A Biomechanical Model of Human Oculomotor Plant Kinematics Based Upon Geometric Algebra

A biomechanical model of the human oculomotor plant kinematics in 3-D as a function of muscle length changes is presented. It can represent a range of alternative interpretations of the data as a function of one parameter. The model is free from such deficits as singularities and the nesting of axes found in alternative formulations such as the spherical wrist (Paul, l98l). The equations of motion are defined on a quaternion based representation of eye rotations and are compact atnd computationally efficient.

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.

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.

Systematic Verification of Safety Properties of Arbitrary Network Protocol Compositions Using CHAIN

Formal correctness of complex multi-party network protocols can be difficult to verify. While models of specific fixed compositions of agents can be checked against design constraints, protocols which lend themselves to arbitrarily many compositions of agents-such as the chaining of proxies or the peering of routers-are more difficult to verify because they represent potentially infinite state spaces and may exhibit emergent behaviors which may not materialize under particular fixed compositions. We address this challenge by developing an algebraic approach that enables us to reduce arbitrary compositions of network agents into a behaviorally-equivalent (with respect to some correctness property) compact, canonical representation, which is amenable to mechanical verification. Our approach consists of an algebra and a set of property-preserving rewrite rules for the Canonical Homomorphic Abstraction of Infinite Network protocol compositions (CHAIN). Using CHAIN, an expression over our algebra (i.e., a set of configurations of network protocol agents) can be reduced to another behaviorally-equivalent expression (i.e., a smaller set of configurations). Repeated applications of such rewrite rules produces a canonical expression which can be checked mechanically. We demonstrate our approach by characterizing deadlock-prone configurations of HTTP agents, as well as establishing useful properties of an overlay protocol for scheduling MPEG frames, and of a protocol for Web intra-cache consistency.

Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems, by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n^3) inference algorithm.

A Memory Model for Concept Hierarchy Representation and Commonsense Reasoning

Most associative memory models perform one level mapping between predefined sets of input and output patterns1 and are unable to represent hierarchical knowledge. Complex AI systems allow hierarchical representation of concepts, but generally do not have learning capabilities. In this paper, a memory model is proposed which forms concept hierarchy by learning sample relations between concepts. All concepts are represented in a concept layer. Relations between a concept and its defining lower level concepts, are chunked as cognitive codes represented in a coding layer. By updating memory contents in the concept layer through code firing in the coding layer, the system is able to perform an important class of commonsense reasoning, namely recognition and inheritance.

Unsupervised Neural Network for the Control of a Mobile Robot

This article introduces an unsupervised neural architecture for the control of a mobile robot. The system allows incremental learning of the plant during robot operation, with robust performance despite unexpected changes of robot parameters such as wheel radius and inter-wheel distance. The model combines Vector associative Map (VAM) learning and associate learning, enabling the robot to reach targets at arbitrary distances without knowledge of the robot kinematics and without trajectory recording, but relating wheel velocities with robot movements.

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.