A hierarchical classification of first-order recurrent neural networks

Authors:
Jérémie Cabessa;Alessandro E. P. Villa
Affiliations:
GIN Inserm UMRS 836, University Joseph Fourier, Grenoble;GIN Inserm UMRS 836, University Joseph Fourier, Grenoble
Venue:
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Year:
2010

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Abstract

We provide a refined hierarchical classification of first-order recurrent neural networks made up of McCulloch and Pitts cells. The classification is achieved by first proving the equivalence between the expressive powers of such neural networks and Muller automata, and then translating the Wadge classification theory from the automata-theoretic to the neural network context. The obtained hierarchical classification of neural networks consists of a decidable pre-well ordering of width 2 and height ωω, and a decidability procedure of this hierarchy is provided. Notably, this classification is shown to be intimately related to the attractive properties of the networks, and hence provides a new refined measurement of the computational power of these networks in terms of their attractive behaviours.