TY - GEN
T1 - Neural addition and fibonacci numbers
AU - Beiu, Valeriu
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
PY - 1999
Y1 - 1999
N2 - This paper presents an intriguing relation between neural networks having as weights the Fibonacci numbers and the addition of (two) binary numbers. The practical application of interest is that such ‘Fibonacci’ networks are VLSI-optimal with respect to the area of the circuit. We shortly present the state- of-the-art, and detail a class of multilayer solutions for addition. For this class we will prove constructively that the weights of the threshold gates implementing the Boolean functions are the Fibonacci numbers. As the weights are the smallest integers (by construction), the area of the VLSI circuit—estimated as the sum of the digits needed to represent the weights—is minimised. Therefore this class of solutions is VLSI-optimal. Conclusions and open questions are ending the paper.
AB - This paper presents an intriguing relation between neural networks having as weights the Fibonacci numbers and the addition of (two) binary numbers. The practical application of interest is that such ‘Fibonacci’ networks are VLSI-optimal with respect to the area of the circuit. We shortly present the state- of-the-art, and detail a class of multilayer solutions for addition. For this class we will prove constructively that the weights of the threshold gates implementing the Boolean functions are the Fibonacci numbers. As the weights are the smallest integers (by construction), the area of the VLSI circuit—estimated as the sum of the digits needed to represent the weights—is minimised. Therefore this class of solutions is VLSI-optimal. Conclusions and open questions are ending the paper.
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U2 - 10.1007/BFb0100486
DO - 10.1007/BFb0100486
M3 - Conference contribution
AN - SCOPUS:84958063522
SN - 3540660682
SN - 9783540660682
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 198
EP - 207
BT - Engineering Applications of Bio-Inspired Artificial Neural Networks - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings
A2 - Mira, Jose
A2 - Sanchez-Andres, Juan V.
PB - Springer Verlag
T2 - 5th International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999
Y2 - 2 June 1999 through 4 June 1999
ER -