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.

How Spinal Neural Networks Reduce Discrepancies between Motor Intention and Motor Realization

This paper attempts a rational, step-by-step reconstruction of many aspects of the mammalian neural circuitry known to be involved in the spinal cord's regulation of opposing muscles acting on skeletal segments. Mathematical analyses and local circuit simulations based on neural membrane equations are used to clarify the behavioral function of five fundamental cell types, their complex connectivities, and their physiological actions. These cell types are: α-MNs, γ-MNs, IaINs, IbINs, and Renshaw cells. It is shown that many of the complexities of spinal circuitry are necessary to ensure near invariant realization of motor intentions when descending signals of two basic types independently vary over large ranges of magnitude and rate of change. Because these two types of signal afford independent control, or Factorization, of muscle LEngth and muscle TEnsion, our construction was named the FLETE model (Bullock and Grossberg, 1988b, 1989). The present paper significantly extends the range of experimental data encompassed by this evolving model.

An Integrated Neural Network-Event-Related Potentials Model of Temporal and Probability Context Effects on Event Categorization

We present a neural network that adapts and integrates several preexisting or new modules to categorize events in short term memory (STM), encode temporal order in working memory, evaluate timing and probability context in medium and long term memory. The model shows how processed contextual information modulates event recognition and categorization, focal attention and incentive motivation. The model is based on a compendium of Event Related Potentials (ERPs) and behavioral results either collected by the authors or compiled from the classical ERP literature. Its hallmark is, at the functional level, the interplay of memory registers endowed with widely different dynamical ranges, and at the structural level, the attempt to relate the different modules to known anatomical structures.

Dynamic Programming for Optimal Control of Set-Up Scheduling with Neural Network Modifications

This paper demonstrates an optimal control solution to change of machine set-up scheduling based on dynamic programming average cost per stage value iteration as set forth by Cararnanis et. al. [2] for the 2D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces.

A Self-Organizing Neural Network Model for Redundant Sensory-Motor Control, Motor Equivalence, and Tool Use

A neural network is introduced which provides a solution of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space. To do this, the network self-organizes a mapping from motion directions in 3-D space to velocity commands in joint space. Computer simulations demonstrate that, without any additional learning, the network can generate accurate movement commands that compensate for variable tool lengths, clamping of joints, distortions of visual input by a prism, and unexpected limb perturbations. Blind reaches have also been simulated.

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.

Construction of Neural Network Classification Expert Systems Using Switching Theory Algorithms

A new family of neural network architectures is presented. This family of architectures solves the problem of constructing and training minimal neural network classification expert systems by using switching theory. The primary insight that leads to the use of switching theory is that the problem of minimizing the number of rules and the number of IF statements (antecedents) per rule in a neural network expert system can be recast into the problem of minimizing the number of digital gates and the number of connections between digital gates in a Very Large Scale Integrated (VLSI) circuit. The rules that the neural network generates to perform a task are readily extractable from the network's weights and topology. Analysis and simulations on the Mushroom database illustrate the system's performance.

A Neural Network Model of Spatio-Temporal Pattern Recognition, Recall and Timing

This paper describes the design of a self~organizing, hierarchical neural network model of unsupervised serial learning. The model learns to recognize, store, and recall sequences of unitized patterns, using either short-term memory (STM) or both STM and long-term memory (LTM) mechanisms. Timing information is learned and recall {both from STM and from LTM) is performed with a learned rhythmical structure. The network, bearing similarities with ART (Carpenter & Grossberg 1987a), learns to map temporal sequences to unitized patterns, which makes it suitable for hierarchical operation. It is therefore capable of self-organizing codes for sequences of sequences. The capacity is only limited by the number of nodes provided. Selected simulation results are reported to illustrate system properties.

Genetically Generated Neural Networks I: Representational Effects

This paper studies several applications of genetic algorithms (GAs) within the neural networks field. After generating a robust GA engine, the system was used to generate neural network circuit architectures. This was accomplished by using the GA to determine the weights in a fully interconnected network. The importance of the internal genetic representation was shown by testing different approaches. The effects in speed of optimization of varying the constraints imposed upon the desired network were also studied. It was observed that relatively loose constraints provided results comparable to a fully constrained system. The type of neural network circuits generated were recurrent competitive fields as described by Grossberg (1982).

Genetically Generated Neural Networks II: Searching for an Optimal Representation

Genetic Algorithms (GAs) make use of an internal representation of a given system in order to perform optimization functions. The actual structural layout of this representation, called a genome, has a crucial impact on the outcome of the optimization process. The purpose of this paper is to study the effects of different internal representations in a GA, which generates neural networks. A second GA was used to optimize the genome structure. This structure produces an optimized system within a shorter time interval.

Equilibria and Dynamics of a Neural Network Model for Opponent Muscle Control

One of the advantages of biological skeleto-motor systems is the opponent muscle design, which in principle makes it possible to achieve facile independent control of joint angle and joint stiffness. Prior analysis of equilibrium states of a biologically-based neural network for opponent muscle control, the FLETE model, revealed that such independent control requires specialized interneuronal circuitry to efficiently coordinate the opponent force generators. In this chapter, we refine the FLETE circuit variables specification and update the equilibrium analysis. We also incorporate additional neuronal circuitry that ensures efficient opponent force generation and velocity regulation during movement.