Fractal Transition in continuous Recurrent Neural Networks

A theory for continuous dynamical systems stochastically excited by temporal external inputs has been presented. The theory suggests that the dynamics of continuous-time recurrent neural networks (...

[1]  Morris W. Hirsch,et al.  Convergent activation dynamics in continuous time networks , 1989, Neural Networks.

[2]  C. Lee Giles,et al.  Extraction of rules from discrete-time recurrent neural networks , 1996, Neural Networks.

[3]  James L. McClelland,et al.  Finite State Automata and Simple Recurrent Networks , 1989, Neural Computation.

[4]  Morris W. Hirsch,et al.  Saturation at high gain in discrete time recurrent networks , 1994, Neural Networks.

[5]  Raymond L. Watrous,et al.  Induction of Finite-State Languages Using Second-Order Recurrent Networks , 1992, Neural Computation.

[6]  Michael C. Mozer,et al.  A Unified Gradient-Descent/Clustering Architecture for Finite State Machine Induction , 1993, NIPS.

[7]  Mikel L. Forcada,et al.  Stable Encoding of Finite-State Machines in Discrete-Time Recurrent Neural Nets with Sigmoid Units , 2000, Neural Computation.

[8]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[9]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Xin Wang,et al.  Period-doublings to chaos in a simple neural network , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[11]  Padhraic Smyth,et al.  Learning Finite State Machines With Self-Clustering Recurrent Networks , 1993, Neural Computation.

[12]  L. K. Li,et al.  Fixed point analysis for discrete-time recurrent neural networks , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[13]  Kazutoshi Gohara,et al.  Poincaré Mapping of continuous Recurrent Neural Networks excited by Temporal External Input , 2000, Int. J. Bifurc. Chaos.

[14]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[15]  Michael I. Jordan.  Attractor dynamics and parallelism in a connectionist sequential machine , 1990 .

[16]  Kazutoshi Gohara,et al.  DYNAMICAL SYSTEMS EXCITED BY TEMPORAL INPUTS: FRACTAL TRANSITION BETWEEN EXCITED ATTRACTORS , 1999 .

[17]  Peter Tiňo,et al.  Finite State Machines and Recurrent Neural Networks -- Automata and Dynamical Systems Approaches , 1995 .

[18]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[19]  Kazutoshi Gohara,et al.  FRACTAL TRANSITION: HIERARCHICAL STRUCTURE AND NOISE EFFECT , 1999 .

[20]  C. Lee Giles,et al.  Learning and Extracting Finite State Automata with Second-Order Recurrent Neural Networks , 1992, Neural Computation.

[21]  Mike Casey,et al.  The Dynamics of Discrete-Time Computation, with Application to Recurrent Neural Networks and Finite State Machine Extraction , 1996, Neural Computation.

[22]  Xin Wang,et al.  Stability of fixed points and periodic orbits and bifurcations in analog neural networks , 1992, Neural Networks.