Solving arithmetic problems using feed-forward neural networks

Neurocomputing

Volumn 18, Issue 1-3, 1998, Pages 61-79

  Franco, Leonardo ^a   Cannas, Sergio A ^a  

^a UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

Author keywords

Arithmetic operations; Neural networks; Shifter circuit

Indexed keywords

DIGITAL ARITHMETIC; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

ELEMENTARY ARITHMETIC OPERATIONS;

FEEDFORWARD NEURAL NETWORKS;

ARITHMETIC; ARTICLE; ARTIFICIAL NEURAL NETWORK; POSITIVE FEEDBACK; PRIORITY JOURNAL; PROBLEM SOLVING;

EID: 0031911201     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(97)00069-6     Document Type: Article

References (14)

1. [1] N. Alon, J. Bruck, Explicit constructions of depth-2 majority circuits for comparison and addition, SIAM J. Discrete. Math. 7 (1991) 1-8.
2. [2] C.H. Anderson, D.C. Van Essen, Shifter circuits: A computational strategy for dynamic aspects of visual processing, Proc. Nat. Acad. Sci. USA 84 (1987) 6297-6301.
3. [3] S. Cannas, Arithmetic Perceptrons, Neural Comput. 7 (1) (1995) 173-181.
4. [4] A. Hajnal, W. Maass, P. Pudlak, M. Szegedy, G. Turan, Threshold circuits of bounded depth, IEEE Symp. Found. Comput. Sci. 28 (1987) 99-110.
5. [5] J. Hertz, A. Krogh R. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Santa fe Institute, 1991.
6. [6] T. Hofmeister, W. Hohberg, S. Kohling, Some notes on threshold circuits and multiplication in depth 4, Inform. Procces. Lett. 39 (1991) 99-110.
7. [8] R. Lauwereins, J. Bruck, Efficient implementation of a neural multiplier, IBM Research, Tech. Report RJ 8138, 1991.
8. [9] B. Muller, J. Reinhardt, Neural Networks: An Introduction, Springer, Berlin, 1991.
9. [10] M. Paterson, N. Pippenger, U. Zwick, Optimal carry save networks, Research Report RR166, Dept. of Computer Science:, Univ. of Warwick, Coventry, UK, 1990.
10. [11] L. Prechelt, A quantitative study of experimental evaluations of neural network learning algorithms: current research practice, Neural Networks 9 (1996) 457-462.
11. [12] F. Rosenblatt, Principles of Neurodynamics, Spartan, New York, 1962.
12. [13] K. Siu, J. Bruck, T. Kailath, Depth efficient neural networks for division and related problems, IEEE Trans. Inform. Theory 39 (3) (1993).
13. [14] K. Siu, V. Roychowdhury, On optimal depth threshold circuits for multiplication and related problems. SIAM J. Discrete Math. 7 (2) (1994).
14. [15] T.L.H. Watkin, A. Rau, M. Biehl, The statistical mechanics of learning a rule, Rev. Mod. Phys. 65 (1993) 499-556.