A neural network model for the emergence of grating cells

A correlation-based learning (CBL) neural network model is proposed, which simulates the emergence of grating cells as well as some of their response characteristics to periodic pattern stimuli. These cells, found in areas V1 and V2 of the visual cortex of monkeys, respond vigorously and exclusively to bar gratings of a preferred orientation and periodicity. Their non-linear behaviour differentiates grating cells from other orientation-selective cells, which show linear spatial frequency filtering. Received: 9 June 1997 / Accepted in revised form: 9 February 1998     

A computational model of monkey cortical grating cells

Grating cells were discovered in the V1 and V2 areas of the monkey visual cortex by von der Heydt et al. (1992). These cells responded vigorously to grating patterns of appropriate orientation and periodicity. Computational models inspired by these findings were used as texture operator (Kruzinga and Petkov 1995, 1999; Petkov and Kruzinga 1997) and for the emergence and self-organization of grating cells (Brunner et al. 1998; Bauer et al. 1999). The aim of this paper is to create a grating cell operator that demonstrates similar responses to monkey grating cells by applying operator to the same stimuli as in the experiments carried out by von der Heydt et al. (1992). Operator will be tested on images that contain periodic patterns as suggested by De Valois (1988). In order to learn more about the role of grating cells in natural vision, operator is applied to 338 real-world images of textures obtained from three different databases. The results suggest that grating cells respond strongly to regular alternating periodic patterns of a certain orientation. Such patterns are common in images of human-made structures, like buildings, fabrics, and tiles, and to regular natural periodic patterns, which are relatively rare in nature.     

Mathematical model for the self-organization of neural networks

Mutual inhibition between neurons combined with a learning principle similar to that proposed by Hebb is shown to secure a powerful selforganizing property for neural networks. Numerical analysis reveals that the system investigated always organizes itself into the same final state from any arbitrarily chosen initial state.     

A self-organizing neural network model for the development of complex cells

On the basis of recent neurophysiological findings on the mammalian visual cortex, a selforganizing neural network model is proposed for the understanding of the development of complex cells. The model is composed of two kinds of connections from LGN cells to a complex cell. One is direct excitatory connections and the other is indirect inhibitory connections via simple cells. Inhibitory synapses between simple cells and complex cells are assumed to be modifiable. The model was simulated on a computer to confirm its behavior.     

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 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 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 dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the neural velocity on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.On leave of absencefrom the Institute of Molecular Genetics, Russian Academy of Sciences, Moscow, Russia.     

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 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 of the McCollough effect

A self-organizing, feature-extracting network (von der Malsburg, 1973) is extended to two feature dimensions to encompass line orientation and color. It is applied to McCollough effects, particularly longlasting, contingent-aftereffects. McCollough effects are thought to involve low-level associative memory in the form of synaptic modification. The McCollough-Malsburg Model (MMM) embodies positive synaptic modification with correlated firing of units in an input layer and an excitatory cortical layer. Computer simulation of MMM reproduces orientation-contingent color aftereffects. The model embodies many of the mechanisms thought to be operating in developmental plasticity, suggesting that equivalent mechanisms may be involved in adult long-term adaptation as well.This work was supported in part by NIH Grant No. 5 R01 NS09755-4 COM of the National Institute of Neurological Diseases and Stroke (M.A. Arbib, Principal Investigator)     

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 model of myoglobin self-organization

The self-organization of helical regions of myoglobin into a compact tertiary structure is considered on the basis of the hypothesis on the step-wise mechanism of self-organization of protein molecules. It is assumed that the self-organization begins with the formation of “ centers of crystallization ” and proceeds with the growth of one such center or by a sequential collapse of two or more grown centers.Different pathways of self-organization of myoglobin are considered; the most favourable structures corresponding to the greatest number of dehydrated bulky hydroptiobic groups and to all the strongly hydrophilic groups exposed to water are selected at every stage of the given pathway and the others are neglected. One of the two most favourable structures obtained in such a way coincides in rough resolution with the native tertiary structure of protein.     

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 neural network model of attention-modulated neurodynamics

Visual attention appears to modulate cortical neurodynamics and synchronization through various cholinergic mechanisms. In order to study these mechanisms, we have developed a neural network model of visual cortex area V4, based on psychophysical, anatomical and physiological data. With this model, we want to link selective visual information processing to neural circuits within V4, bottom-up sensory input pathways, top-down attention input pathways, and to cholinergic modulation from the prefrontal lobe. We investigate cellular and network mechanisms underlying some recent analytical results from visual attention experimental data. Our model can reproduce the experimental findings that attention to a stimulus causes increased gamma-frequency synchronization in the superficial layers. Computer simulations and STA power analysis also demonstrate different effects of the different cholinergic attention modulation action mechanisms.     

A multilayer neural network model for perception of rotational motion

A multilayer neural nerwork model for the perception of rotational motion has been developed usingReichardt's motion detector array of correlation type, Kohonen's self-organized feature map and Schuster-Wagner's oscillating neural network. It is shown that the unsupervised learning could make the neurons on the second layer of the network tend to be self-organized in a form resembling columnar organization of selective directions in area MT of the primate's visual cortex. The output layer can interpret rotation information and give the directions and velocities of rotational motion. The computer simulation results are in agreement with some psychophysical observations of rotation-al perception. It is demonstrated that the temporal correlation between the oscillating neurons would be powerful for solving the "binding problem" of shear components of rotational motion.