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Title: :  LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS
PaperId: :  6184
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 3 Issue 4 2017
DUI:    16.0415/IJARIIE-6184
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
C.REVATHIVivekanandha College of Arts and Sciences for Women (Autonomous), Tamilnadu, India
S.RAMADEVIVivekanandha College of Arts and Sciences for Women (Autonomous), Tamilnadu, India

Abstract

MATHEMATICS
Discontinuous neural networks; Global exponential stability; convergence in finite time
The paper considers a class of additive neural networks where the neuron activations are modelled by discontinuous functions or by continuous non-lipschitz functions. Some tools are developed which enable us to apply a Lyapunov-like approach to differential equations with discontinuous right-hand side modelling the neural network dynamics. The tools include a chain rule for computing the time derivative along the neural network solutions of a non differentiable Lyapunov function, and a comparison principal for this time derivative, which yields conditions for exponential convergence or convergence in finite time. By means of Lyapunov-like approach, a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions, Moreover, new results on global convergence in finite time are established, which are applicable to neuron activations with jump discontinuities, or neuron activations modelled by means of continuous (non-Lipschitz) Holder functions.

Citations

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IJARIIE C.REVATHI, and S.RAMADEVI. "LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS" International Journal Of Advance Research And Innovative Ideas In Education Volume 3 Issue 4 2017 Page 1500-1506
MLA C.REVATHI, and S.RAMADEVI. "LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS." International Journal Of Advance Research And Innovative Ideas In Education 3.4(2017) : 1500-1506.
APA C.REVATHI, & S.RAMADEVI. (2017). LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS. International Journal Of Advance Research And Innovative Ideas In Education, 3(4), 1500-1506.
Chicago C.REVATHI, and S.RAMADEVI. "LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS." International Journal Of Advance Research And Innovative Ideas In Education 3, no. 4 (2017) : 1500-1506.
Oxford C.REVATHI, and S.RAMADEVI. 'LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS', International Journal Of Advance Research And Innovative Ideas In Education, vol. 3, no. 4, 2017, p. 1500-1506. Available from IJARIIE, http://ijariie.com/AdminUploadPdf/LYAPUNOV___LIKE_APPROACH_FOR_STUDYING_GLOBAL_CONVERGENCE_OF_NEURAL_NETWORKS_WITH_DISCONTINUOUS_OR_NON_LIPSCHITZ_ACTIVATIONS_ijariie6184.pdf (Accessed : 21 July 2017).
Harvard C.REVATHI, and S.RAMADEVI. (2017) 'LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS', International Journal Of Advance Research And Innovative Ideas In Education, 3(4), pp. 1500-1506IJARIIE [Online]. Available at: http://ijariie.com/AdminUploadPdf/LYAPUNOV___LIKE_APPROACH_FOR_STUDYING_GLOBAL_CONVERGENCE_OF_NEURAL_NETWORKS_WITH_DISCONTINUOUS_OR_NON_LIPSCHITZ_ACTIVATIONS_ijariie6184.pdf (Accessed : 21 July 2017)
IEEE C.REVATHI, and S.RAMADEVI, "LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS," International Journal Of Advance Research And Innovative Ideas In Education, vol. 3, no. 4, pp. 1500-1506, Jul-Aug 2017. [Online]. Available: http://ijariie.com/AdminUploadPdf/LYAPUNOV___LIKE_APPROACH_FOR_STUDYING_GLOBAL_CONVERGENCE_OF_NEURAL_NETWORKS_WITH_DISCONTINUOUS_OR_NON_LIPSCHITZ_ACTIVATIONS_ijariie6184.pdf [Accessed : 21 July 2017].
Turabian C.REVATHI, and S.RAMADEVI. "LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 3 number 4 (21 July 2017).
Vancouver C.REVATHI, and S.RAMADEVI. LYAPUNOV - LIKE APPROACH FOR STUDYING GLOBAL CONVERGENCE OF NEURAL NETWORKS WITH DISCONTINUOUS OR NON-LIPSCHITZ ACTIVATIONS. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2017 [Cited : 21 July 2017]; 3(4) : 1500-1506. Available from: http://ijariie.com/AdminUploadPdf/LYAPUNOV___LIKE_APPROACH_FOR_STUDYING_GLOBAL_CONVERGENCE_OF_NEURAL_NETWORKS_WITH_DISCONTINUOUS_OR_NON_LIPSCHITZ_ACTIVATIONS_ijariie6184.pdf
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