Neural networks for computing eigenvalues and eigenvectors

We consider two electrically coupled oscillators described by modified Fitzhugh-Nagumo equations. We study the relative influence of the individual cellular characteristics and the electrical coupling on the behavior of the coupled system. We show that, for similar oscillators, the load effect of the slow oscillator increases with the coupling strength. We prove that an asymmetry between the uncoupled bursters can accelerate the system with respect to the free cells, this effect depending on the characteristics of the coupling.On leave from Centre de Physique Théoruique (UPR A0014 CNRS), Palaiseau, France     

A neural network model for cognitive activity

A consideration of the storage of information as an energized neuronal state leads to the development of a new type of neural network model which is capable of pattern recognition, concept formation and recognition of patterns of events in time. The network consists of several layers of cells, each cell representing by connections from the lower levels some combination of features or concepts. Information travels toward higher layers by such connections during an association phase, and then reverses during a recognition phase, where higher-order concepts can redirect the flow to more appropriate elements, revising the perception of the environment. This permits a more efficient method of distinguishing closely-related patterns and also permits the formation of negative associations, which is a likely requirement for formation of "abstract" concepts.     

A neural network model for texture discrimination

A model of texture discrimination in visual cortex was built using a feedforward network with lateral interactions among relatively realistic spiking neural elements. The elements have various membrane currents, equilibrium potentials and time constants, with action potentials and synapses. The model is derived from the modified programs of MacGregor (1987). Gabor-like filters are applied to overlapping regions in the original image; the neural network with lateral excitatory and inhibitory interactions then compares and adjusts the Gabor amplitudes in order to produce the actual texture discrimination. Finally, a combination layer selects and groups various representations in the output of the network to form the final transformed image material. We show that both texture segmentation and detection of texture boundaries can be represented in the firing activity of such a network for a wide variety of synthetic to natural images. Performance details depend most strongly on the global balance of strengths of the excitatory and inhibitory lateral interconnections. The spatial distribution of lateral connective strengths has relatively little effect. Detailed temporal firing activities of single elements in the lateral connected network were examined under various stimulus conditions. Results show (as in area 17 of cortex) that a single element's response to image features local to its receptive field can be altered by changes in the global context.     

A neural network for processing olfactory-like stimuli

Several critical issues associated with the processing of olfactory stimuli in animals (but focusing on insects) are discussed with a view to designing a neural network which can process olfactory stimuli. This leads to the construction of a neural network that can learn and identify the quality (direction cosines) of an input vector or extract information from a sequence of correlated input vectors, where the latter corresponds to sampling a time varying olfactory stimulus (or other generically similar pattern recognition problems). The network is constructed around a discrete time content-addressable memory (CAM) module which basically satisfies the Hopfield equations with the addition of a unit time delay feedback. This modification improves the convergence properties of the network and is used to control a switch which activates the learning or template formation process when the input is “unknown”. The network dynamics are embedded within a sniff cycle which includes a larger time delay (i.e. an integert _s <1) that is also used to control the template formation switch. In addition, this time delay is used to modify the input into the CAM module so that the more dominant of two mingling odors or an odor increasing against a background of odors is more readily identified. The performance of the network is evaluated using Monte Carlo simulations and numerical results are presented.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

A neural network architecture for data classification

This article aims at showing an architecture of neural networks designed for the classification of data distributed among a high number of classes. A significant gain in the global classification rate can be obtained by using our architecture. This latter is based on a set of several little neural networks, each one discriminating only two classes. The specialization of each neural network simplifies their structure and improves the classification. Moreover, the learning step automatically determines the number of hidden neurons. The discussion is illustrated by tests on databases from the UCI machine learning database repository. The experimental results show that this architecture can achieve a faster learning, simpler neural networks and an improved performance in classification.     

A biologically inspired neural network for dynamic programming

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.     

A maximum neural network approach for N-queens problems

 A novel neural network approach using the maximum neuron model is presented for N-queens problems. The goal of the N-queens problem is to find a set of locations of N queens on an N×N chessboard such that no pair of queens commands each other. The maximum neuron model proposed by Takefuji et al. has been applied to two optimization problems where the optimization of objective functions is requested without constraints. This paper demonstrates the effectiveness of the maximum neuron model for constraint satisfaction problems through the N-queens problem. The performance is verified through simulations in up to 500-queens problems on the sequential mode, the N-parallel mode, and the N ²-parallel mode, where our maximum neural network shows the far better performance than the existing neural networks. Received: 4 June 1996/Accepted in revised form: 13 November 1996     

