This article surveys the development of mathematical laws, circuits, and architectures that model how our brains make our minds, and shows how these contributions provide a blueprint for developing general-purpose autonomous adaptive algorithms and robots for intelligent applications in engineering and technology. The mathematical laws for short-term memory, medium-term memory, and long-term memory that provide the contemporary foundation for all subsequent biological neural network models were published in 1968, followed by a steady stream of model discovery and development to the present time. The Cohen-Grossberg model and theorem that was published in this journal in 1983 was one step in this series of developments. It proved global limit theorems for a general class of neural networks using a Lyapunov function as one tool. These theorems provide a guarantee that learning in these networks generates stable memories. This article surveys additional mathematical foundations for neural network design and applications and describes a modeling method for the incremental discovery of models with increasingly powerful and general functional capabilities. This method is illustrated by the adaptive resonance theory, or ART, architectures which explain how our brains autonomously learn to attend, recognize, and predict objects and events in a changing world, along the way explaining how our brains become conscious, as well as the computational constraints on learning that forced evolution to discover conscious states of mind. Multiple types of resonances support different kinds of conscious awareness and enable the explanation and prediction of large psychological and neurobiological databases about perception, cognition, emotion, and action. Because ART can be derived from a thought experiment about a universal problem of error correction in a changing world, its expanding applications to the development of autonomously intelligent systems should transform future technologies.

The hard problem of consciousness is the problem of explaining how we experience qualia or phenomenal experiences, such as seeing, hearing, and feeling, and knowing what they are. To solve this problem, a theory of consciousness needs to link brain to mind by modeling how emergent properties of several brain mechanisms interacting together embody detailed properties of individual conscious psychological experiences. This article summarizes evidence that Adaptive Resonance Theory, or ART, accomplishes this goal. ART is a cognitive and neural theory of how advanced brains autonomously learn to attend, recognize, and predict objects and events in a changing world. ART has predicted that "all conscious states are resonant states" as part of its specification of mechanistic links between processes of consciousness, learning, expectation, attention, resonance, and synchrony. It hereby provides functional and mechanistic explanations of data ranging from individual spikes and their synchronization to the dynamics of conscious perceptual, cognitive, and cognitive-emotional experiences. ART has reached sufficient maturity to begin classifying the brain resonances that support conscious experiences of seeing, hearing, feeling, and knowing. Psychological and neurobiological data in both normal individuals and clinical patients are clarified by this classification. This analysis also explains why not all resonances become conscious, and why not all brain dynamics are resonant. The global organization of the brain into computationally complementary cortical processing streams (complementary computing), and the organization of the cerebral cortex into characteristic layers of cells (laminar computing), figure prominently in these explanations of conscious and unconscious processes. Alternative models of consciousness are also discussed.

Behavioral economics and neuroeconomics concern how humans process multiple alternatives to make their decisions, and propose how discoveries about how the brain works can inform models of economic behavior. This lecture will survey how results about cooperative-competitive and cognitive-emotional dynamics that were discovered to better understand how brains control behavior can shed light on issues of importance in economics, including results about the voting paradox, how to design stable economic markets, irrational decision making under risk (Prospect Theory), probabilistic decision making, preferences for previously unexperienced alternatives over rewarded experiences, and bounded rationality.

This invited talk will begin with an appreciation of John Taylor and then present a review of classical and recent research results on topics that were of particular interest to John Taylor, notably neural models that contribute to our understanding of how attention and consciousness work. This extended abstract summarizes some of the main themes of the talk.

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic "neural relativity" that may clarify how episodic memories are learned.

Visually guided navigation through a cluttered natural scene is a challenging problem that animals and humans accomplish with ease. A neural model proposes how primates use motion information to segment objects and determine heading for purposes of goal approach and obstacle avoidance in response to video inputs from real and virtual environments. The model produces trajectories similar to those of human navigators by use of computationally complementary processes in its analogs of cortical areas MT-/MSTv and MT+/MSTd to determine object motion for tracking and self-motion for navigation, respectively. The model retina responds to transients in the input stream. Model V1 generates a local speed and direction estimate that is ambiguous due to the neural aperture problem. Model MT+ interacts with MSTd via an attentive feedback loop to compute accurate heading estimates in MSTd that quantitatively simulate properties of human heading estimation data. Model MT- interacts with MSTv via an attentive feedback loop to compute estimates of speed, direction and position of moving objects. This object information is combined with heading information to produce steering decisions wherein goals behave like attractors and obstacles behave like repellers. These steering decisions lead to navigational trajectories that closely match human performance.

