Vector Associative Maps: Unsupervised Real-time Error-based Learning and Control of Movement Trajectories

This article describes neural network models for adaptive control of arm movement trajectories during visually guided reaching and, more generally, a framework for unsupervised real-time error-based learning. The models clarify how a child, or untrained robot, can learn to reach for objects that it sees. Piaget has provided basic insights with his concept of a circular reaction: As an infant makes internally generated movements of its hand, the eyes automatically follow this motion. A transformation is learned between the visual representation of hand position and the motor representation of hand position. Learning of this transformation eventually enables the child to accurately reach for visually detected targets. Grossberg and Kuperstein have shown how the eye movement system can use visual error signals to correct movement parameters via cerebellar learning. Here it is shown how endogenously generated arm movements lead to adaptive tuning of arm control parameters. These movements also activate the target position representations that are used to learn the visuo-motor transformation that controls visually guided reaching. The AVITE model presented here is an adaptive neural circuit based on the Vector Integration to Endpoint (VITE) model for arm and speech trajectory generation of Bullock and Grossberg. In the VITE model, a Target Position Command (TPC) represents the location of the desired target. The Present Position Command (PPC) encodes the present hand-arm configuration. The Difference Vector (DV) population continuously.computes the difference between the PPC and the TPC. A speed-controlling GO signal multiplies DV output. The PPC integrates the (DV)·(GO) product and generates an outflow command to the arm. Integration at the PPC continues at a rate dependent on GO signal size until the DV reaches zero, at which time the PPC equals the TPC. The AVITE model explains how self-consistent TPC and PPC coordinates are autonomously generated and learned. Learning of AVITE parameters is regulated by activation of a self-regulating Endogenous Random Generator (ERG) of training vectors. Each vector is integrated at the PPC, giving rise to a movement command. The generation of each vector induces a complementary postural phase during which ERG output stops and learning occurs. Then a new vector is generated and the cycle is repeated. This cyclic, biphasic behavior is controlled by a specialized gated dipole circuit. ERG output autonomously stops in such a way that, across trials, a broad sample of workspace target positions is generated. When the ERG shuts off, a modulator gate opens, copying the PPC into the TPC. Learning of a transformation from TPC to PPC occurs using the DV as an error signal that is zeroed due to learning. This learning scheme is called a Vector Associative Map, or VAM. The VAM model is a general-purpose device for autonomous real-time error-based learning and performance of associative maps. The DV stage serves the dual function of reading out new TPCs during performance and reading in new adaptive weights during learning, without a disruption of real-time operation. YAMs thus provide an on-line unsupervised alternative to the off-line properties of supervised error-correction learning algorithms. YAMs and VAM cascades for learning motor-to-motor and spatial-to-motor maps are described. YAM models and Adaptive Resonance Theory (ART) models exhibit complementary matching, learning, and performance properties that together provide a foundation for designing a total sensory-cognitive and cognitive-motor autonomous system.

ART 2-A: An Adaptive Resonance Algorithm for Rapid Category Learning and Recognition

This article introduces ART 2-A, an efficient algorithm that emulates the self-organizing pattern recognition and hypothesis testing properties of the ART 2 neural network architecture, but at a speed two to three orders of magnitude faster. Analysis and simulations show how the ART 2-A systems correspond to ART 2 dynamics at both the fast-learn limit and at intermediate learning rates. Intermediate learning rates permit fast commitment of category nodes but slow recoding, analogous to properties of word frequency effects, encoding specificity effects, and episodic memory. Better noise tolerance is hereby achieved without a loss of learning stability. The ART 2 and ART 2-A systems are contrasted with the leader algorithm. The speed of ART 2-A makes practical the use of ART 2 modules in large-scale neural computation.

Sequential Memory with ART: A Self-Organizing Network Capable of Learning Sequences of Patterns

A model which extends the adaptive resonance theory model to sequential memory is presented. This new model learns sequences of events and recalls a sequence when presented with parts of the sequence. A sequence can have repeated events and different sequences can share events. The ART model is modified by creating interconnected sublayers within ART's F2 layer. Nodes within F2 learn temporal patterns by forming recency gradients within LTM. Versions of the ART model like ART I, ART 2, and fuzzy ART can be used.

