Siu, Kai-Yeung and Bruck, Jehoshua (1990) Neural computation of arithmetic functions. Proceedings of the IEEE, 78 (10). pp. 1669-1675. ISSN 0018-9219 http://resolver.caltech.edu/CaltechAUTHORS:20120503-090033553
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A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n -bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.
|Additional Information:||© 1990 IEEE. Manuscript received Nov. 14, 1989; revised March 14, 1990. This work was done while K.-Y. Siu was a research student associate at IBM Almaden Research Center and was supported in part by the Joint Services Program at Stanford University (US Army, US Navy, US Air Force) under Contract DAAL03-88-C-0011, and the Department of the Navy (NAVELEX) under Contract N00039-84-C-0211, NASA Headquarters, Center for Aeronautics and Space Information Sciences under Grant NAGW-419-S6. The first author would like to thank Prof. Thomas Kailath for his guidance, constant encouragement, and financial support.|
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|Official Citation:||Siu, K.-Y.; Bruck, J.; , "Neural computation of arithmetic functions," Proceedings of the IEEE , vol.78, no.10, pp.1669-1675, Oct 1990 doi: 10.1109/5.58350 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=58350&isnumber=2116|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||03 May 2012 22:45|
|Last Modified:||26 Dec 2012 15:09|
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