Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new 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. 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. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

Cortical Dynamics of Visual Motion Perception: Short-Range and Long-Range Apparent Motion

This article describes further evidence for a new neural network theory of biological motion perception. The theory clarifies why parallel streams Vl --> V2, Vl --> MT, and Vl --> V2 --> MT exist for static form and motion form processing among the areas Vl, V2, and MT of visual cortex. The theory suggests that the static form system (Static BCS) generates emergent boundary segmentations whose outputs are insensitive to direction-ofcontrast and insensitive to direction-of-motion, whereas the motion form system (Motion BCS) generates emergent boundary segmentations whose outputs are insensitive to directionof-contrast but sensitive to direction-of-motion. The theory is used to explain classical and recent data about short-range and long-range apparent motion percepts that have not yet been explained by alternative models. These data include beta motion; split motion; gamma motion and reverse-contrast gamma motion; delta motion; visual inertia; the transition from group motion to element motion in response to a Ternus display as the interstimulus interval (ISI) decreases; group motion in response to a reverse-contrast Ternus display even at short ISIs; speed-up of motion velocity as interflash distance increases or flash duration decreases; dependence of the transition from element motion to group motion on stimulus duration and size; various classical dependencies between flash duration, spatial separation, ISI, and motion threshold known as Korte's Laws; dependence of motion strength on stimulus orientation and spatial frequency; short-range and long-range form-color interactions; and binocular interactions of flashes to different eyes.

Synchronized Oscillations During Cooperative Feature Linking in a Cortical Model of Visual Perception

A neural network model of synchronized oscillator activity in visual cortex is presented in order to account for recent neurophysiological findings that such synchronization may reflect global properties of the stimulus. In these recent experiments, it was reported that synchronization of oscillatory firing responses to moving bar stimuli occurred not only for nearby neurons, but also occurred between neurons separated by several cortical columns (several mm of cortex) when these neurons shared some receptive field preferences specific to the stimuli. These results were obtained not only for single bar stimuli but also across two disconnected, but colinear, bars moving in the same direction. Our model and computer simulations obtain these synchrony results across both single and double bar stimuli. For the double bar case, synchronous oscillations are induced in the region between the bars, but no oscillations are induced in the regions beyond the stimuli. These results were achieved with cellular units that exhibit limit cycle oscillations for a robust range of input values, but which approach an equilibrium state when undriven. Single and double bar synchronization of these oscillators was achieved by different, but formally related, models of preattentive visual boundary segmentation and attentive visual object recognition, as well as nearest-neighbor and randomly coupled models. In preattentive visual segmentation, synchronous oscillations may reflect the binding of local feature detectors into a globally coherent grouping. In object recognition, synchronous oscillations may occur during an attentive resonant state that triggers new learning. These modelling results support earlier theoretical predictions of synchronous visual cortical oscillations and demonstrate the robustness of the mechanisms capable of generating synchrony.

A Neural Network of Adaptively Timed Reinforcement Learning and Hippocampal Dynamics

A neural model is described of how adaptively timed reinforcement learning occurs. The adaptive timing circuit is suggested to exist in the hippocampus, and to involve convergence of dentate granule cells on CA3 pyramidal cells, and NMDA receptors. This circuit forms part of a model neural system for the coordinated control of recognition learning, reinforcement learning, and motor learning, whose properties clarify how an animal can learn to acquire a delayed reward. Behavioral and neural data are summarized in support of each processing stage of the system. The relevant anatomical sites are in thalamus, neocortex, hippocampus, hypothalamus, amygdala, and cerebellum. Cerebellar influences on motor learning are distinguished from hippocampal influences on adaptive timing of reinforcement learning. The model simulates how damage to the hippocampal formation disrupts adaptive timing, eliminates attentional blocking, and causes symptoms of medial temporal amnesia. It suggests how normal acquisition of subcortical emotional conditioning can occur after cortical ablation, even though extinction of emotional conditioning is retarded by cortical ablation. The model simulates how increasing the duration of an unconditioned stimulus increases the amplitude of emotional conditioning, but does not change adaptive timing; and how an increase in the intensity of a conditioned stimulus "speeds up the clock", but an increase in the intensity of an unconditioned stimulus does not. Computer simulations of the model fit parametric conditioning data, including a Weber law property and an inverted U property. Both primary and secondary adaptively timed conditioning are simulated, as are data concerning conditioning using multiple interstimulus intervals (ISIs), gradually or abruptly changing ISis, partial reinforcement, and multiple stimuli that lead to time-averaging of responses. Neurobiologically testable predictions are made to facilitate further tests of the model.