This article summarizes recent progress towards understanding how the brain can intelligently scan a scene and use fast incremental unsupervised and supervised learning to learn scenic type and view-invariant representations of the objects within it.

This paper describes a self-organizing neural model that is capable of controlling the kinematics of robots with redundant degrees of freedom. The self-organized learning process is based on action perception cycles where the robot is perturbed minimally about a given joint configuration and learns to map these perturbations to changes in sensor readings corresponding to these minimal perturbations. This motor babbling phase provides self-generated movement commands that activate correlated sensory, spatial and motor information that are used to learn an internal coordinate transformation between sensory and motor systems. This idea was tested on two different tasks: reaching targets in 2-D space with a three degree of freedom robot and saccading to targets in 3-D with a twelve degree of freedom head-neck-eye system. Computer simulations show that the resulting controller is highly fault-tolerant and robust to previously unseen disturbances much like biological systems.

How do humans and animals learn to recognize objects and events? Two classical views are that exemplars or prototypes are learned. A hybrid view is that a mixture, called rule-plus-exceptions, is learned. None of these models learn their categories. A distributed ARTMAP neural network with self-supervised learning incrementally learns categories that match human learning data on a class of thirty diagnostic experiments called the 5-4 category structure. Key predictions of ART models have received behavioral, neurophysiological, and anatomical support. The ART prediction about what goes wrong during amnesic learning has also been supported: a lesion in its orienting system causes a low vigilance parameter.

The neocortex is the seat of all higher biological intelligence. All sensory and cognitive neocortex is organized into layered circuits. A recent family or LAMINART models proposes how these layered circuit embody bottom-up, top-down, and horizontal interactions within the visual cortex to generate percepts of visual form. Results to date quantitatively explain perceptual, anatomical, and neurophysiological data about cortical development, learning, attention, perceptual grouping, and 3D vision. This foundation is rapidly leading to discoveries of how other cortical areas are specialized to carry out different perceptual and cognitive tasks. The parsimony and power of the circuits is also leading to more efficient algorithms for computer vision.

The fuzzy ARTMAP neural network is used to classify data that is incomplete in one or more ways. These include a limited number of training cases, missing components, missing class labels, and missing classes. Modifications for dealing with such incomplete data are introduced, and performance is assessed on an emitter identification task using a database of radar pulses.

The visual cortex has a laminar organization whose circuits form functional columns in cortical maps. How this laminar architecture supports visual percepts is not well understood. A neural model proposes how the laminar circuits of V1 and V2 generate perceptual groupings that maintain sensitivity to the contrasts and spatial organization of scenic cues. The model can decisively choose which groupings cohere and survive, even while balanced excitatory and inhibitory interactions preserve contrast-sensitive measures of local boundary likelihood or strength. In the model, excitatory inputs from lateral geniculate nucleus (LGN) activate layers 4 and 6 of V1. Layer 6 activates an on-center off-surround network of inputs to layer 4. Together these layer 4 inputs preserve analog sensitivity to LGN input contrasts. Layer 4 cells excite pyramidal cells in layer 2/3, which activate monosynaptic long-range horizontal excitatory connections between layer 2/3 pyramidal cells, and short-range disynaptic inhibitory connections mediated by smooth stellate cells. These interactions support inward perceptual grouping between two or more boundary inducers, but not outward grouping from a single inducer. These boundary signals feed back to layer 4 via the layer 6-to-4 on-center off-surround network. This folded feedback joins cells in different layers into functional columns while selecting winning groupings. Layer 6 in V1 also sends top-down signals to LGN using an on-center off-surround network, which suppresses LGN cells that do not receive feedback, while selecting, enhancing, and synchronizing activity of those that do. The model is used to simulate psychophysical and neurophysiological data about perceptual grouping, including various Gestalt grouping laws.

