Evolving recurrent neural networks are super-Turing

Cabessa, Jérémie; Siegelmann, Hava T.

doi:10.1109/ijcnn.2011.6033645

Cited by 24 publications

(22 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this context, static rational RNNs were proven to be Turing equivalent [60], whereas static real (or analog) RNNs were proven to be super-Turing [59]. Furthermore, evolving RNNs were shown to be also super-Turing, irrespective of whether their synaptic weights are modeled by rational or real numbers [10]. The three following theorems state these results in details.…”

Section: Computational Power Of Classical Neural Networkmentioning

confidence: 91%

“…Thirdly, evolving RNNs were shown to be also super-Turing, irrespective of whether their synaptic weights are modeled by rational or real numbers [10]. Hence, the translation from static rational to the evolving rational context does also bring up additional computational power to the networks.…”

Section: Theorem 2 St-rnn[r]s Are Super-turing More Precisely Any mentioning

confidence: 98%

“…Besides, Cabessa and Siegelmann introduced the model of an evolving recurrent neural network (Ev-RNN) as a RNN whose synaptic weights have the possibility to evolve over time rather than remaining static [10]. Formally, an evolving recurrent neural network (Ev-RNN) consists of an RNN whose dynamics is given by the following equation:…”

Section: Recurrent Neural Networkmentioning

confidence: 99%

“…Hence, similarly to the Turing machine model which represents a definitely relevant conceptualization of current algorithmic, the interactive Turing machine with advice model also seems to encompass a particularly suitable conceptualization of brain computation, or even of natural computation in general [55,7,73], since it is capable to capture crucial features, like analogue considerations [60], evolvability [10,9,14], chaotic behaviors [63], that are impossible to be achieved via the simple Turing machine model.…”

Section: Theorem 7 the Four Models Of Computations That Are I-st-rnnmentioning

confidence: 99%

“…From a theoretical perspective, Turova and Villa showed that neural networks with embedded spike timing-dependent plasticity are able to exhibit a sustained level of activity under special choice of parameters [66,67]. More recently, Cabessa and Siegelmann, introduced and studied the computational capabilities of a biologically oriented neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve rather than stay static [10]. They proved that the so-called evolving recurrent neural networks are super-Turing, equivalent to static analog networks, irrespective of whether their synaptic weights are modeled by rational or real numbers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Recurrent Neural Networks and Super-Turing Interactive Computation

Cabessa

Villa

2015

Springer Series in Bio-/Neuroinformatics

View full text Add to dashboard Cite

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.

show abstract

Section: Computational Power Of Classical Neural Networkmentioning

confidence: 91%

Section: Theorem 2 St-rnn[r]s Are Super-turing More Precisely Any mentioning

confidence: 98%

Section: Recurrent Neural Networkmentioning

confidence: 99%

Section: Theorem 7 the Four Models Of Computations That Are I-st-rnnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recurrent Neural Networks and Super-Turing Interactive Computation

Cabessa

Villa

2015

Springer Series in Bio-/Neuroinformatics

View full text Add to dashboard Cite

show abstract

Can Biological Quantum Networks Solve NP‐Hard Problems?

Wendin

2019

Adv Quantum Tech

View full text Add to dashboard Cite

There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines, let alone ordinary classical computers. During the last decades the question has therefore been raised whether it is needed to consider quantum effects to explain the imagined cognitive power of a conscious mind. Not surprisingly, the conclusion is that quantum‐enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence signaling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. The conclusion is that biological quantum networks can only approximately solve small instances of nonpolynomial (NP)‐hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to solve NP‐hard problems approximately. In the end it is a question of precision—Nature is approximate.

show abstract

Interactive Evolving Recurrent Neural Networks Are Super-Turing Universal

Cabessa

Villa

2014

Artificial Neural Networks and Machine Learning – ICANN 2014

View full text Add to dashboard Cite

Evolving recurrent neural networks are super-Turing

Cited by 24 publications

References 7 publications

Recurrent Neural Networks and Super-Turing Interactive Computation

Recurrent Neural Networks and Super-Turing Interactive Computation

Can Biological Quantum Networks Solve NP‐Hard Problems?

Interactive Evolving Recurrent Neural Networks Are Super-Turing Universal

Contact Info

Product

Resources

About