A Neural Network Realization of Fuzzy ART

A neural network realization of the fuzzy Adaptive Resonance Theory (ART) algorithm is described. Fuzzy ART is capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns, thus enabling the network to learn both analog and binary input patterns. In the neural network realization of fuzzy ART, signal transduction obeys a path capacity rule. Category choice is determined by a combination of bottom-up signals and learned category biases. Top-down signals impose upper bounds on feature node activations.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Perception of Globally Coherent Motion

How do human observers perceive a coherent pattern of motion from a disparate set of local motion measures? Our research has examined how ambiguous motion signals along straight contours are spatially integrated to obtain a globally coherent perception of motion. Observers viewed displays containing a large number of apertures, with each aperture containing one or more contours whose orientations and velocities could be independently specified. The total pattern of the contour trajectories across the individual apertures was manipulated to produce globally coherent motions, such as rotations, expansions, or translations. For displays containing only straight contours extending to the circumferences of the apertures, observers' reports of global motion direction were biased whenever the sampling of contour orientations was asymmetric relative to the direction of motion. Performance was improved by the presence of identifiable features, such as line ends or crossings, whose trajectories could be tracked over time. The reports of our observers were consistent with a pooling process involving a vector average of measures of the component of velocity normal to contour orientation, rather than with the predictions of the intersection-of-constraints analysis in velocity space.

Working Memories for Storage and Recall of Arbitrary Temporal Sequences

A working memory model is described that is capable of storing and recalling arbitrary temporal sequences of events, including repeated items. These memories encode the invariant temporal order of sequential events that may be presented at widely differing speeds, durations, and interstimulus intervals. This temporal order code is designed to enable all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system.

Comparative Performance Measures of Fuzzy ARTMAP, Learned Vector Quantization, and Back Propagation for Handwritten Character Recognition

This article compares the performance of Fuzzy ARTMAP with that of Learned Vector Quantization and Back Propagation on a handwritten character recognition task. Training with Fuzzy ARTMAP to a fixed criterion used many fewer epochs. Voting with Fuzzy ARTMAP yielded the highest recognition rates.

A What-and-Where Neural Network for Invariant Image Preprocessing

A feedforward neural network for invariant image preprocessing is proposed that represents the position1 orientation and size of an image figure (where it is) in a multiplexed spatial map. This map is used to generate an invariant representation of the figure that is insensitive to position1 orientation, and size for purposes of pattern recognition (what it is). A multiscale array of oriented filters followed by competition between orientations and scales is used to define the Where filter.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

A Neural Pattern Generator that Exhibits Frequency-Dependent In-Phase and Anti-Phase Oscillations

This article describes a. neural pattern generator based on a cooperative-competitive feedback neural network. The two-channel version of the generator supports both in-phase and anti-phase oscillations. A scalar arousal level controls both the oscillation phase and frequency. As arousal increases, oscillation frequency increases and bifurcations from in-phase to anti-phase, or anti-phase to in-phase oscillations can occur. Coupled versions of the model exhibit oscillatory patterns which correspond to the gaits used in locomotion and other oscillatory movements by various animals.

A Neural Network for Synthesizing the Pitch of an Acoustic Source

This article describes a neural network model capable of generating a spatial representation of the pitch of an acoustic source. Pitch is one of several auditory percepts used by humans to separate multiple sound sources in the environment from each other. The model provides a neural instantiation of a type of "harmonic sieve". It is capable of quantitatively simulating a large body of psychoacoustical data, including new data on octave shift perception.

Processing of Synthetic Aperture Radar Images by the Boundary Contour System and Feature Contour System

An improved Boundary Contour System (BCS) and Feature Contour System (FCS) neural network model of preattentive vision is applied to two large images containing range data gathered by a synthetic aperture radar (SAR) sensor. The goal of processing is to make structures such as motor vehicles, roads, or buildings more salient and more interpretable to human observers than they are in the original imagery. Early processing by shunting center-surround networks compresses signal dynamic range and performs local contrast enhancement. Subsequent processing by filters sensitive to oriented contrast, including short-range competition and long-range cooperation, segments the image into regions. Finally, a diffusive filling-in operation within the segmented regions produces coherent visible structures. The combination of BCS and FCS helps to locate and enhance structure over regions of many pixels, without the resulting blur characteristic of approaches based on low spatial frequency filtering alone.

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.