Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks

Ellias, Samuel; Grossberg, Stephen

doi:10.1007/bf00327046

Cited by 260 publications

(118 citation statements)

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“…Our concern herein is with global methods. A global analysis of equilibrium behavior is of importance for an understanding both of CAM and of the types of nonequilibrium behavior-such as traveling waves, bursts, standing waves, and chaos-which can be obtained by perturbing off systems which always approach equilibrium (Carpenter, 1977a(Carpenter, , 1977b(Carpenter, , 1979(Carpenter, , 1981Cohen & Grossberg, 1983;Ellias & Grossberg, 1975;Ermentrout & Cowan, 1979, 1980Hastings, 1976Hastings, , 1982Hodgson, 1983;Kaczmarek & Babloyantz, 1977). A global mathematical analysis of nonlinear associative learning networks was begun in Grossberg (1967Grossberg ( , 1968b.…”

Section: Principles Mechanisms and Architecfuresmentioning

confidence: 99%

“…In addition, the selfsignal function b;(y;) in (49) is not necessarily linear, notably because the feedback signal jj(x; -C;} is often nonlinear in applications of the shunting model; in particular it is often a sigmoid or multiple sigmoid signal function (Ellias & Grossberg, 1975;Grossberg, 1973Grossberg, , 1977Grossberg, , 1978cGrossberg & Levine, 1975;Sperling, 1981). Sigmoid signal functions, and approximations thereto, also appear in applications of the additive model and its variants (Ackney, Hinton, & Sejnowski, 1985;Amari & Arbib, 1982;Freeman, 1975Freeman, , 1979Grossberg, 1969aGrossberg, , 1982Grossberg & Kuperstein, 1986;Hinton & Anderson, 1981;Hopfield, 1984;.…”

Section: The Boltzmann Machinementioning

confidence: 99%

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Nonlinear neural networks: Principles, mechanisms, and architectures

1988

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Abstract-An historical discussion is provided of the intellectual trends that caused nineteenth century interdisciplinary studies of physics and psychobiology by leading scientists such as Helmholtz, Maxwell, and Mach to splinter into separate twentieth-century scientific movements. The nonlinear, nonstationary, and nonlocal nature of behavioral and brain data are emphasized. Three sources of contemporary neural network research-the binary, linear, and continuous-nonlinear models-are noted. The remainder of the article describes results about continuous-nonlinear models: Many models of content-addressable memory are shown to be special cases of the Cohen-Grossberg model and global Liapunov function, including the additive, brain-state-in-a-box, McCulloch-Pitts, Boltzmann machine, Hartline-Ratliff-Millet; shunting, maskingfield, bidirectional associative memory, Volterra-Lotka, Gilpin-Ayala, and Eigen-Schuster models. A Liapunov functional method is described for proving global limit or oscillation theorems for nonlinear competitive systems when their decision schemes are globally consistent or inconsistent, respectively. The former case is illustrated by a model of a globally stable economic market, and the latter case is illustrated by a model of the voting paradox. Key properties of shunting competitive feedback networks are summarized, including the role of sigmoid signalling, automatic gain control, competitive choice and quantization, tunable filtering, total activity normalization, and noise suppression in pattern transformation and memory storage applications. Connections to models of competitive learning, vector quantization, and categorical perception are noted. Adaptive resonance theory (ART) models for selJstabilizing adaptive pattern recognition in response to complex real-time nonstationary input environments are compared with off-line models such as autoassociators, the Boltzmann machine, and back propagation. Special attention is paid to the stability and capacity of these models, and to the role of top-down expectations and attentional processing in the active regulation of both learning and fast information processing. Models whose performance and learning are regulated by internal gating and matching signals, or by external environmentally generated error signals, are contrasted with models whose learning is regulated by external teacher signals that have no analog in natural real-time environments. Examples from sensory-motor control of adaptive vector encoders, adaptive coordinate transformations. adaptive gain control by visual error signals. and automatic generation of synchronous multijoint movement trajectories illustrate the former model types. Internal matching processes are shown capable of discovering several different types of inyariant environmental properties. These include ART mechanisms which discover recognition invariants. adaptive vector encoder mechanisms which discover movement invariants. and autoreceptive associative mechanisms which discover invariants of selJregulating t...