A hierarchical neural network model for associative memory

A hierarchical neural network model with feedback interconnections, which has the function of associative memory and the ability to recognize patterns, is proposed. The model consists of a hierarchical multi-layered network to which efferent connections are added, so as to make positive feedback loops in pairs with afferent connections. The cell-layer at the initial stage of the network is the input layer which receives the stimulus input and at the same time works as an output layer for associative recall. The deepest layer is the output layer for pattern-recognition. Pattern-recognition is performed hierarchically by integrating information by converging afferent paths in the network. For the purpose of associative recall, the integrated information is again distributed to lower-order cells by diverging efferent paths. These two operations progress simultaneously in the network. If a fragment of a training pattern is presented to the network which has completed its self-organization, the entire pattern will gradually be recalled in the initial layer. If a stimulus consisting of a number of training patterns superposed is presented, one pattern gradually becomes predominant in the recalled output after competition between the patterns, and the others disappear. At about the same time when the recalled pattern reaches a steady state in he initial layer, in the deepest layer of the network, a response is elicited from the cell corresponding to the category of the finally-recalled pattern. Once a steady state has been reached, the response of the network is automatically extinguished by inhibitory signals from a steadiness-detecting cell. If the same stimulus is still presented after inhibition, a response for another pattern, formerly suppressed, will now appear, because the cells of the network have adaptation characteristics which makes the same response unlikely to recur. Since inhibition occurs repeatedly, the superposed input patterns are recalled one by one in turn.     

A neural network model for stroboscopic alternative motion

A neural network which models multistable perception is presented. The network consists of sensor and inner neurons. The dynamics is established by a stochastic neuronal dynamics, a formal Hebb-type coupling dynamics and a resource mechanism that corresponds to saturation effects in perception. From this a system of coupled differential equations is derived and analyzed. Single stimuli are bound to exactly one percept, even in ambiguous situations where multistability occurs. The network exhibits discontinuous as well as continuous phase transitions and models various empirical findings, including the percepts of succession, alternative motion and simultaneity; the percept of oscillation is explained by oscillating percepts at a continuous phase transition. Received: 13 September 1995 / Accepted: 3 June 1996     

A neural network model for limb trajectory formation

This paper deals with the problem of representing and generating unconstrained aiming movements of a limb by means of a neural network architecture. The network produced time trajectories of a limb from a starting posture toward targets specified by sensory stimuli. Thus the network performed a sensory-motor transformation. The experimenters trained the network using a bell-shaped velocity profile on the trajectories. This type of profile is characteristic of most movements performed by biological systems. We investigated the generalization capabilities of the network as well as its internal organization. Experiments performed during learning and on the trained network showed that: (i) the task could be learned by a three-layer sequential network; (ii) the network successfully generalized in trajectory space and adjusted the velocity profiles properly; (iii) the same task could not be learned by a linear network; (iv) after learning, the internal connections became organized into inhibitory and excitatory zones and encoded the main features of the training set; (v) the model was robust to noise on the input signals; (vi) the network exhibited attractor-dynamics properties; (vii) the network was able to solve the motorequivalence problem. A key feature of this work is the fact that the neural network was coupled to a mechanical model of a limb in which muscles are represented as springs. With this representation the model solved the problem of motor redundancy.     

A global competitive neural network

 A study is presented of a set of coupled nets proposed to function as a global competitive network. One net, of hidden nodes, is composed solely of inhibitory neurons and is excitatorily driven and feeds back in a disinhibitory manner to an input net which itself feeds excitatorily to a (cortical) output net. The manner in which the former input and hidden inhibitory net function so as to enhance outputs as compared with inputs, and the further enhancements when the cortical net is added, are explored both mathematically and by simulation. This is extended to learning on cortical afferent and lateral connections. A global wave structure, arising on the inhibitory net in a similar manner to that of pattern formation in a negative laplacian net, is seen to be important to all of these activities. Simulations are only performed in one dimension, although the global nature of the activity is expected to extend to higher dimensions. Possible implications are briefly discussed. Received: 21 November 1993/Accepted in revised form: 30 June 1994     

A neural network for the Steiner minimal tree problem

The problem of finding the shortest tree connecting a set of points is called the Steiner minimal tree problem and is nearly three centuries old. It has applications in transportation, computer networks, agriculture, telephony, building layout and very large scale integrated circuit (VLSI) design, among others, and is known to be NP-complete. We propose a neural network which self-organizes to find a minimal tree. Solutions found by the network compare favourably with the best known or optimal results on test problems from the literature. To the best of our knowledge, the proposed network is the first neural-based solution to the problem. We show that the neural network has a built-in mechanism to escape local minima.     

A dynamical neural network for hitting an approaching object

Besides making contact with an approaching ball at the proper place and time, hitting requires control of the effector velocity at contact. A dynamical neural network for the planning of hitting movements was derived in order to account for both these requirements. The model in question implements continuous required velocity control by extending the Vector Integration To Endpoint model while providing explicit control of effector velocity at interception. It was shown that the planned movement trajectories generated by the model agreed qualitatively with the kinematics of hitting movements as observed in two recent experiments. Outstanding features of this comparison concerned the timing and amplitude of the empirical backswing movements, which were largely consistent with the predictions from the model. Several theoretical implications as well as the informational basis and possible neural underpinnings of the model were discussed.     