Self-Supervised ARTMAP

Computational models of learning typically train on labeled input patterns (supervised learning), unlabeled input patterns (unsupervised learning), or a combination of the two (semisupervised learning). In each case input patterns have a fixed number of features throughout training and testing. Human and machine learning contexts present additional opportunities for expanding incomplete knowledge from formal training, via self-directed learning that incorporates features not previously experienced. This article defines a new self-supervised learning paradigm to address these richer learning contexts, introducing a neural network called self-supervised ARTMAP. Self-supervised learning integrates knowledge from a teacher (labeled patterns with some features), knowledge from the environment (unlabeled patterns with more features), and knowledge from internal model activation (self-labeled patterns). Self-supervised ARTMAP learns about novel features from unlabeled patterns without destroying partial knowledge previously acquired from labeled patterns. A category selection function bases system predictions on known features, and distributed network activation scales unlabeled learning to prediction confidence. Slow distributed learning on unlabeled patterns focuses on novel features and confident predictions, defining classification boundaries that were ambiguous in the labeled patterns. Self-supervised ARTMAP improves test accuracy on illustrative lowdimensional problems and on high-dimensional benchmarks. Model code and benchmark data are available from: http://techlab.bu.edu/SSART/.

Grid Cell Hexagonal Patterns Formed by Fast Self-Organized Learning within Entorhinal Cortex

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. How these hexagonal patterns arise has excited intense interest. It has previously been shown how a selforganizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? A neural model is proposed that converts path integration signals into hexagonal grid cell patterns of multiple scales. This GRID model creates only grid cell patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support a unified computational framework for explaining how entorhinal-hippocampal interactions support spatial navigation.

A Self-Organizing Neural Network for Learning a Body-Centered Invariant Representation of 3-D Target Position

This paper describes a self-organizing neural network that rapidly learns a body-centered representation of 3-D target positions. This representation remains invariant under head and eye movements, and is a key component of sensory-motor systems for producing motor equivalent reaches to targets (Bullock, Grossberg, and Guenther, 1993).

A Neural Network Architecture for Autonomous Learning, Recognition, and Prediction in a Nonstationary World

In a constantly changing world, humans are adapted to alternate routinely between attending to familiar objects and testing hypotheses about novel ones. We can rapidly learn to recognize and narne novel objects without unselectively disrupting our memories of familiar ones. We can notice fine details that differentiate nearly identical objects and generalize across broad classes of dissimilar objects. This chapter describes a class of self-organizing neural network architectures--called ARTMAP-- that are capable of fast, yet stable, on-line recognition learning, hypothesis testing, and naming in response to an arbitrary stream of input patterns (Carpenter, Grossberg, Markuzon, Reynolds, and Rosen, 1992; Carpenter, Grossberg, and Reynolds, 1991). The intrinsic stability of ARTMAP allows the system to learn incrementally for an unlimited period of time. System stability properties can be traced to the structure of its learned memories, which encode clusters of attended features into its recognition categories, rather than slow averages of category inputs. The level of detail in the learned attentional focus is determined moment-by-moment, depending on predictive success: an error due to over-generalization automatically focuses attention on additional input details enough of which are learned in a new recognition category so that the predictive error will not be repeated. An ARTMAP system creates an evolving map between a variable number of learned categories that compress one feature space (e.g., visual features) to learned categories of another feature space (e.g., auditory features). Input vectors can be either binary or analog. Computational properties of the networks enable them to perform significantly better in benchmark studies than alternative machine learning, genetic algorithm, or neural network models. Some of the critical problems that challenge and constrain any such autonomous learning system will next be illustrated. Design principles that work together to solve these problems are then outlined. These principles are realized in the ARTMAP architecture, which is specified as an algorithm. Finally, ARTMAP dynamics are illustrated by means of a series of benchmark simulations.

Fast Learning VIEWNET Architectures for Recognizing 3-D Objects from Multiple 2-D Views

The recognition of 3-D objects from sequences of their 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 arc 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 also be used for scene understanding by using a preprocessor and classifier 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 sequence 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. ln 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 image using slow and fast learning. Slow learning at the fuzzy ARTMAP map field 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 l28x128 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.

From Synapse to Self: Spikes, Synchrony, and Attentive Learning by Laminar Thalamocortical Circuits

How do our brains transform the "blooming buzzing confusion" of daily experience into a coherent sense of self that can learn and selectively attend to important information? How do local signals at multiple processing stages, none of which has a global view of brain dynamics or behavioral outcomes, trigger learning at multiple synaptic sites when appropriate, and prevent learning when inappropriate, to achieve useful behavioral goals in a continually changing world? How does the brain allow synaptic plasticity at a remarkably rapid rate, as anyone who has gone to an exciting movie is readily aware, yet also protect useful memories from catastrophic forgetting? A neural model provides a unified answer by explaining and quantitatively simulating data about single cell biophysics and neurophysiology, laminar neuroanatomy, aggregate cell recordings (current-source densities, local field potentials), large-scale oscillations (beta, gamma), and spike-timing dependent plasticity, and functionally linking them all to cognitive information processing requirements.

ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network

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 pa When ρa 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.

Fuzzy ART: An Adaptive Resonance Algorithm for Rapid, Stable Classification of Analog Patterns

The Fuzzy ART system introduced herein incorporates computations from fuzzy set theory into ART 1. For example, the intersection (n) operator used in ART 1 learning is replaced by the MIN operator (A) of fuzzy set theory. Fuzzy ART reduces to ART 1 in response to binary input vectors, but can also learn stable categories in response to analog input vectors. In particular, the MIN operator reduces to the intersection operator in the binary case. Learning is stable because all adaptive weights can only decrease in time. A preprocessing step, called complement coding, uses on-cell and off-cell responses to prevent category proliferation. Complement coding normalizes input vectors while preserving the amplitudes of individual feature activations.

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.

Linking Attention to Learning, Expectation, Competition, and Consciousness

The concept of attention has been used in many senses, often without clarifying how or why attention works as it does. Attention, like consciousness, is often described in a disembodied way. The present article summarizes neural models and supportive data and how attention is linked to processes of learning, expectation, competition, and consciousness. A key them is that attention modulates cortical self-organization and stability. Perceptual and cognitive neocortex is organized into six main cell layers, with characteristic sub-lamina. Attention is part of unified design of bottom-up, horizontal, and top-down interactions among indentified cells in laminar cortical circuits. Neural models clarify how attention may be allocated during processes of visual perception, learning and search; auditory streaming and speech perception; movement target selection during sensory-motor control; mental imagery and fantasy; and hallucination during mental disorders, among other processes.

Self-Organizing Hierarchical Knowledge Discovery by an ARTMAP Image Fusion System

Classifying novel terrain or objects front sparse, complex data may require the resolution of conflicting information from sensors working at different times, locations, and scales, and from sources with different goals and situations. Information fusion methods can help resolve inconsistencies, as when evidence variously suggests that an object's class is car, truck, or airplane. The methods described here consider a complementary problem, supposing that information from sensors and experts is reliable though inconsistent, as when evidence suggests that an object's class is car, vehicle, and man-made. Underlying relationships among objects are assumed to be unknown to the automated system or the human user. The ARTMAP information fusion system used distributed code representations that exploit the neural network's capacity for one-to-many learning in order to produce self-organizing expert systems that discover hierarchical knowledge structures. The system infers multi-level relationships among groups of output classes, without any supervised labeling of these relationships.

SOVEREIGN: A Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goal-Oriented Navigation System

Both animals and mobile robots, or animats, need adaptive control systems to guide their movements through a novel environment. Such control systems need reactive mechanisms for exploration, and learned plans to efficiently reach goal objects once the environment is familiar. How reactive and planned behaviors interact together in real time, and arc released at the appropriate times, during autonomous navigation remains a major unsolved problern. This work presents an end-to-end model to address this problem, named SOVEREIGN: A Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goal-oriented Navigation system. The model comprises several interacting subsystems, governed by systems of nonlinear differential equations. As the animat explores the environment, a vision module processes visual inputs using networks that arc sensitive to visual form and motion. Targets processed within the visual form system arc categorized by real-time incremental learning. Simultaneously, visual target position is computed with respect to the animat's body. Estimates of target position activate a motor system to initiate approach movements toward the target. Motion cues from animat locomotion can elicit orienting head or camera movements to bring a never target into view. Approach and orienting movements arc alternately performed during animat navigation. Cumulative estimates of each movement, based on both visual and proprioceptive cues, arc stored within a motor working memory. Sensory cues are stored in a parallel sensory working memory. These working memories trigger learning of sensory and motor sequence chunks, which together control planned movements. Effective chunk combinations arc selectively enhanced via reinforcement learning when the animat is rewarded. The planning chunks effect a gradual transition from reactive to planned behavior. The model can read-out different motor sequences under different motivational states and learns more efficient paths to rewarded goals as exploration proceeds. Several volitional signals automatically gate the interactions between model subsystems at appropriate times. A 3-D visual simulation environment reproduces the animat's sensory experiences as it moves through a simplified spatial environment. The SOVEREIGN model exhibits robust goal-oriented learning of sequential motor behaviors. Its biomimctic structure explicates a number of brain processes which are involved in spatial navigation.