Stephen Grossberg

Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps

A neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors, which may represent fuzzy or crisp sets of features. The architecture, called fuzzy ARTMAP, achieves a synthesis of fuzzy logic and adaptive resonance theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Four classes of simulation illustrated fuzzy ARTMAP performance in relation to benchmark backpropagation and generic algorithm systems. These simulations include finding points inside versus outside a circle, learning to tell two spirals apart, incremental approximation of a piecewise-continuous function, and a letter recognition database. The fuzzy ARTMAP system is also compared with Salzbergs NGE systems and with Simpsons FMMC system.

Absolute stability of global pattern formation and parallel memory storage by competitive neural networks

Systems that are competitive and possess symmetric interactions admit a global Lyapunov function. However, a global Lyapunov function whose equilibrium set can be effectively analyzed has not yet been discovered. It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the Lyapunov functional approach, which sidesteps a direct study of equilibrium points will ultimately handle all of the physically important cases.

System for self-organization of stable category recognition codes for analog input patterns

Adaptive resonance architectures are neural networks that self-organize stable pattern recognition codes in real-time in response to arbitrary sequences of input patterns. This article introduces ART 2, a class of adaptive resonance architectures which rapidly self-organize pattern recognition categories in response to arbitrary sequences of either analog or binary input patterns. In order to cope with arbitrary sequences of analog input patterns-ART 2 architectures embody solutions to a number of design principles, such as the stability-plasticity tradeoff, the search-direct access tradeoff, and the match-reset tradeoff. In these architectures, top-down learned expectation and matching mechanisms are critical in self-stabilizing the code learning process. A parallel search scheme updates itself adaptively as the learning process unfolds, and realizes a form of real-time hypothesis discovery, testing, learning, and recognition. After learning selfstabilizes, the search process is automatically disengaged. Thereafter input patterns directly access their recognition codes without any search. Thus recognition time for familiar inputs does not increase with the complexity of the learned code. A novel input pattern can directly access a category if it shares invariant properties with the set of familiar exemplars of that category. A parameter called the attentional vigilance parameter determines how fine the categories will be. If vigilance increases (decreases) due to environmental feedback, then the system automatically searches for and learns finer (coarser) recognition categories. Gain control parameters enable the architecture to suppress noise up to a prescribed level. The architectures global design enables it to learn effectively despite the high degree of nonlinearity of such mechanisms.

A massively parallel architecture for a self-organizing neural pattern recognition machine

A neural network architecture for the learning of recognition categories is derived. Real-time network dynamics are completely characterized through mathematical analysis and computer simulations. The architecture self-organizes and self-stabilizes its recognition codes in response to arbitrary orderings of arbitrarily many and arbitrarily complex binary input patterns. Top-down attentional and matching mechanisms are critical in self-stabilizing the code learning process. The architecture embodies a parallel search scheme which updates itself adaptively as the learning process unfolds. After learning self-stabilizes, the search process is automatically disengaged. Thereafter input patterns directly access their recognition codes without any search. Thus recognition time does not grow as a function of code complexity. A novel input pattern can directly access a category if it shares invariant properties with the set of familiar exemplars of that category. These invariant properties emerge in the form of learned critical feature patterns, or prototypes. The architecture possesses a context-sensitive self-scaling property which enables its emergent critical feature patterns to form. They detect and remember statistically predictive configurations of featural elements which are derived from the set of all input patterns that are ever experienced. Four types of attentional process—priming, gain control, vigilance, and intermodal competition—are mechanistically characterized. Top—down priming and gain control are needed for code matching and self-stabilization. Attentional vigilance determines how fine the learned categories will be. If vigilance increases due to an environmental disconfirmation, then the system automatically searches for and learns finer recognition categories. A new nonlinear matching law (the ⅔ Rule) and new nonlinear associative laws (the Weber Law Rule, the Associative Decay Rule, and the Template Learning Rule) are needed to achieve these properties. All the rules describe emergent properties of parallel network interactions. The architecture circumvents the noise, saturation, capacity, orthogonality, and linear predictability constraints that limit the codes which can be stably learned by alternative recognition models.

Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors

This paper analyses a model for the parallel development and adult coding of neural feature detectors. The model was introduced in Grossberg (1976). We show how experience can retune feature detectors to respond to a prescribed convex set of spatial patterns. In particular, the detectors automatically respond to average features chosen from the set even if the average features have never been experienced. Using this procedure, any set of arbitrary spatial patterns can be recoded, or transformed, into any other spatial patterns (universal recoding), if there are sufficiently many cells in the networks cortex. The network is built from short term memory (STM) and long term memory (LTM) mechanisms, including mechanisms of adaptation, filtering, contrast enhancement, tuning, and nonspecific arousal. These mechanisms capture some experimental properties of plasticity in the kitten visual cortex. The model also suggests a classification of adult feature detector properties in terms of a small number of functional principles. In particular, experiments on retinal dynamics, including amarcrine cell function, are suggested.

Nonlinear neural networks: Principles, mechanisms, and architectures ☆ ☆☆

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-Miller, shunting, masking field, 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 self-stabilizing 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 invariant 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 self-regulating target position maps.

