Expressive power of first-order recurrent neural networks determined by their attractor dynamics

作者：

Highlights：

• We characterize the attractor-based expressive power of several models of recurrent neural networks.

• The deterministic rational-weighted networks are Muller Turing equivalent.

• The deterministic real-weighted and evolving networks recognize the class of BC(Π20) neural ω languages.

• The nondeterministic rational and real networks recognize the class of Σ11 neural ω-languages.

摘要

•We characterize the attractor-based expressive power of several models of recurrent neural networks.•The deterministic rational-weighted networks are Muller Turing equivalent.•The deterministic real-weighted and evolving networks recognize the class of BC(Π20) neural ω languages.•The nondeterministic rational and real networks recognize the class of Σ11 neural ω-languages.

论文关键词：Recurrent neural networks,Neural computation,Analog computation,Evolving systems,Learning,Attractors,Spatiotemporal patterns,Turing machines,Expressive power,ω-languages

论文评审过程：Received 19 October 2015, Revised 31 March 2016, Accepted 19 April 2016, Available online 27 June 2016, Version of Record 15 July 2016.

论文官网地址：https://doi.org/10.1016/j.jcss.2016.04.006