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Section: Principles Mechanisms and Architecfuresmentioning

confidence: 99%

Section: The Boltzmann Machinementioning

confidence: 99%

Nonlinear neural networks: Principles, mechanisms, and architectures

1988

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“…That is, the network makes an orientational choice at each active position. The design of the CC loop is based upon theorems that characterize the factors that enable contrastenhancement and choices to occur within nonlinear cooperative-competitive feedback networks (Ellias & Grossberg, 1975;Grossberg, 1973;Grossberg & Levine, 1975).…”

Section: Localmentioning

confidence: 99%

Neural dynamics of perceptual grouping: Textures, boundaries, and emergent segmentations

Grossberg

Mingolla

1985

Perception & Psychophysics

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757

172

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A real-time visual processing theory is used to analyze and explain a wide variety of perceptual grouping and segmentation phenomena, including the grouping of textured images, randomly defined images, and images built up from periodic scenic elements. The theory explains how "local" feature processing and "emergent" features work together to segment a scene, how segmentations may arise across image regions that do not contain any luminance differences, how segmentations may override local image properties in favor of global statistical factors, and why segmentations that powerfully influence object recognition may be barely visible or totally invisible. Network interactions within a Boundary Contour (BC) System, a Feature Contour (FC) System, and an Object Recognition (OR) System are used to explain these phenomena. The BC System is defined by a hierarchy of orientationally tuned interactions, which can be divided into two successive subsystems called the OC filter and the CC loop. The OC filter contains two successive stages of oriented receptive fields which are sensitive to different properties of image contrasts. The OC filter generates inputs to the CC loop, which contains successive stages of spatially short-range competitive interactions and spatially long-range cooperative interactions. Feedback between the competitive and cooperative stages synthesizes a global context-sensitive segmentation from among the many possible groupings of local featural elements. The properties of the BC System provide a unified explanation of several ostensibly different Gestalt rules. The BC System also suggests explanations and predictions concerning the architecture of the striate and prestriate visual cortices. The BC System embodies new ideas concerning the foundations of geometry, on-line statistical decision theory, and the resolution of uncertainty in quantum measurement systems. Computer simulations establish the formal competence of the BC System as a perceptual grouping system. The properties of the BC System are compared with probabilistic and artificial intelligence models of segmentation. The total network suggests a new approach to the design of computer vision systems, and promises to provide a universal set of rules for perceptual grouping of scenic edges, textures, and smoothly shaded regions.

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“…A similar computational model utilizing coupled oscillators was investigated earlier by Grossberg and Somers (1991). (See Ellias and Grossberg (1975) for an analysis of the dynamic properties of such networks.) This model, however, utilized only one-dimensional chains of oscillators in order to study binding properties as observed in previous physiological ndings of stimulus-evoked synchronized oscillatory ring by E c khorn et al (1998) and Gray et al (1989).…”

Section: Other Modelsmentioning

confidence: 96%

Computational Neural Models of Spatial Integration in Perceptual Grouping

Neumann

Mingolla

2001

From Fragments to Objects - Segmentation and Grouping in Vision

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Recent developments in the neural computational modeling of perceptual grouping are described with reference to a newly proposed taxonomy to formalize mechanisms of spatial integration. This notational framework and nomenclature is introduced in order to clarify key properties common to all or most models, while permitting unique attributes of each approach to be independently examined. The strength of spatial integration in the models that are considered is always some function of the distances and relative alignments in perceptual space of the centers of units representing orientational features or energy in a visual scene. We discuss the signi cance of variations of the constituents of an activation function for spatial integration, and also consider the larger modeling framework in which this function is applied in each approach. We also discuss the relationship of feedforward and feedback m e c hanisms and the issues of self-organization as core principles underlying the establishment of spatial integration mechanisms. The relationship of the grouping models to models of other visual competencies is considered with respect to prospects for future research.

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Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks

Cited by 260 publications

References 27 publications

Nonlinear neural networks: Principles, mechanisms, and architectures

Nonlinear neural networks: Principles, mechanisms, and architectures

Neural dynamics of perceptual grouping: Textures, boundaries, and emergent segmentations

Computational Neural Models of Spatial Integration in Perceptual Grouping

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