ARTMAP: Supervised real-time learning and classification of nonstationary data by a self-organizing neural network

Abstract This article introduces a new neural network architecture, called ARTMAP, that autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success. This supervised learning system is built up from a pair of Adaptive Resonance Theory modules (ARTa and ARTb) that are capable of self-organizing stable recognition categories in response to arbitrary sequences of input patterns. During training trials, the ARTa module receives a stream [a(p)] of input patterns, and ARTb receives a stream [b(p)] of input patterns, where b(p) is the correct prediction given a(p). These ART modules are linked by an associative learning network and an internal controller that ensures autonomous system operation in real time. During test trials, the remaining patterns a(p) are presented without b(p), and their predictions at ARTb are compared with b(p). Tested on a benchmark machine learning database in both on-line and off-line simulations, the ARTMAP system learns orders of magnitude more quickly, efficiently, and accurately than alternative algorithms, and achieves 100% accuracy after training on less than half the input patterns in the database. It achieves these properties by using an internal controller that conjointly maximizes predictive generalization and minimizes predictive error by linking predictive success to category size on a trial-by-trial basis, using only local operations. This computation increases the vigilance parameter ϱa of ARTa by the minimal amount needed to correct a predictive error at ARTb. Parameter ϱa calibrates the minimum confidence that ARTa must have in a category, or hypothesis, activated by an input a(p) in order for ARTa to accept that category, rather than search for a better one through an automatically controlled process of hypothesis testing. Parameter ϱa is compared with the degree of match between a(p) and the top-down learned expectation, or prototype, that is read-out subsequent to activation of an ARTa category. Search occurs if the degree of match is less than ϱa. ARTMAP is hereby a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success. As a result, rare but important events can be quickly and sharply distinguished even if they are similar to frequent events with different consequences. Between input trials ϱa relaxes to a baseline vigilance ϱ a . When ϱ a is large, the system runs in a conservative mode, wherein predictions are made only if the system is confident of the outcome. Very few false-alarm errors then occur at any stage of learning, yet the system reaches asymptote with no loss of speed. Because ARTMAP learning is self-stabilizing, it can continue learning one or more databases, without degrading its corpus of memories, until its full memory capacity is utilized.

Adaptive pattern classification and universal recoding: II. Feedback, expectation, olfaction, illusions

Part I of this paper describes a model for the parallel development and adult coding of neural feature detectors. It shows how any set of arbitrary spatial patterns can be recoded, or transformed, into any other spatial patterns (universal recoding), if there are sufficiently many cells in the networks cortex. This code is, however, unstable through time if arbitrarily many patterns can perturb a fixed number of cortical cells. This paper shows how to stabilize the code in the general case using feedback between cellular sites. A biochemically defined critical period is not necessary to stabilize the code, nor is it sufficient to ensure useful coding properties.We ask how short term memory can be reset in response to temporal sequences of spatial patterns. This leads to a context-dependent code in which no feature detector need uniquely characterize an input pattern; yet unique classification by the pattern of activity across feature detectors is possible. This property uses learned expectation mechanisms whereby unexpected patterns are temporarily suppressed and/or activate nonspecific arousal. The simplest case describes reciprocal interactions via trainable synaptic pathways (long term memory traces) between two recurrent on-center off-surround networks undergoing mass action (shunting) interactions. This unit can establish an adaptive resonance, or reverberation, between two regions if their coded patterns match, and can suppress the reverberation if their patterns do not match. This concept yields a model of olfactory coding within the olfactory bulb and prepyriform cortex. The resonance idea also includes the establishment of reverberation between conditioned reinforcers and generators of contingent negative variation if presently avialable sensory cues are compatible with the networks drive requirements at that time; and a search and lock mechanism whereby the disparity between two patterns can be minimized and the minimal disparity images locked into position. Stabilizing the code uses attentional mechanisms, in particular nonspecific arousal as a tuning and search device. We suggest that arousal is gated by a chemical transmitter system—for example, norepinephrine—whose relative states of accumulation at antagonistic pairs of on-cells and off-cells through time can shift the spatial pattern of STM activity across a field of feature detectors. For example, a sudden arousal increment in response to an un-expected pattern can reverse, or rebound, these relative activities, thereby suppressing incorrectly classified populations. The rebound mechanism has formal properties analogous to negative afterimages and spatial frequency adaptation.

NEURAL DYNAMICS OF PERCEPTUAL GROUPING: TEXTURES, BOUNDARIES, AND EMERGENT SEGMENTATIONS

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 founda-tions of geometry, on-line statistical decision theory, and the resolution of uncertainty in quan-tum 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.

Competitive Learning: From Interactive Activation to Adaptive Resonance

Functional ond mechanistic comparisons are mode between several network models of cognitive processing: competitive learning, interactive activation, adaptive resonance, and back propagation. The starting point of this comparison is the article of Rumelhart ond Zipser (1985) on feature discovery through competitive learning. All the models which Rumelhart and Zipser (1985) have described were shown in Grossberg (1976b) to exhibit a type of learning which is temporally unstable. Competitive learning mechanisms con be stabilized in response to an arbitrary input environment by being supplemented with mechanisms for learning top-down expectancies, or templates; for matching bottom-up input patterns with the top-down expectancies; and for releasing orienting reactions in o mismatch situation, thereby updating short-term memory ond searching for another internal representation. Network architectures which embody all of these mechonisms were called adaptive resonance models by Grossberg (1976~). Self-stabilizing learning models are candidates for use in real-world applications where unpredictable changes can occur in complex input environments. Competitive learning postulates ore inconsistent with the postulates of the interactive activotion model of McClelland and Rumelhart (1981). and suggest different levels of processing and interaction rules for the analysis of word recognition. Adaptive resonance models use these alternative levels and interaction rules. The selforganizing learning of on odaptive resonance model is compared ond contrasted with the teacher-directed learning of a back propagation model. A number of criteria for evaluating reol-time network models of cognitive processing ore described and applied.