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A Hierarchical Classification of First-Order Recurrent Neural Networks

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 !!, 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.
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https://www.hal.inserm.fr/inserm-00624083
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Submitted on : Thursday, September 15, 2011 - 4:49:07 PM
Last modification on : Friday, November 6, 2020 - 4:04:02 AM
Long-term archiving on: : Friday, December 16, 2011 - 2:27:02 AM

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Jérémie Cabessa, Alessandro Villa. A Hierarchical Classification of First-Order Recurrent Neural Networks. 4th International Conference on Language and Automata Theory and Applications, May 2011, Trier, Germany. pp.142-153, ⟨10.1007/978-3-642-13089-2_12⟩. ⟨inserm-00624083⟩

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