The Super-Turing Computational Power of Interactive Evolving Recurrent Neural Networks

Cabessa, Jérémie; Villa, Alessandro E. P.

doi:10.1007/978-3-642-40728-4_8

Cited by 18 publications

(17 citation statements)

References 12 publications

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“…They show that the power of evolution provides the possibility to break the Turing barrier of computation. A concise form of these results has already appeared in [9,14]. The results are proven here in details.…”

Section: Computational Power Of Interactive Evolving Neural Networkmentioning

confidence: 68%

“…They further introduced the concept of interactive Turing machine with advice (I-TM/A) as a relevant non-uniform computational model in the context of interactive computation [69,70]. Interactive Turing machines with advice were proven to be strictly more powerful than interactive Turing machines without advice [70,Proposition 5] and [69,Lemma 1], and were shown to be computationally equivalent to several other non-uniform models of interactive computation, like sequences of interactive finite automata, site machines, web Turing machines [69,70], and more recently to interactive analog neural networks and interactive evolving neural networks [9,11,14].…”

Section: Historical Backgroundmentioning

confidence: 99%

“…Interactive computation also provides a particularly appropriate framework for the consideration of natural and bio-inspired complex information processing systems [69,73,14]. Wegner first proposed a foundational approach to interactive computation [78].…”

Section: Historical Backgroundmentioning

confidence: 99%

“…In this chapter, we first review the main results concerning the Turing and superTuring capabilities of classical and interactive recurrent neural networks, and next provide a detailed proof of these last results stated in [9,14].…”

Section: Introductionmentioning

confidence: 95%

“…Finally, Cabessa proved that neural models combining the two crucial features of evolvability and interactivity were actually capable of super-Turing computational capabilities, irrespective of whether their synaptic weights are modeled by rational or real numbers [9,14].…”

Section: Introductionmentioning

confidence: 98%

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Recurrent Neural Networks and Super-Turing Interactive Computation

Cabessa

Villa

2015

Springer Series in Bio-/Neuroinformatics

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Abstract. We present a complete overview of the computational power of recurrent neural networks involved in an interactive bio-inspired computational paradigm. More precisely, we recall the results stating that interactive rational-and realweighted neural networks are Turing-equivalent and super-Turing, respectively. We further prove that interactive evolving neural networks are super-Turing, irrespective of whether their synaptic weights are modeled by rational or real numbers. These results show that the computational powers of neural nets involved in a classical or in an interactive computational framework follow similar patterns of characterization. They suggest that some intrinsic computational capabilities of the brain might lie beyond the scope of Turing-equivalent models of computation, hence surpass the potentialities every current standard artificial models of computation.

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Section: Computational Power Of Interactive Evolving Neural Networkmentioning

confidence: 68%