Physical Models of Cognition
This paper presents and discusses physical models for simulationg some aspects of neural intelligence, and in particular, the process of cognition.
neural↗
Engineering topics
Zak, Michail
Publications and source records attributed to Zak, Michail.
Model Of Neural Network With Creative Dynamics
Paper presents analysis of mathematical model of one-neuron/one-synapse neural network featuring coupled activation and learning dynamics and parametrical periodic excitation. Demonstrates self-programming, partly random behavior of suitable designed neural network; believed to be related to spontaneity and creativity of biological neural networks.
Zak, Michail↗
Neural nets with terminal chaos for simulation of non-deterministic patterns
Models for simulating some aspects of neural intelligence are presented and discussed. Special attention is given to terminal neurodynamics as a particular architecture of terminal dynamics suitable for modeling information flows. Applications of terminal chaos to information fusion as well as to planning and modeling coordination among neurons in biological systems are disussed.
Zak, Michail↗
Neurodynamical model of collective brain
A dynamical system which mimics collective purposeful activities of a set of units of intelligence is introduced and discussed. A global control of the unit activities is replaced by the probabilistic correlations between them. These correlations are learned during a long term period of performing collective tasks, and are stored in the synaptic interconnections. The model is represented by a system of ordinary differential equations with terminal attractors and repellers, and does not contain any man-made digital devices.
Zak, Michail↗
An unpredictable-dynamics approach to neural intelligence
The theoretical basis for a dynamic neural network architecture that takes advantage of the notion of terminal chaos to process information in a way that is phenomenologically similar to brain activity is presented. The architecture exploits the phenomenology of nonlinear dynamic systems as an alternative to the traditional paradigm of finite-state machines. It is based on some effects of non-Lipschitzian dynamics. The nonlinear phenomenon of terminal chaos and its relevance to brain activity are examined.
Zak, Michail↗
Mid-course multi-target tracking using continuous representation
The thrust of this paper is to present a new approach to multi-target tracking for the mid-course stage of the Strategic Defense Initiative (SDI). This approach is based upon a continuum representation of a cluster of flying objects. We assume that the velocities of the flying objects can be embedded into a smooth velocity field. This assumption is based upon the impossibility of encounters in a high density cluster between the flying objects. Therefore, the problem is reduced to an identification of a moving continuum based upon consecutive time frame observations. In contradistinction to the previous approaches, here each target is considered as a center of a small continuous neighborhood subjected to a local-affine transformation, and therefore, the target trajectories do not mix. Obviously, their mixture in plane of sensor view is apparent. The approach is illustrated by an example.
Zak, Michail↗
Non-Lipschitzian Dynamics For Modeling Neural Networks
Theoretical study explores failure of Lipschitz condition at points of unstable equilibrium in some dynamical systems.
Zak, Michail↗
Propagation Of Pulse Vibrations In Large Structures
Study yields new insights into propagation of pulse-excited vibrations in large, complicated structures. Special attention paid to dispersion, damping, and trapping of pulses. Understanding of these effects help such endeavors as designing tall, thin buildings to resist high winds and earthquakes.
Zak, Michail↗
Characteristic-Wave Approach Complements Modal Analysis
Aspects of estimation of unmodeled dynamics discussed. Report discusses solution of nonhomogeneous governing matrix equation for dynamics of short vibrational pulses propagating as characteristic waves in large structure. Applied to analyze response, to repeated pulses, of beam clamped at one end and free at other. Shows all qualitative characteristics occuring under arbitrary periodic excitations of beam and those of quasi-periodic excitations, in as much as such excitations obtained by linear superpositions of periodic excitations.
Zak, Michail↗
Weakly connected neural nets
A new neural network architecture is proposed based upon effects of non-Lipschitzian dynamics. The network is fully connected, but these connections are active only during vanishingly short time periods. The advantages of this architecture are discussed.
Zak, Michail↗
Weakly connected neural nets
A new neural network architecture is proposed based upon effects of non-Lipschitzian dynamics. The network is fully connected, but these connections are active only during vanishingly short time periods. The advantages of this architecture are discussed.
Zak, Michail↗
Non-Lipschitzian neural dynamics
A novel approach is presented which is motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks: their rigid behavior as compared with even the simplest biological systems. It is demonstrated that non-Lipschitzian dynamics, based on the faliure of the Lipschitz conditions at repellers, displays a new qualitative effect, i.e., a multichoice response to periodic external excitations. This makes it possible to construct unpredictable systems, represented in the form of coupled activation and learning dynamical equations. It is shown that unpredictable systems can be controlled by sign strings which uniquely define the system behavior by specifying the direction of the motions at the critical points. Unpredictable systems driven by sign strings are extremely flexible and can serve as a powerful tool for complex pattern recognition.
Barhen, Jacob↗
Neural learning of constrained nonlinear transformations
Two issues that are fundamental to developing autonomous intelligent robots, namely, rudimentary learning capability and dexterous manipulation, are examined. A powerful neural learning formalism is introduced for addressing a large class of nonlinear mapping problems, including redundant manipulator inverse kinematics, commonly encountered during the design of real-time adaptive control mechanisms. Artificial neural networks with terminal attractor dynamics are used. The rapid network convergence resulting from the infinite local stability of these attractors allows the development of fast neural learning algorithms. Approaches to manipulator inverse kinematics are reviewed, the neurodynamics model is discussed, and the neural learning algorithm is presented.
Barhen, Jacob↗
The least constraint principle for learning in neurodynamics
An adaptive neural network for auto-associative memories operating in continuous time is considered. A new learning algorithm for the weight matrix defined by explicit locations of desirable equilibrium points is introduced. The approach is based upon the minimum 'strength energy' of the weight matrix for each prescribed performance of the neural network.
Zak, Michail↗
Non-Lipschitzian dynamics for neural net modelling
Failure of the Lipschitz condition in unstable equilibrium points of dynamical systems leads to a multiple-choice response to an initial deterministic input. The evolution of such systems is characterized by a special type of unpredictability measured by unbounded Liapunov exponents. Possible relation of these systems to future neural networks is discussed.
Zak, Michail↗
Chaos as a part of logical structure in neurodynamics
It is proposed that chaotic attractors incorporated in neural net models can represent classes of patterns in the same way in which a set of static attractors represent unrelated patterns. Therefore, chaotic states of neuron activity are associated with higher level cognitive processes such as generalization and abstraction.
Zak, Michail↗
Unsupervised learning in neurodynamics using example-interaction approach
A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines diverge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from the minimization of the strength energy, while the node velocities play the role of constraints.
Zak, Michail↗
Real-time neuromorphic algorithms for inverse kinematics of redundant manipulators
The paper presents an efficient neuromorphic formulation to accurately solve the inverse kinematics problem for redundant manipulators. The approach involves a dynamical learning procedure based on a novel formalism in neural network theory: the concept of 'terminal' attractors. Topographically mapped terminal attractors are used to define a neural network whose synaptic elements can rapidly encapture the inverse kinematics transformations, and, subsequently generalize to compute joint-space coordinates required to achieve arbitrary end-effector configurations. Unlike prior neuromorphic implementations, this technique can also systematically exploit redundancy to optimize kinematic criteria, e.g., torque optimization. Simulations on 3-DOF and 7-DOF redundant manipulators, are used to validate the theoretical framework and illustrate its computational efficacy.
Barhen, Jacob↗