A neural network system for boundary segmentation and surface representation, inspired by a new local-circuit model of visual processing in the cerebral cortex, is used to enhance images of range data gathered by a synthetic aperture radar (SAR) sensor. Boundary segmentation is accomplished by an improved Boundary Contour System (BCS) model which completes coherent boundaries that retain their sensitivity to image contrasts and locations. A Feature Contour System (FCS) model compensates for local contrast variations and uses the compensated signals to diffusively fill-in surface regions within the BCS boundaries. Image noise pixels that are not supported by BCS boundaries are hereby eliminated. More generally, BCS/FCS processing normalizes input dynamic range, reduces noise, and enhances contrasts between surface regions. BCS/FCS processing hereby makes structures such as motor vehicles, roads, and buildings more salient to human observers than in original imagery. The new BCS model improves image enhancement with significant reductions in processing time and complexity over previous BCS applications. The new system also outperforms several established techniques for image enhancement.

The What-and-Where filter forms part of a neural network architecture for spatial mapping, object recognition, and image understanding. The Where filter responds to an image figure that has been separated from its background. It generates a spatial map whose cell activations simultaneously represent the position, orientation, and size of all the figures in a scene (where they are). This spatial map may be used to direct spatially localized attention to these image features. A multiscale array of oriented detectors, followed by competitive and interpolative interactions between position, orientation, and size scales, is used to define the Where filter. This analysis discloses several issues that need to be dealt with by a spatial mapping system that is based upon oriented filters, such as the role of cliff filters with and without normalization, the double peak problem of maximum orientation across size scale, and the different self-similar interpolation properties across orientation than across size scale. Several computationally efficient Where filters are proposed. The Where filter may be used for parallel transformation of multiple image figures into invariant representations that are insensitive to the figures' original position, orientation, and size. These invariant figural representations form part of a system devoted to attentive object learning and recognition (what it is). Unlike some alternative models where serial search for a target occurs, a What and Where representation can be used to rapidly search in parallel for a desired target in a scene. Such a representation can also be used to learn multidimensional representations of objects and their spatial relationships for purposes of image understanding. The What-and-Where filter is inspired by neurobiological data showing that a Where processing stream in the cerebral cortex is used for attentive spatial localization and orientation, whereas a What processing stream is used for attentive object learning and recognition.

This article describes a self-organizing neural network architecture that transforms optic flow and eye position information into representations of heading, scene depth, and moving object locations. These representations are used to navigate reactively in simulations involving obstacle avoidance and pursuit of a moving target. The network's weights are trained during an action-perception cycle in which self-generated eye and body movements produce optic flow information, thus allowing the network to tune itself without requiring explicit knowledge of sensor geometry. The confounding effect of eye movement during translation is suppressed by learning the relationship between eye movement outflow commands and the optic flow signals that they induce. The remaining optic flow field is due to only observer translation and independent motion of objects in the scene. A self-organizing feature map categorizes normalized translational flow patterns, thereby creating a map of cells that code heading directions. Heading information is then recombined with translational flow patterns in two different ways to form maps of scene depth and moving object locations. Most of the learning processes take place concurrently and evolve through unsupervised learning. Mapping the learned heading representations onto heading labels or motor commands requires additional structure. Simulations of the network verify its performance using both noise-free and noisy optic flow information.

A neural model is developed of the neural circuitry in the reticular formation that is used to generate saccadic eye movements. The model simulates the behavior of identified cell types-such as long-lead burst neurons, short-lead excitatory and inhibitory burst neurons, omnipause neurons, and tonic neurons-under many experimental conditions. Simulated phenomena include: saccade staircases, duration and amplitude of cell discharges for saccades of variable amplitude, component stretching to achieve straight oblique saccades, saturation of saccade velocity after saturation of saccade amplitude in response to high stimulation frequencies, trade-offs between saccade velocity and duration to generate constant saccade amplitude, conservation of saccade amplitude in response to sufficiently brief stimulation of omnipause neurons, and high velocity smooth eye movements evoked by high levels of electrical stimulation of the superior colliculus. Previous saccade generator models have not explained this range of data. These models have also invoked mechanisms for which no neurophysiological evidence has been forthcoming, such as resetable integrators, perfect integrators, or target position movement commands. The present model utilizes only known reticular formation neurons. It suggests that a key part of the feedback loop within the saccade generator is realized by inhibitory feedback from short-lead to long-lead burst neurons, in response to excitatory feedforward signals from long-lead to short-lead burst neurons. When this property is combined with opponent interactions between agonist and antagonist muscle-controlling neurons, and motor error, or vector, inputs from the superior colliculus and other saccade-controlling brain regions, all of the above data can be explained. Taken together, these components generate a saccade reset cycle whereby activation of long-lead burst neurons inhibits omnipause neurons and thereby disinhibits short-lead excitatory burst neurons. The excitatory short-lead burst neurons can then respond to excitatory inputs from the long-lead burst neurons. Outputs from the excitatory short-lead burst neurons are integrated by the tonic cells while they also inhibit the long-lead burst neurons via inhibitory burst interneurons. When this inhibition is complete, the omnipause neurons are disinhibited. The omnipause neurons can then, once again, inhibit the short-lead burst neurons, whose inhibition of the long-lead burst neurons is thereby removed. The saccadic cycle can then begin again. In response to sustained electrical input, this cycle generates a staircase of identical saccades whose properties match the data much better than the staircases proposed by alternative models. A comparative analysis of the hypotheses and predictive capabilities of other saccade generator models is provided.

