The CNN is universal as the Turing machine

Chua, Leon O.; Roska, Tamás; Venetianer, P.L.

doi:10.1109/81.224308

Cited by 54 publications

(24 citation statements)

References 6 publications

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“…As opposed to numerous architectures (especially implemented on reconfigurable hardware), our design is not application-specific but universal in terms of a Turing machine [11] and particularly suitable for low-level image processing. In [7] the performance of the NERO architecture has been compared to other analogue and digital designs that either implement the CNN-UM or support CNN-like computing [15,30].…”

Section: Comparisonmentioning

confidence: 99%

NEROvideo: a general-purpose CNN-UM video processing system

Müller

Tetzlaff

2014

J Real-Time Image Proc

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Emulations of cellular nonlinear networks (CNN) on digital reconfigurable hardware have proved to be adequate for highly-efficient computation of massive data, exceeding the accuracy and flexibility of full-custom designs. Based on a recently-proposed architecture for the emulation of a largescale CNN universal machine, a new real-time video processing system has been developed. Due to its free programmability and massively-parallel architecture the system is very suitable for high-speed computation of complex algorithms that follow the idea of spatio-temporal computing. Implemented on a stateof-the-art Xilinx Zynq system-on-chip, the proposed setup is capable of processing a 640 Â 480p video stream with up to 1,700 fps, depending on the respective algorithm.

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Section: Comparisonmentioning

confidence: 99%

NEROvideo: a general-purpose CNN-UM video processing system

Müller

Tetzlaff

2014

J Real-Time Image Proc

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“…The CNN is an array of analog dynamical cells performing parallel continuous-time processing, effectively solving a system of coupled ordinary differential equations (ODEs) with programmable coupling parameters. Roska and Chua proved the CNN to be at least as universal as a Turing machine [16].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Continuous-Time Neural Networks without Local Traps for Solving Constraint Satisfaction Problems

Molnár

Ercsey-Ravasz

2013

PLoS ONE

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There has been a long history of using neural networks for combinatorial optimization and constraint satisfaction problems. Symmetric Hopfield networks and similar approaches use steepest descent dynamics, and they always converge to the closest local minimum of the energy landscape. For finding global minima additional parameter-sensitive techniques are used, such as classical simulated annealing or the so-called chaotic simulated annealing, which induces chaotic dynamics by addition of extra terms to the energy landscape. Here we show that asymmetric continuous-time neural networks can solve constraint satisfaction problems without getting trapped in non-solution attractors. We concentrate on a model solving Boolean satisfiability (k-SAT), which is a quintessential NP-complete problem. There is a one-to-one correspondence between the stable fixed points of the neural network and the k-SAT solutions and we present numerical evidence that limit cycles may also be avoided by appropriately choosing the parameters of the model. This optimal parameter region is fairly independent of the size and hardness of instances, this way parameters can be chosen independently of the properties of problems and no tuning is required during the dynamical process. The model is similar to cellular neural networks already used in CNN computers. On an analog device solving a SAT problem would take a single operation: the connection weights are determined by the k-SAT instance and starting from any initial condition the system searches until finding a solution. In this new approach transient chaotic behavior appears as a natural consequence of optimization hardness and not as an externally induced effect.

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“…Figure 2 shows the universal machine on flows (UMF) diagram of the algorithm. It is a special flowchart description of the algorithms executable on CNN-UM so that it is complete and unique [20]. Templates AND, OR denote elementary logic, AND-NOT performs logic subtraction (Op1 ∧ ¬Op2), DIL4 and ERODE4 are the four connected dilatation and erosion (spatial logic).…”

Section: A Case Study On Cnn-ummentioning

confidence: 99%

“…The CNN universal machine (CNN-UM) [20] is a virtual machine construct like the Turing machine. It is Turing complete and it is universal in the sense that a CNN-UM can present all the behaviors that a predefined CNN dynamics can show.…”

Section: Cnn Universal Machinementioning

confidence: 99%

Initial condition for efficient mapping of level set algorithms on many-core architectures

Tornai

Cserey

2014

EURASIP J. Adv. Signal Process.

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In this paper, we investigated the effect of adding more small curves to the initial condition which determines the required number of iterations of a fast level set (LS) evolution. As a result, we discovered two new theorems and developed a proof on the worst case of the required number of iterations. Furthermore, we found that these kinds of initial conditions fit well to many-core architectures. To show this, we have included two case studies which are presented on different platforms. One runs on a graphical processing unit (GPU) and the other is executed on a cellular nonlinear network universal machine (CNN-UM). With the new initial conditions, the steady-state solutions of the LS are reached in less than eight iterations depending on the granularity of the initial condition. These dense iterations can be calculated very quickly on many-core platforms according to the two case studies. In the case of the proposed dense initial condition on GPU, there is a significant speedup compared to the sparse initial condition in all cases since our dense initial condition together with the algorithm utilizes the properties of the underlying architecture. Therefore, greater performance gain can be achieved (up to 18 times speedup compared to the sparse initial condition on GPU). Additionally, we have validated our concept against numerically approximated LS evolution of standard flows (mean curvature, Chan-Vese, geodesic active regions). The dice indexes between the fast LS evolutions and the evolutions of the numerically approximated partial differential equations are in the range of 0.99 ± 0.003.

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The CNN is universal as the Turing machine

Cited by 54 publications

References 6 publications

NEROvideo: a general-purpose CNN-UM video processing system

NEROvideo: a general-purpose CNN-UM video processing system

Asymmetric Continuous-Time Neural Networks without Local Traps for Solving Constraint Satisfaction Problems

Initial condition for efficient mapping of level set algorithms on many-core architectures

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