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 equations, reducing non-visual problems to geometric maps, modelling biological vision and other sensory-motor organs. CNN is not to be confused with convolutional neural networks (also colloquially called CNN). == CNN architecture == Due to their number and variety of architectures, it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as neurons or cells. Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of Continuous-Time CNN (CT-CNN) processors, but can be discrete, as in the case of Discrete-Time CNN (DT-CNN) processors. Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically real-valued, but can be complex or even quaternion, i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells. === Chua-Yang CNN === In the original Chua-Yang CNN (CY-CNN) processor, the state of the cell was a weighted sum of the inputs and the output was a piecewise linear function. However, like the original perceptron-based neural networks, the functions it could perform were limited: specifically, it was incapable of modeling non-linear functions, such as XOR. More complex functions are realizable via Non-Linear CNN (NL-CNN) processors. Cells are defined in a normed gridded space like two-dimensional Euclidean geometry. However, the cells are not limited to two-dimensional spaces; they can be defined in an arbitrary number of dimensions and can be square, triangle, hexagonal, or any other spatially invariant arrangement. Topologically, cells can be arranged on an infinite plane or on a toroidal space. Cell interconnect is local, meaning that all connections between cells are within a specified radius (with distance measured topologically). Connections can also be time-delayed to allow for processing in the temporal domain. Most CNN architectures have cells with the same relative interconnects, but there are applications that require a spatially variant topology, i.e. Multiple-Neighborhood-Size CNN (MNS-CNN) processors. Also, Multiple-Layer CNN (ML-CNN) processors, where all cells on the same layer are identical, can be used to extend the capability of CNN processors. The definition of a system is a collection of independent, interacting entities forming an integrated whole, whose behavior is distinct and qualitatively greater than its entities. Although connections are local, information exchange can happen globally through diffusion. In this sense, CNN processors are systems because their dynamics are derived from the interaction between the processing units and not within processing units. As a result, they exhibit emergent and collective behavior. Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor. When the coupling laws are modeled by fuzzy logic, it is a fuzzy CNN. When these laws are modeled by computational verb logic, it becomes a computational verb CNN. Both fuzzy and verb CNNs are useful for modelling social networks when the local couplings are achieved by linguistic terms. == History == The idea of CNN processors was introduced by Leon Chua and Lin Yang in 1988. In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). Leon Chua is still active in CNN research and publishes many of his articles in the International Journal of Bifurcation and Chaos, of which he is an editor. Both IEEE Transactions on Circuits and Systems and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors. In 1993, Tamas Roska and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world. The multi-national effort was funded by the Office of Naval Research, the National Science Foundation, and the Hungarian Academy of Sciences, and researched by the Hungarian Academy of Sciences and the University of California. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology. === 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. The paper provides a concise intro to definitions, CNN types, dynamics, implementations, and applications. "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 was also a workshop held in Santiago de Composetela, Spain. Topics included theory, design, applications, algorithms, physical implementations and programming and 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. == Related processing architectures == CNN processors could be thought of as a hybrid between artificial neural network (ANN) and Continuous Automata (CA). === Artificial Neural Networks === The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, dynamical systems, and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. However, in CNN processors, connections are made locally, whereas in ANN, connections are global. For example, 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 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
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