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Volumn 15, Issue 6, 2004, Pages 1350-1366

Feedforward sigmoidal networks - Equicontinuity and fault-tolerance properties

Author keywords

Equicontinuity; Fault tolerance; Feedforward artificial neural networks (FFANNs); Function sets; Sigmoidal networks

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

EID: 9244245241     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2004.831198     Document Type: Article
Times cited : (46)

References (47)
  • 4
    • 0025488663 scopus 로고
    • "30 years of adaptive neural networks: Perceptron, madaline, and backpropagation"
    • B. Widrow and M. A. Lehr, "30 years of adaptive neural networks: Perceptron, madaline, and backpropagation," Proc. IEEE, vol. 78, pp. 1415-1442, 1990.
    • (1990) Proc. IEEE , vol.78 , pp. 1415-1442
    • Widrow, B.1    Lehr, M.A.2
  • 5
    • 0024124325 scopus 로고
    • "There exists a neural network that does not make avoidable mistakes"
    • A. R. Gallant and H. White, "There exists a neural network that does not make avoidable mistakes," in Proc. Second Int. Joint Conf. Neural Networks, vol. I, 1988, pp. 593-606.
    • (1988) Proc. Second Int. Joint Conf. Neural Networks , vol.1 , pp. 593-606
    • Gallant, A.R.1    White, H.2
  • 6
    • 0003095817 scopus 로고
    • "Approximation by superposition of a sigmoidal function"
    • G. Cybenko, "Approximation by superposition of a sigmoidal function," Math. Contr., Signal, and Syst., vol. 5, pp. 233-243, 1989.
    • (1989) Math. Contr., Signal, and Syst. , vol.5 , pp. 233-243
    • Cybenko, G.1
  • 7
    • 0024866495 scopus 로고
    • "On the approximate realization of continuous mappings by neural networks"
    • K. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Networks, vol. 2, pp. 183-192, 1989.
    • (1989) Neural Networks , vol.2 , pp. 183-192
    • Funahashi, K.1
  • 8
    • 0024880831 scopus 로고
    • "Multilayer feedforward networks are universal approximators"
    • K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, vol. 2, pp. 359-366, 1989.
    • (1989) Neural Networks , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 9
    • 0025627940 scopus 로고
    • "Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks"
    • K. Hornik, "Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks," Neural Networks, vol. 3, pp. 551-560, 1990.
    • (1990) Neural Networks , vol.3 , pp. 551-560
    • Hornik, K.1
  • 10
    • 0025558060 scopus 로고
    • "Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights"
    • M. Stinchcombe and H. White, "Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights," in Proc. IJCNN, vol. III, 1990, pp. 7-16.
    • (1990) Proc. IJCNN , vol.3 , pp. 7-16
    • Stinchcombe, M.1    White, H.2
  • 11
    • 0025751820 scopus 로고
    • "Approximation capabilities of multilayer feedforward networks"
    • K. Hornik, "Approximation capabilities of multilayer feedforward networks," Neural Networks, vol. 4, pp. 251-257, 1991.
    • (1991) Neural Networks , vol.4 , pp. 251-257
    • Hornik, K.1
  • 12
    • 0027599793 scopus 로고
    • "Universal approximation bounds for superposition of a sigmoidal function"
    • A. R. Barron, "Universal approximation bounds for superposition of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, pp. 930-945, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 13
    • 0029207175 scopus 로고
    • n ) by multilayer feedforward networks and related problems"
    • n ) by multilayer feedforward networks and related problems," IEEE Trans. Neural Networks, vol. 6, pp. 25-30, 1995.
    • (1995) IEEE Trans. Neural Networks , vol.6 , pp. 25-30
    • Chen, T.1    Chen, H.2    Liu, R.W.3
  • 14
    • 0032961240 scopus 로고    scopus 로고
    • "Neural network approximation of continuous functionals and continuous functions on compactifications"
    • M. B. Stinchcombe, "Neural network approximation of continuous functionals and continuous functions on compactifications," Neural Networks, vol. 12, pp. 467-477, 1999.
