A Model of Self-Organizing Head-Centered Visual Responses in Primate Parietal Areas

We present a hypothesis for how head-centered visual representations in primate parietal areas could self-organize through visually-guided learning, and test this hypothesis using a neural network model. The model consists of a competitive output layer of neurons that receives afferent synaptic connections from a population of input neurons with eye position gain modulated retinal receptive fields. The synaptic connections in the model are trained with an associative trace learning rule which has the effect of encouraging output neurons to learn to respond to subsets of input patterns that tend to occur close together in time. This network architecture and synaptic learning rule is hypothesized to promote the development of head-centered output neurons during periods of time when the head remains fixed while the eyes move. This hypothesis is demonstrated to be feasible, and each of the core model components described is tested and found to be individually necessary for successful self-organization.     

Short-term prediction of chaotic time series by using RBF network with regression weights

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist 'What' and 'Where' pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives 'where', for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The compu- tational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

A computational perspective on the neural basis of multisensory spatial representations

We argue that current theories of multisensory representations are inconsistent with the existence of a large proportion of multimodal neurons with gain fields and partially shifting receptive fields. Moreover, these theories do not fully resolve the recoding and statistical issues involved in multisensory integration. An alternative theory, which we have recently developed and review here, has important implications for the idea of 'frame of reference' in neural spatial representations. This theory is based on a neural architecture that combines basis functions and attractor dynamics. Basis function units are used to solve the recoding problem, whereas attractor dynamics are used for optimal statistical inferences. This architecture accounts for gain fields and partially shifting receptive fields, which emerge naturally as a result of the network connectivity and dynamics.     

Neural network model of visual cortex for determining surface curvature from images of shaded surfaces

The visual system can extract information about shape from the pattern of light and dark surface shading on an object. Very little is known about how this is accomplished. We have used a learning algorithm to construct a neural network model that computes the principal curvatures and orientation of elliptic paraboloids independently of the illumination direction. Our chief finding is that receptive fields developed by units of such model network are surprisingly similar to some found in the visual cortex. It appears that neurons that can make use of the continuous gradations of shading have receptive fields similar to those previously interpreted as dealing with contours (i.e. 'bar' detectors or 'edge' detectors). This study illustrates the difficulty of deducing neuronal function within a network solely from receptive fields. It is also important to consider the pattern of connections a neuron makes with subsequent stages, which we call the 'projective field'.     

From sensors to spikes: evolving receptive fields to enhance sensorimotor information in a robot-arm

In biological systems, instead of actual encoders at different joints, proprioception signals are acquired through distributed receptive fields. In robotics, a single and accurate sensor output per link (encoder) is commonly used to track the position and the velocity. Interfacing bio-inspired control systems with spiking neural networks emulating the cerebellum with conventional robots is not a straight forward task. Therefore, it is necessary to adapt this one-dimensional measure (encoder output) into a multidimensional space (inputs for a spiking neural network) to connect, for instance, the spiking cerebellar architecture; i.e. a translation from an analog space into a distributed population coding in terms of spikes. This paper analyzes how evolved receptive fields (optimized towards information transmission) can efficiently generate a sensorimotor representation that facilitates its discrimination from other "sensorimotor states". This can be seen as an abstraction of the Cuneate Nucleus (CN) functionality in a robot-arm scenario. We model the CN as a spiking neuron population coding in time according to the response of mechanoreceptors during a multi-joint movement in a robot joint space. An encoding scheme that takes into account the relative spiking time of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons is proposed. Due to the enormous number of possible encodings, we have applied an evolutionary algorithm to evolve the sensory receptive field representation from random to optimized encoding. Following the nature-inspired analogy, evolved configurations have shown to outperform simple hand-tuned configurations and other homogenized configurations based on the solution provided by the optimization engine (evolutionary algorithm). We have used artificial evolutionary engines as the optimization tool to circumvent nonlinearity responses in receptive fields.     

A neural network dynamic model reproducing the output signal of the ganglion cell

A functional model of a neural network reproducing the output signal of the ganglion cell is proposed. The model assumes that receptive fields with antagonistic center and periphery are formed.     

Cognitron: A self-organizing multilayered neural network

A new hypothesis for the organization of synapses between neurons is proposed: “The synapse from neuron x to neuron y is reinforced when x fires provided that no neuron in the vicinity of y is firing stronger than y”. By introducing this hypothesis, a new algorithm with which a multilayered neural network is effectively organized can be deduced. A self-organizing multilayered neural network, which is named “cognitron”, is constructed following this algorithm, and is simulated on a digital computer. Unlike the organization of a usual brain models such as a three-layered perceptron, the self-organization of a cognitron progresses favorably without having a “teacher” which instructs in all particulars how the individual cells respond. After repetitive presentations of several stimulus patterns, the cognitron is self-organized in such a way that the receptive fields of the cells become relatively larger in a deeper layer. Each cell in the final layer integrates the information from whole parts of the first layer and selectively responds to a specific stimulus pattern or a feature.     

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.     

Organization of receptive fields in networks with Hebbian learning: the connection between synaptic and phenomenological models

In this paper we address the question of how interactions affect the formation and organization of receptive fields in a network composed of interacting neurons with Hebbian-type learning. We show how to partially decouple single cell effects from network effects, and how some phenomenological models can be seen as approximations to these learning networks. We show that the interaction affects the structure of receptive fields. We also demonstrate how the organization of different receptive fields across the cortex is influenced by the interaction term, and that the type of singularities depends on the symmetries of the receptive fields.     