Prenatal development of the primary visual cortex leads to simple cells with spatially distinct and oriented ON and OFF subregions. These simple cells are organized into spatial maps of orientation and ocular dominance that exhibit singularities, fractures, and linear zones. On a finer spatial scale, simple cells occur that are sensitive to similar orientations but opposite contrast polarities, and exhibit both even-symmetric and odd-symmetric receptive fields. Pooling of outputs from oppositely polarized simple cells leads to complex cells that respond to both contrast polarities. A neural network model is described which simulates how simple and complex cells self-organize starting from unsegregated and unoriented geniculocortical inputs during prenatal development. Neighboring simple cells that are sensitive to opposite contrast polarities develop from a combination of spatially short-range inhibition and high-gain recurrent habituative excitation between cells that obey membrane equations. Habituation, or depression, of synapses controls reset of cell activations both through enhanced ON responses and OFF antagonistic rebounds. Orientation and ocular dominance maps form when high-gain medium-range recurrent excitation and long-range inhibition interact with the short-range mechanisms. The resulting structure clarifies how simple and complex cells contribute to perceptual processes such as texture segregation and perceptual grouping.

Previous models of stereopsis have concentrated on the task of binocularly matching left and right eye primitives uniquely. A disparity smoothness constraint is often invoked to limit the number of possible matches. These approaches neglect the fact that surface discontinuities are both abundant in natural everyday scenes, and provide a useful cue for scene segmentation. da Vinci stereopsis refers to the more general problem of dealing with surface discontinuities and their associated unmatched monocular regions within binocular scenes. This study develops a mathematical realization of a neural network theory of biological vision, called FACADE theory, that shows how early cortical stereopsis processes are related to later cortical processes of three-dimensional surface representation. The mathematical model demonstrates through computer simulation how the visual cortex may generate three-dimensional boundary segmentations and use them to control filling-in of three-dimensional surface properties in response to visual scenes. Model mechanisms correctly match disparate binocular regions while filling-in monocular regions with the correct depth within a binocularly viewed scene. This achievement required the introduction of a new multiscale binocular filter for stereo matching which clarifies how cortical complex cells match image contours of like contrast polarity, while pooling signals from opposite contrast polarities. The filter also suggests how false binocular matches and unmatched monocular cues are automatically handled across multiple spatial scales. Pooling of signals from even- and odd-symmetric simple cells at complex cells helps to eliminate spurious activity peaks in matchable signals. Later stages of cortical processing by the blob and interblob streams, including refined models of cooperative boundary grouping and reciprocal stream interactions between boundary and surface representations, are modeled to provide a complete simulation of the da Vinci stereopsis percept.