    • (1999) Neural Networks , vol.12 , pp. 467-477
    • Stinchcombe, M.B.1
  • 15
    • 0034233437 scopus 로고    scopus 로고
    • "Neural networks with a continuous squashing function in the output are universal approximators"
    • J.I. Castro, C. J. Mantas, and J. M. Bentez, "Neural networks with a continuous squashing function in the output are universal approximators," Neural Networks, vol. 13, pp. 561-563, 2000.
    • (2000) Neural Networks , vol.13 , pp. 561-563
    • Castro, J.I.1    Mantas, C.J.2    Bentez, J.M.3
  • 17
    • 0010263084 scopus 로고
    • "The power of approximating: A comparision of activation functions"
    • C. L. Giles, S. J. Hanson, and J. D. Cowan, Eds. San Mateo, CA: Morgan Kaufmann
    • B. DasGupta and G. Schnitger, "The power of approximating: A comparision of activation functions," in Advances in Neural Information Processing Systems, C. L. Giles, S. J. Hanson, and J. D. Cowan, Eds. San Mateo, CA: Morgan Kaufmann, 1993, vol. 5, pp. 615-622.
    • (1993) Advances in Neural Information Processing Systems , vol.5 , pp. 615-622
    • DasGupta, B.1    Schnitger, G.2
  • 18
    • 9244225564 scopus 로고
    • "Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives"
    • Tech. Rep. NC-TR-95-004, Neuro-COLT
    • K. Hornik, M. Stinchcombe, H. White, and P. Auer, "Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives,", Tech. Rep. NC-TR-95-004, 1995. Neuro-COLT.
    • (1995)
    • Hornik, K.1    Stinchcombe, M.2    White, H.3    Auer, P.4
  • 19
    • 0000041417 scopus 로고    scopus 로고
    • "Neural networks for optimal approximation of smooth and analytic functions"
    • H. Mhasker, "Neural networks for optimal approximation of smooth and analytic functions," Neural Comput., vol. 8, pp. 164-177, 1996.
    • (1996) Neural Comput. , vol.8 , pp. 164-177
    • Mhasker, H.1
  • 20
    • 9244254691 scopus 로고    scopus 로고
    • Lower bounds on the complexity of approximating continuous functions by sigmoidal neural networks
    • [Online]. Available
    • M. Schmitt. (2000) Lower bounds on the complexity of approximating continuous functions by sigmoidal neural networks. [Online]. Available: http://www.neurocolt.com
    • (2000)
    • Schmitt, M.1
  • 21
    • 0012019432 scopus 로고
    • "Networks and the Best Approximation Property"
    • Artificial Intelligence Laboratory, Mass. Inst. Technol., MA, Tech. Rep. AI Memo no. 1164
    • T. Poggio and E Girosi, "Networks and the Best Approximation Property," Artificial Intelligence Laboratory, Mass. Inst. Technol., MA, Tech. Rep. AI Memo no. 1164, 1989.
    • (1989)
    • Poggio, T.1    Girosi, E.2
  • 22
    • 9244239657 scopus 로고    scopus 로고
    • Bounded weight sigmoidal FFANN's have the best approximation property
    • submitted
    • P. Chandra and Y. Singh, Bounded weight sigmoidal FFANN's have the best approximation property, in IEEE Trans. Neural Networks, 2003. submitted.
    • (2003) IEEE Trans. Neural Networks
    • Chandra, P.1    Singh, Y.2
  • 23
    • 9244247541 scopus 로고    scopus 로고
    • Closure property of function sets represented by feedforward sigmoidal networks
    • submitted
    • P. Chandra, Closure property of function sets represented by feedforward sigmoidal networks, in Int. J. Neural Systems of Neural Systems, 2003. submitted.
