Noisy recurrent neural networks: the continuous-time case

1998 ◽  
Vol 9 (5) ◽  
pp. 913-936 ◽  
Author(s):  
S. Das ◽  
O. Olurotimi
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Continuous Time

POINCARÉ MAPPING OF CONTINUOUS RECURRENT NEURAL NETWORKS EXCITED BY TEMPORAL EXTERNAL INPUT

2000 ◽  
Vol 10 (07) ◽  
pp. 1677-1695 ◽  
Author(s):  
SHOZO SATO ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Neural Networks ◽  
Bifurcation Diagram ◽  
Recurrent Neural Networks ◽  
Continuous Time ◽  
Product Space ◽  
External Input ◽  
Poincaré Mapping ◽  
Network Behavior ◽  
Input Space ◽  
Poincare Mapping

This paper presents qualitative analyses of the dynamics of continuous-time recurrent neural networks (RNNs) with continuous temporal external input. We show how to analyze continuous-time RNNs using Poincaré mapping. We introduce an input space in which the external input is parametrized, and define the product space which consists of the input space and the phase space. We numerically examine the bifurcation caused by changing the external input in the product space. It is shown that the network dynamics can be considered as rapid transitions in the bifurcation diagram. From the bifurcation viewpoint, the learning process of the RNN can be considered as a process to adjust the bifurcation diagram in order to satisfy a given input–output relation. We also numerically investigate the network behavior against the noise of the external input, and show the qualitative conditions for robustness.

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