A neural model of peripheral auditory processing is described and used to separate features of coarticulated vowels and consonants. After preprocessing of speech via a filterbank, the model splits into two parallel channels, a sustained channel and a transient channel. The sustained channel is sensitive to relatively stable parts of the speech waveform, notably synchronous properties of the vocalic portion of the stimulus. It extends the dynamic range of eighth nerve filters using coincidence detectors that combine operations of raising to a power, rectification, delay, multiplication, time averaging, and preemphasis. The transient channel is sensitive to critical features at the onsets and offsets of speech segments. It is built up from fast excitatory neurons that are modulated by slow inhibitory interneurons. These units are combined over high-frequency and low-frequency ranges using operations of rectification, normalization, multiplicative gating, and opponent processing. Detectors sensitive to frication and to onset or offset of stop consonants and vowels are described. Model properties are characterized by mathematical analysis and computer simulations. Neural analogs of model cells in the cochlear nucleus and inferior colliculus are noted, as are psychophysical data about perception of CV syllables that may be explained by the sustained-transient channel hypothesis. The proposed sustained and transient processing seems to be an auditory analog of the sustained and transient processing that is known to occur in vision.

The recognition of three-dimensional (3-D) objects from sequences of their two-dimensional (2-D) views is modeled by a family of self-organizing neural architectures, called VIEWNET, that use View Information Encoded With NETworks. VIEWNET incorporates a preprocessor that generates a compressed but 2-D invariant representation of an image, a supervised incremental learning system that classifies the preprocessed representations into 2-D view categories whose outputs are combined into 3-D invariant object categories, and a working memory that makes a 3-D object prediction by accumulating evidence from 3-D object category nodes as multiple 2-D views are experienced. The simplest VIEWNET achieves high recognition scores without the need to explicitly code the temporal order of 2-D views in working memory. Working memories are also discussed that save memory resources by implicitly coding temporal order in terms of the relative activity of 2-D view category nodes, rather than as explicit 2-D view transitions. Variants of the VIEWNET architecture may be used for scene understanding by using a preprocessor and classier that can determine both what objects are in a scene and where they are located. The present VIEWNET preprocessor includes the CORT-X 2 filter, which discounts the illuminant, regularizes and completes figural boundaries, and suppresses image noise. This boundary segmentation is rendered invariant under 2-D translation, rotation, and dilation by use of a log polar transform. The invariant spectra undergo Gaussian coarse coding to further reduce noise and 3-D foreshortening effects, and to increase generalization. These compressed codes are input into the classifier, a supervised learning system based on the fuzzy ARTMAP algorithm. Fuzzy ARTMAP learns 2-D view categories that are invariant under 2-D image translation, rotation, and dilation as well as 3-D image transformations that do not cause a predictive error. Evidence from sequences of 2-D view categories converges at 3-D object nodes that generate a response invariant under changes of 2-D view. These 3-D object nodes input to a working memory that accumulates evidence over time to improve object recognition. In the simplest working memory, each occurrence (nonoccurrence) of a 2-D view category increases (decreases) the corresponding node's activity in working memory. The maximally active node is used to predict the 3-D object. Recognition is studied with noisy and clean images using slow and fast learning. Slow learning at thefuzzy ARTMAP mapfield is adapted to learn the conditional probability of the 3-D object given the selected 2-D view category. VIEWNET is demonstrated on an MIT Lincoln Laboratory database of 128 × 128 2-D views of aircraft with and without additive noise. A recognition rate of up to 90% is achieved with one 2-D view and of up to 98.5% correct with three 2-D views. The properties of 2-D view and 3-D object category nodes are compared with those of cells in monkey inferotemporal cortex.

A neural network model of boundary segmentation and surface representation is developed to process images containing range data gathered by a synthetic aperture radar (SAR) sensor. The boundary and surface processing are accomplished by an improved Boundary Countour System (BCS) and Feature Countour System (FCS), respectively, that have been derived from analyses of perceptual and neurobiological data. BCS/FCS processing makes structures such as motor vehicles, roads, and buildings more salient and interpretable to human observers than they are in the original imagery. Early processing by ON cells and OFF cells embedded in shunting center-surround network models preprocessing by lateral geniculate nucleus (LGN). Such preprocessing compensates for illumination gradients, normalizes input dynamic range, and extracts local ratio contrasts. ON cell and OFF cell outputs are combined in the BCS to define oriental filters that model corticla simple cells. Pooling ON and OFF outputs at simple cells overcomes complementary processing deficiencies of each cell type along concave and convex contours, and enhances simpl;e cell sensitivity to image edges. Oriented filter outputs are rectified and outputs sensitive to opposite contrast polarities are pooled to define complex cells. The complex cells output to stages of short-range spatial competition (or endstopping) and orientational competition among hypercomplex cells. Hypercomplex cells activate long-range cooperative bipole cells that begin to group image boundaries. Nonlinear feedback between bipole cells and hypercomplex cell segments image regions by cooperatively completing and regularizing the most favored boundaries while suppressing image noise and weaker boundary groupings. Boundary segmentation is performed by three copies of the BCS at small, medium, and large filter scales, whose subsequent interaction distances covary with the size of the filter. Filling-in of multiple surface representations occurs within the FCS at each scale via a boundary-gated diffusion process. Diffusion is activated by the normalized LGN ON and OFF outputs within ON and OFFfilling-in domains. Diffusion is restricted to the regions defined by gating signals from the corresponding BCS boundary segmentation. The filled-in opponent ON and OFFsignals are subtracted to form double opponent surface representations. These surface representations are shown by any of three methods to be sensitive to both image ratio contrasts and background luminance. The three scales of surface representation are then added to yield a final multiple-scale output. The BCS and FCS are shown to perform favorably in comparison to several other techniques for speckle removal.

