Abstract
This paper presents the definition of a formal data structure, which assists in the characterization of any neural paradigm, with no restriction, including higher-order networks. Within this model, a neural network is mathematically described by specifying some static parameters (number of neurons, order) as well as a set of statistical distributions (which we call the network ‘dynamics’). Once a concrete set of distributions is defined, a single algorithm can simulate any neural paradigm. The presented structure assists in an exhaustive and precise description of the network characteristics and the simulation parameters, providing us with a unified criterion for comparing models and evaluating proposed systems. Though not presented here, the formal model has inspired a software simulator, which implements any system defined according to this structure, thus facilitating the analysis and modelling of neuronal paradigms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Atencia, M. A.: An arbitrary order neural network design and simulation environment, graduating work, Dpto. Tecnología Electrónica, Univ. Málaga (Spain), (in Spanish), 1997.
García del Valle, M., García, C., López, F. J. and Acevedo, I.: Generic neural network model and simulation toolkit, In: Mira, Moreno-Díaz and Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology, Lecture Notes in Computer Science, No. 1240, Springer-Verlag, (1997), pp. 313-322.
Garey, M. R. and Johnson, D. S.: Computers and Intractability. A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, (1979).
Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Nat. Acad. Sci. U.S.A., 81 (1984), 3088-3092.
Hopfield, J. J. and Tank, D. W.: Neural computation of decisions in optimization problems, Biological Cybernetics, 52 (1985), 141-152.
Joya, G., Atencia, M. A. and Sandoval, F.: Application of high-order Hopfield neural networks to the solution of diophantine equations, In: A. Prieto (ed.), Artificial Neural Networks, Lecture Notes in Computer Science, No. 540, Springer-Verlag, (1991), pp. 395-400.
Joya, G., Atencia, M. A. and Sandoval, F.: Associating arbitrary-order energy functions to an artificial neural network. Implications concerning the resolution of optimization problems, Neurocomputing, 14 (1997), 139-156.
Joya, G., Atencia, M. A. and Sandoval, F.: Hopfield Neural Network applied to optimization problems: some theoretical and simulation results, In:Mira, Moreno-Díaz and Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology, Lecture Notes in Computer Science, No. 1240, Springer-Verlag, (1997), pp. 556-565.
Joya, G.: Contributions of high order artificial neural networks to the design of autonomous systems. Doctoral Thesis, Dpto. Tecnología Electrónica, Univ. Málaga. Servicio de Publicaciones e Intercambio Científico de la Universidad de Málaga, (in Spanish), 1997.
Mira, J., Herrero, J. C. and Delgado, A. E.: A Generic formulation of neural nets as a model of parallel and self-programming computation, In: Mira, Moreno-Díaz and Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology, Lecture Notes in Computer Science, No. 1240, Springer-Verlag, (1997), pp. 195-206.
Müller, B. and Reinhardt, J.: Learning Boolean Functions with Back-Propagation, Neural Networks. An Introduction, Springer-Verlag, (1990), pp. 222-227.
Santos, J., Cabarcos, M., Otero, R. P. and Mira, J.: Parallelization of connectionist models based on a symbolic formalism, In: Mira, Moreno-Díaz and Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology, Lecture Notes in Computer Science No. 1240, Springer-Verlag, (1997), pp. 304-312.
Strey, A.: EpsiloNN-A specification language for the Efficient Parallel Simulation of Neural Networks, inMira, Moreno-Díaz and Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology, Lecture Notes in Computer Science No. 1240, Springer-Verlag, (1997), pp. 714-722.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Atencia, M.A., Joya, G. & Sandoval, F. A Formal Model for Definition and Simulation of Generic Neural Networks. Neural Processing Letters 11, 87–105 (2000). https://doi.org/10.1023/A:1009678528953
Issue Date:
DOI: https://doi.org/10.1023/A:1009678528953