 | unknown title – Rumelhart - 1986 |
| 10 | The capacity of multilevel threshold functions – Olafsson, Abu-Mostafa - 1988 |
| 6 | Learning with discrete multivalued neurons – Obradovi'c, Parberry - 1994 |
