Bounds on the number of hidden neurons in three-layer binary neural networks

Neural Networks

Volumn 16, Issue 7, 2003, Pages 995-1002

  Zhang, Zhaozhi ^a   Ma, Xiaomin ^b   Yang, Yixian ^b  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b ORAL ROBERTS UNIVERSITY   (United States)

Author keywords

Boolean function; Hamming space; Set covering algorithm; Three layer binary neural network; Unit sphere covering; Weighted distance sphere

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; ESTIMATION; NUMERICAL METHODS; PROBLEM SOLVING;

NEURONS;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL; WEIGHT;

EID: 0742307322     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(03)00006-6     Document Type: Article

References (15)

1. Abu-Mostafa Y.S., Jacques J.M. Information capacity of the Hopfield model. IEEE Transactions on Information Theory. 31:1985;461-464.
2. Arai M. Bounds on the number of hidden units in binary-valued three-layer neural networks. Neural Networks. 6:1993;855-860.
3. Blass U., Litsyn S. Several new lower bounds on the size of codes with covering radius one. IEEE Transactions on Information Theory. 44:1998;1998-2002.
4. Hamming R.W. Error-detecting and error-correcting. Bell System Technical Journal. 29:1950;147-160.
5. Kabatyanskii G.A., Panchenko V.I. Unit sphere packing and coverings of the Hamming space. Problemy Peredachi Informatsii (in Russian). 24:1988;3-16. English translation in (1988) Problem Information Transmission, 24 261-272.
6. Kim J.K., Park S.K. The geometrical learning of binary neural networks. IEEE Transactions on Neural Networks. 6:1995;237-247.
7. Li D., Chen W. New lower bounds for binary covering codes. IEEE Transactions on Information Theory. 40:1994;1122-1129.
8. Ma X., Yang Y., Zhang Z. Boolean neural network design using set covering in Hamming geometrical space. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E82-A:1999;2285-2290.
9. Muroga S., Tsuboi T., Baugh C.R. Enumeration of threshold functions of eight variables. IEEE Transactions on Electronic Computer. EC-14:1970;136-148.
10. Ojha P.C. Enumeration of linear threshold functions from the lattice of hyperplane intersections. IEEE Transactions on Neural Networks. 11:2000;839-850.
11. Sontag E.D. VC dimension of neural networks. Bishop C.M. Neural networks and machine learning. 1998;69-95 Springer, Berlin.
12. Wee G.J.M.V. Some new lower bounds for binary and ternary covering codes. IEEE Transactions on Information Theory. 39:1993;1422-1424.
13. Wille L.T. New binary covering codes obtained by simulated annealing. IEEE Transactions on Information Theory. 42:1996;300-302.
14. Zhang Z., Lo C. Linear inequalities for covering codes: part II-Triple covering inequalities. IEEE Transactions on Information Theory. 38:1992;1648-1662.
15. Zhang Z., Ma X., Yang Y. A unified method to construct neural network decoders for arbitrary codes and decoding rules. Discrete Mathematics. 238:2001;171-181.