    • (2003) Int. J. Neural Systems of Neural Systems
    • Chandra, P.1
  • 24
    • 33750590619 scopus 로고
    • "Fault Tolerant Multi-Layer Perceptron Networks"
    • Advanced Computer Architecture Group, Dept. Computer Sci., Univ. York, U.K., Tech. Rep. YCS 180
    • G. Bolt, "Fault Tolerant Multi-Layer Perceptron Networks," Advanced Computer Architecture Group, Dept. Computer Sci., Univ. York, U.K., Tech. Rep. YCS 180, 1992.
    • (1992)
    • Bolt, G.1
  • 25
    • 0038648742 scopus 로고    scopus 로고
    • "A class +1 sigmoidal activation functions for FFANNs"
    • Y. Singh and P. Chandra, "A class +l sigmoidal activation functions for FFANNs," J. Economic Dyn. Contr., vol. 28, pp. 183-187, 2003.
    • (2003) J. Economic Dyn. Contr. , vol.28 , pp. 183-187
    • Singh, Y.1    Chandra, P.2
  • 26
    • 0003905011 scopus 로고    scopus 로고
    • Berlin, Germany: Springer-Verlag
    • J. Jost, Postmodern Analysis. Berlin, Germany: Springer-Verlag, 1998.
    • (1998) Postmodern Analysis
    • Jost, J.1
  • 30
    • 0141801432 scopus 로고
    • "The illusion of fault tolerance of neural nets for pattern recognition and signal processing"
    • Durham
    • M. J. Carter, "The illusion of fault tolerance of neural nets for pattern recognition and signal processing," in Proc. Tech. Session on Fault Integrated System. Durham, 1988.
    • (1988) Proc. Tech. Session on Fault Integrated System
    • Carter, M.J.1
  • 32
    • 0029269583 scopus 로고
    • "Complete and partial fault tolerance of feed-forward neural nets"
    • D. S. Phatak and I. Koren, "Complete and partial fault tolerance of feed-forward neural nets," IEEE Trans. Neural Networks, vol. 6, pp. 446-456, 1995.
    • (1995) IEEE Trans. Neural Networks , vol.6 , pp. 446-456
    • Phatak, D.S.1    Koren, I.2
  • 33
    • 0028532748 scopus 로고
    • "Comparative fault-tolerance of parallel distributed processing networks"
    • B. E. Segee and M. J. Carter, "Comparative fault-tolerance of parallel distributed processing networks," IEEE Trans. Comput., vol. 43, pp. 1323-1329, 1994.
    • (1994) IEEE Trans. Comput. , vol.43 , pp. 1323-1329
    • Segee, B.E.1    Carter, M.J.2
  • 34
    • 0001223466 scopus 로고
    • "Fault tolerance of backpropagation neural networks trained with noisy data"
    • J.I. Minnix, "Fault tolerance of backpropagation neural networks trained with noisy data," in IJCNN'91, vol. 1, 1991, pp. 703-708.
    • (1991) IJCNN'91 , vol.1 , pp. 703-708
    • Minnix, J.I.1
  • 35
    • 0026858102 scopus 로고
    • "Noise injection into inputs in backpropagation learning"
    • K. Matasuoka, "Noise injection into inputs in backpropagation learning," IEEE Trans. Syst., Man, Cybern., vol. 22, pp. 436-440, 1992.
    • (1992) IEEE Trans. Syst., Man, Cybern. , vol.22 , pp. 436-440
    • Matasuoka, K.1
  • 36
    • 0026624071 scopus 로고
    • "Using additive noise in backpropagation training"
    • L. Holmstrom and P. Koistinen, "Using additive noise in backpropagation training," IEEE Trans. Neural Networks, vol. 3, pp. 24-28, 1992.
    • (1992) IEEE Trans. Neural Networks , vol.3 , pp. 24-28
    • Holmstrom, L.1    Koistinen, P.2
  • 37
    • 0028494739 scopus 로고
    • "Synaptic weight noise during MLP training: Enhanced MLP performance and fault tolerance resulting from synaptic noise during training"
    • A. F. Murray and P. J. Edwards, "Synaptic weight noise during MLP training: Enhanced MLP performance and fault tolerance resulting from synaptic noise during training," IEEE Trans. Neural Networks, vol. 5, pp. 792-802, 1994.
