Representation of neural networks as Lotka-Volterra systems
作者:
Yves Moreau,
Ste´phane Louie`s,
Joos Vandewalle,
Le´on Brenig,
期刊:
AIP Conference Proceedings
(AIP Available online 1999)
卷期:
Volume 465,
issue 1
页码: 155-168
ISSN:0094-243X
年代: 1999
DOI:10.1063/1.58279
出版商: AIP
数据来源: AIP
摘要:
We study changes of coordinates that allow the representation of the ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models—also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form, where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoı¨d. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. ©1999 American Institute of Physics.
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