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In [[computer science]] and [[machine learning]], '''cellular neural networks (CNN)''' or '''cellular nonlinear networks (CNN)''' are a [[parallel computing]] paradigm similar to [[neural networks]], with the difference that communication is allowed between neighbouring units only. Typical applications include [[image processing]], analyzing 3D surfaces, solving [[partial differential equation]]s, reducing non-visual problems to [[Geometry|geometric]] maps, modelling biological [[visual system|vision]] and other [[Sensory-motor coupling|sensory-motor]] organs.<ref>{{Cite book|last=Slavova|first=A.|url=https://books.google.com/books?id=bt4PUx8CZXIC&q=Cellular+neural+network|title=Cellular Neural Networks: Dynamics and Modelling|date=2003-03-31|publisher=Springer Science & Business Media|isbn=978-1-4020-1192-4|language=en}}</ref>
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=== Literature ===
Two references are considered invaluable since they manage to organize the vast amount of CNN literature into a coherent framework:
* An overview by Valerio Cimagalli and Marco Balsi.<ref>[http://docshare02.docshare.tips/files/23993/239937185.pdf Cellular Neural Networks: A Review] (Neural Nets WIRN Vietri 1993)</ref> The paper provides a concise intro to definitions, CNN types, dynamics, implementations, and applications.
The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature. The proceedings are available online, via [[IEEE Xplore]], for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006. There is also a workshop being held on July 14–16 in Santiago de Composetela, Spain. Topics include theory, design, applications, algorithms, physical implementations and programming/training methods. For an understanding of the analog [[semiconductor]] based CNN technology, AnaLogic Computers has their product line, in addition to the published articles available on their homepage and their publication list. They also have information on other CNN technologies such as optical computing. Many of the commonly used functions have already been implemented using CNN processors. A good reference point for some of these can be found in image processing libraries for CNN based visual computers such as Analogic’s CNN-based systems.▼
* "Cellular Neural Networks and Visual Computing Foundations and Applications", written by Leon Chua and Tamas Roska, which provides examples and exercises. The book covers many different aspects of CNN processors and can serve as a textbook for a Masters or Ph.D. course.
Other resources include
* The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature.
* The proceedings are available online, via [[IEEE Xplore]], for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006.
* There is also a workshop held on 2020 July 14–16 in Santiago de Composetela, Spain. Topics include theory, design, applications, algorithms, physical implementations and programming and training methods.
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==Related processing architectures==
{{Section citations needed|date=December 2020}}
CNN processors could be thought of as a hybrid between [[Artificial neural network|ANN]] and [[Continuous automaton|Continuous Automata]] (CA). The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, [[Dynamical system|dynamical systems]], and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. The main discriminator is that in CNN processors, connections are made locally, whereas in ANN, connections are global. For example, [[Neuron|neurons]] in one layer are fully connected to another layer in a feed-forward NN and all the neurons are fully interconnected in [[Hopfield networks]]. In ANNs, the weights of interconnections contain information on the processing system’s previous state or feedback, but in CNN processors, the weights are used to determine the dynamics of the system. Furthermore, due to the high inter-connectivity of ANNs, they tend not exploit locality in either the data set or the processing and as a result, they usually are highly redundant systems that allow for [[Robustness|robust]], fault-tolerant behavior without catastrophic errors. A cross between an ANN and a CNN processor is a Ratio Memory CNN (RMCNN). In RMCNN processors, the cell interconnect is local and topologically invariant, but the weights are used to store previous states and not to control dynamics. The weights of the cells are modified during some learning state creating long-term memory.