    • (1994) IEEE Trans. Neural Networks , vol.5 , pp. 792-802
    • Murray, A.F.1    Edwards, P.J.2
  • 38
    • 0141461599 scopus 로고    scopus 로고
    • "Fault tolerance of feedforward artificial neural networks - A framework of study"
    • P. Chandra and Y. Singh, "Fault tolerance of feedforward artificial neural networks - A framework of study," in IJCNN'03, 2003, pp. 489-494.
    • (2003) IJCNN'03 , pp. 489-494
    • Chandra, P.1    Singh, Y.2
  • 39
    • 0141633850 scopus 로고    scopus 로고
    • "Regularization and feedforward artificial neural network training with noise"
    • P. Chandra, "Regularization and feedforward artificial neural network training with noise," in IJCNN'03, 2003, pp. 2366-2371.
    • (2003) IJCNN'03 , pp. 2366-2371
    • Chandra, P.1
  • 40
    • 2342565172 scopus 로고    scopus 로고
    • "The effect of adding noise during backpropagation training on a generalization performance"
    • G. Z. An, "The effect of adding noise during backpropagation training on a generalization performance," Neural Comput., vol. 8, pp. 643-674, 1996.
    • (1996) Neural Comput. , vol.8 , pp. 643-674
    • An, G.Z.1
  • 41
    • 0342990011 scopus 로고    scopus 로고
    • "An analysis of noise in recurrent neural networks: Convergence and generalization"
    • K. Jim, C. L. Giles, and B. G. Home, "An analysis of noise in recurrent neural networks: Convergence and generalization," IEEE Trans. Neural Networks, vol. 7, pp. 1424-1439, 1996.
    • (1996) IEEE Trans. Neural Networks , vol.7 , pp. 1424-1439
    • Jim, K.1    Giles, C.L.2    Home, B.G.3
  • 42
    • 0025563947 scopus 로고
    • "Fault tolerance in artificial neural networks"
    • C. H. Sequin and R. D. Clay, "Fault tolerance in artificial neural networks," in IJCNN'90, vol. 1, 1990, pp. 703-708.
    • (1990) IJCNN'90 , vol.1 , pp. 703-708
    • Sequin, C.H.1    Clay, R.D.2
  • 44
    • 0030649974 scopus 로고    scopus 로고
    • "A learning algorithm for fault tolerant feedforward networks"
    • N. C. Hammadi and H. Ito, "A learning algorithm for fault tolerant feedforward networks," IEICE Trans. Inform. Syst., vol. E80-D, pp. 21-27, 1997.
    • (1997) IEICE Trans. Inform. Syst. , vol.E80-D , pp. 21-27
    • Hammadi, N.C.1    Ito, H.2
  • 46
    • 0031681567 scopus 로고    scopus 로고
    • "On the activation function and fault tolerance in feedforward artificial neural networks"
    • N. C. Hammadi and H. Ito, "On the activation function and fault tolerance in feedforward artificial neural networks," IEICE Trans. Inform. Syst., vol. E81-D, pp. 66-72, 1998.
    • (1998) IEICE Trans. Inform. Syst. , vol.E81-D , pp. 66-72
    • Hammadi, N.C.1    Ito, H.2
  • 47
    • 0027668417 scopus 로고
    • "Determining and improving the fault tolerance of multilayer perceptrons in a pattern recognition application"
    • M. D. Emmerson and R. I. Damper, "Determining and improving the fault tolerance of multilayer perceptrons in a pattern recognition application" IEEE Trans. Neural Networks, vol. 4, pp. 788-793, 1993.
    • (1993) IEEE Trans. Neural Networks , vol.4 , pp. 788-793
    • Emmerson, M.D.1    Damper, R.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.