A neural network model for generating complex birdsong syntax

The singing behavior of songbirds has been investigated as a model of sequence learning and production. The song of the Bengalese finch, Lonchura striata var. domestica, is well described by a finite state automaton including a stochastic transition of the note sequence, which can be regarded as a higher-order Markov process. Focusing on the neural structure of songbirds, we propose a neural network model that generates higher-order Markov processes. The neurons in the robust nucleus of the archistriatum (RA) encode each note; they are activated by RA-projecting neurons in the HVC (used as a proper name). We hypothesize that the same note included in different chunks is encoded by distinct RA-projecting neuron groups. From this assumption, the output sequence of RA is a higher-order Markov process, even though the RA-projecting neurons in the HVC fire on first-order Markov processes. We developed a neural network model of the local circuits in the HVC that explains the mechanism by which RA-projecting neurons transit stochastically on first-order Markov processes. Numerical simulation showed that this model can generate first-order Markov process song sequences.     

A model of neural network for spatiotemporal pattern recognition

A model of neural network to recognize spatiotemporal patterns is presented. The network consists of two kinds of neural cells: P-cells and B-cells. A P-cell generates an impulse responding to more than one impulse and embodies two special functions: short term storage (STS) and heterosynaptic facilitation (HSF). A B-cell generates several impulses with high frequency as soon as it receives an impulse. In recognizing process, an impulse generated by a P-cell represents a recognition of stimulus pattern, and triggers the generation of impulses of a B-cell. Inhibitory impulses with high frequency generated by a B-cell reset the activities of all P-cells in the network.Two examples of spatiotemporal pattern recognition are presented. They are achieved by giving different values to the parameters of the network. In one example, the network recognizes both directional and non-directional patterns. The selectivities to directional and non-directional patterns are realized by only adjusting excitatory synaptic weights of P-cells. In the other example, the network recognizes time series of spatial patterns, where the lengths of the series are not necessarily the same and the transitional speeds of spatial patterns are not always the same. In both examples, the HSF signal controls the total activity of the network, which contributes to exact recognition and error recovery. In the latter example, it plays a role to trigger and execute the recognizing process. Finally, we discuss the correspondence between the model and physiological findings.     

A neural network model for the mechanism of feature-extraction

We propose a new multilayered neural network model which has the ability of rapid self-organization. This model is a modified version of the cognitron (Fukushima, 1975). It has modifiable inhibitory feedback connections, as well as conventional modifiable excitatory feedforward connections, between the cells of adjoining layers. If a feature-extracting cell in the network is excited by a stimulus which is already familiar to the network, the cell immediately feeds back inhibitory signals to its presynaptic cells in the preceding layer, which suppresses their response. On the other hand, the feature-extracting cell does not respond to an unfamiliar feature, and the responses from its presynaptic cells are therefore not suppressed because they do not receive any feedback inhibition. Modifiable synapses in the new network are reinforced in a way similar to those in the cognitron, and synaptic connections from cells yielding a large sustained output are reinforced. Since familiar stimulus features do not elicit a sustained response from the cells of the network, only circuits which detect novel stimulus features develop. The network therefore quickly acquires favorable pattern-selectivity by the mere repetitive presentation of set of learning patterns.     

A spring model and equivalent neural network for arm posture control

A model is introduced for the motor program which controls final position. The first part of the model relates the biomechanical properties of the muscles to the EMG activities of the extensor and flexor muscles and thereby generates quatitative predictions for the relationships between the EMGs, final position, external forces, muscle stiffness, and muscle tension. To the extent that comparable data exist, the model is shown to give correct quantitative predictions. When only qualitative comparisons can be made, the model is consistent with the data in the literature. The model is complete and can be tested quantitatively in detail in the future. An equivalent circuit for the neural network that innervates the muscles is given. It is shown to have the advantages of making the programming of final position simple to either compute or lookup in a table. In addition, new situations, such as adapting to a force, or an unusual viewing angle, lead to very simple changes in the basic program in terms of the equivalent circuit.     

A modified LAMSTAR neural network and its applications

This paper describes a modification of the LArge Memory STorage And Retrieval (LAMSTAR) neural network. The purpose of the modification is to allow rare events a larger role in decision-making when they are strongly biased towards a particular decision. As a by-product, the modification also permits the introduction of a confidence measure. This measure allows comparison across different network inputs so that the user may choose the "best" solution. The authors have applied the modified LAMSTAR network to a financial forecasting problem.