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==Model of computation==
{{Section citations needed|date=December 2020}}
The dynamical behaviors of CNN processors can be expressed mathematically as a series of ordinary [[differential equations]], where each equation represents the state of an individual processing unit. The behavior of the entire CNN processor is defined by its initial conditions, the inputs, the cell interconnect (topology and weights), and the cells themselves. One possible use of CNN processors is to generate and respond to signals of specific dynamical properties. For example, CNN processors have been used to generate multi-scroll chaos, [[Synchronization|synchronize]] with chaotic systems, and exhibit multi-level hysteresis. CNN processors are designed specifically to solve local, low-level, processor intensive problems expressed as a function of space and time. For example, CNN processors can be used to implement high-pass and low-pass filters and [[Mathematical morphology|morphological]] operators. They can also be used to approximate a wide range of [[Partial differential equations]] (PDE) such as heat dissipation and wave propagation.
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==Technology==
{{Section citations needed|date=December 2020}}
An information processing platform remains nothing more than an intellectual exercise unless it can be implemented in hardware and integrated into a system. Although processors based on [[Billiard ball|billiard balls]] can be interesting, unless their implementation provides advantages for a system, the only purpose they serve is as a teaching device. CNN processors have been implemented using current technology and there are plans to implement CNN processors into future technologies. They include the necessary interfaces for programming and interfacing, and have been implemented in a variety of systems. What follows is a cursory examination of the different types of CNN processors available today, their advantages and disadvantages, and the future roadmap for CNN processors.
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==Applications==
{{Section citations needed|date=December 2020}}
The philosophy, interests, and methodologies of CNN researchers are varied. Due to the potential of the CNN architecture, this platform has attracted people from a variety of backgrounds and disciplines. Some are exploring practical implementations of CNN processors, others are using CNN processors to model physical phenomena, and there are even researchers exploring theoretical mathematical, computational, and philosophical ideas through CNN processors. Some applications are engineering related, where some known, understood behavior of CNN processors is exploited to perform a specific task, and some are scientific, where CNN processors are used to explore new and different phenomenon. CNN processors are versatile platforms that are being used for a variety of applications.
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CNN processors are [[Neuromorphic engineering|neuromorphic]] processors, meaning that they emulate certain aspects of [[biological neural network]]s. The original CNN processors were based on mammalian retinas, which consist of a layer of [[Photodetector|photodetectors]] connected to several layers of locally coupled neurons. This makes CNN processors part of an interdisciplinary research area whose goal is to design systems that leverage knowledge and ideas from neuroscience and contribute back via real-world validation of theories. CNN processors have implemented a real-time system that replicates mammalian retinas, validating that the original CNN architecture chosen modeled the correct aspects of the biological neural networks used to perform the task in mammalian life. However, CNN processors are not limited to verifying biological neural networks associated with vision processing; they have been used to simulate dynamic activity seen in mammalian neural networks found in the olfactory bulb and locust [[antennal lobe]], responsible for pre-processing sensory information to detect differences in repeating patterns.
CNN processors are being used to understand systems that can be modeled using simple, coupled units, such as living cells, biological networks, physiological systems, and ecosystems. The CNN architecture captures some of the dynamics often seen in nature and is simple enough to analyze and conduct experiments. They are also being used for [[stochastic]] simulation techniques, which allow scientists to explore spin problems, population dynamics, lattice-based gas models, [[percolation]], and other phenomena. Other simulation applications include heat transfer, mechanical vibrating systems, protein production, Josephson Transmission Line (JTL) problems, seismic wave propagation, and geothermal structures. Instances of 3D (Three Dimensional) CNN have been used to prove known complex shapes are emergent phenomena in complex systems, establishing a link between art, dynamical systems and VLSI technology. CNN processors have been used to research a variety of mathematical concepts, such as researching non-equilibrium systems, constructing non-linear systems of arbitrary complexity using a collection of simple, well-understood dynamic systems, studying emergent chaotic dynamics, generating chaotic signals, and in general discovering new dynamic behavior. They are often used in researching systemics, a trandisiplinary, scientific field that studies natural systems. The goal of systemics researchers is to develop a conceptual and mathematical framework necessary to analyze, model, and understand systems, including, but not limited to, atomic, mechanical, molecular, chemical, biological, ecological, social and economic systems. Topics explored are emergence, collective behavior, local activity and its impact on global behavior, and quantifying the complexity of an approximately spatial and topologically invariant system
==Notes==
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