An incremental, nonparametric probability estimation procedure using the fuzzy ARTMAP (adaptive resonance theory-supervised predictive mapping) neural network is introduced. In the slow-learning mode, fuzzy ARTMAP searches for patterns of data on which to build ever more accurate estimates. In max-nodes mode, the network initially learns a fixed number of categories, and weights are then adjusted gradually.

The apparent dichotomy between symbolic AI processing and distributed neural processing cannot be absolute, since neural networks that capture essential features of human intelligence will also model some of the symbolic processes of which humans are capable. Indeed, a primary goal of biological neural network research is to design systems that can self-organize intelligent symbolic processing capabilities. One such system is the ARTMAP family of neural networks [l], [a]. Most if not all of the purported dichotomies between traditional artificial intelligence and neural network research dissolve within these systems. Although ARTMAP systems are neural networks, they are also a type of selforganizing production system capable of hypothesis testing and memory search. They embody continuous and discrete, .parallel and serial, and distributed and localized properties. Their symbols are compressed, often digital representations, yet they are formed and stabilized through a process of resonant binding that is distributed across the system. They are used to explain and predict data on both the psychological and the neurobiological levels, yet their unique combinations of computational properties are also rapidly finding their way into technology. They are capable of autonomously discovering rules about the environments to which they adapt, yet these rules are emergent properties of network dynamics rather than formal algorithmic statements. On the other hand, these emergent rules can be rewritten as algorithmic if-then rules. This synthesis has become possible because such systems embody genuinely new computational principles. These are not the princi

Working memory neural networks, called Sustained Temporal Order REcurrent (STORE) models, encode the invariant temporal order of sequential events in short-term memory (STM). Inputs to the networks may be presented with widely differing growth rates, amplitudes, durations, and interstimulus intervals without altering the stored STM representation. The STORE temporal order code is designed to enable groupings of the stored events to be stably learned and remembered in real time, even as new events perturb the system. Such invariance and stability properties are needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensorimotor planning, or three-dimensional (3-D) visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described. The new model is based on the model of Seibert and Waxman (1990a), which builds a 3-D representation of an object from a temporally ordered sequence of its two-dimensional (2-D) aspect graphs. The new model, called an ARTSTORE model, consists of the following cascade of processing modules: Invariant Preprocessor → ART 2 → STORE Model → ART 2 → Outstar Network.

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 Salzberg's NGE systems and with Simpson's FMMC system.

Summary form only given. The author describes the development of a general-purpose automatic vision architecture. He clarifies how, with this architecture, scenic data about boundaries, textures, shading, depth, multiple spatial scales, and motion can be cooperatively synthesized in real time into a coherent representation of three-dimensional form. In order to computationally understand the labile relationships known to occur between recognized emergent segmentations and the seen brightness and colors that result from filling-in, it has been necessary to develop a qualitatively different type of vision theory. This theory provides a fresh analysis of how the human visual system is designed to detect relatively invariant surface colors under variable illumination conditions, to detect relatively invariant object boundary structures amid noise caused by the eye's own optics or occluding objects, and to recognize familiar objects or events in the environment. These three functions are performed by the three main subsystems of the system, the feature contour system, the boundary contour system and the object recognition system.>

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.