Binding and segmentation of multiple objects through neural oscillators inhibited by contour information

 Temporal correlation of neuronal activity has been suggested as a criterion for multiple object recognition. In this work, a two-dimensional network of simplified Wilson-Cowan oscillators is used to manage the binding and segmentation problem of a visual scene according to the connectedness Gestalt criterion. Binding is achieved via original coupling terms that link excitatory units to both excitatory and inhibitory units of adjacent neurons. These local coupling terms are time independent, i.e., they do not require Hebbian learning during the simulations. Segmentation is realized by a two-layer processing of the visual image. The first layer extracts all object contours from the image by means of “retinal cells” with an “on-center” receptive field. Information on contour is used to selectively inhibit Wilson-Cowan oscillators in the second layer, thus realizing a strong separation among neurons in different objects. Accidental synchronism between oscillations in different objects is prevented with the use of a global inhibitor, i.e., a global neuron that computes the overall activity in the Wilson-Cowan network and sends back an inhibitory signal. Simulations performed in a 50×50 neural grid with 21 different visual scenes (containing up to eight objects + background) with random initial conditions demonstrate that the network can correctly segment objects in almost 100% of cases using a single set of parameters, i.e., without the need to adjust parameters from one visual scene to the next. The network is robust with reference to dynamical noise superimposed on oscillatory neurons. Moreover, the network can segment both black objects on white background and vice versa and is able to deal with the problem of “fragmentation.” The main limitation of the network is its sensitivity to static noise superimposed on the objects. Overcoming this problem requires implementation of more robust mechanisms for contour enhancement in the first layer in agreement with mechanisms actually realized in the visual cortex. Received: 25 October 2001 / Accepted: 26 February 2003 / Published online: 20 May 2003 Correspondence to: Mauro Ursino (e-mail: mursino@deis.unibo.it, Tel.: +39-051-2093008, Fax: +39-051-2093073)     

Coarse coding: applications to the visual system of salamanders

In a previous study, we calculated the resolution obtained by a population of overlapping receptive fields, assuming a coarse coding mechanism. The results, which favor large receptive fields, are applied to the visual system of tongue-projecting salamanders. An analytical calculation gives the number of neurons necessary to determine the direction of their prey. Direction localization and distance determination are studied in neural network simulations of the orienting movement an d the tongue projection, respectively. In all cases, large receptive fields are found to be essential to yield a high sensory resolution. The results are in good agreement with anatomical, electrophysiological and behavioral data. Received: 7 January 1996 / Accepted: 16 April 1997     

Principle of neuronal organization of defensive reflexes in mollusks

Spontaneous and evoked synaptic activity of command neurons for the defensive response of spiracle closing were studied by simultaneous intracellular recording of activity of several identified CNS neurons in snails. Comparison of monosynaptic EPSPs in command neurons evoked by discharges of presynaptic neurons with spontaneous synaptic potentials indicated that the central organization of the defensive reflex is in the form of a two-layered neuron net in which each neuron of the afferent layer possesses a local receptive field, but which overlaps with other afferent neurons. Each neuron of the afferent layer is connected with each neuron of the efferent layer by monosynaptic excitatory connections that differ in efficiency (maximal only with one neuron of the efferent layer). Both receptive fields of neurons of the afferent layer and "fields of efficiency of synaptic connections" are distributed according to the normal law. As a result of this organization the neuron net acquires a new quality: The action of different stimuli leads to the appearance of differently located "spatial excitation profiles" of efferent layer neurons even when this action of the stimulus occurs not at the center of the receptive field.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 16, No. 1, pp. 26–34, January-February, 1984.     

A recurrent neural network for partitioning of hand drawn characters into strokes of different orientations.

A neural network is described which is intended to extract orientation features that should be used for recognition of hand drawn characters. The network partitions the input hand drawn characters into separate line segments (strokes) according to their orientations. The network consists of several neural layers; each layer serves for extracting strokes of a certain orientation. Every neural layer has one-to-one correspondence with an input screen. The network uses an iterative update procedure which includes interactions of neurons inside each layer through oriented excitatory connections and inhibitory interrelations between the corresponding neurons of different layers. Computer simulation of the network was performed. Experiments showed that the network efficiently classifies all pixels of any hand drawn characters according to the orientations of the strokes constituting these characters and performs, as a result of that, a reasonable segmentation of characters.     

Sparse Coding Models Can Exhibit Decreasing Sparseness while Learning Sparse Codes for Natural Images

The sparse coding hypothesis has enjoyed much success in predicting response properties of simple cells in primary visual cortex (V1) based solely on the statistics of natural scenes. In typical sparse coding models, model neuron activities and receptive fields are optimized to accurately represent input stimuli using the least amount of neural activity. As these networks develop to represent a given class of stimulus, the receptive fields are refined so that they capture the most important stimulus features. Intuitively, this is expected to result in sparser network activity over time. Recent experiments, however, show that stimulus-evoked activity in ferret V1 becomes less sparse during development, presenting an apparent challenge to the sparse coding hypothesis. Here we demonstrate that some sparse coding models, such as those employing homeostatic mechanisms on neural firing rates, can exhibit decreasing sparseness during learning, while still achieving good agreement with mature V1 receptive field shapes and a reasonably sparse mature network state. We conclude that observed developmental trends do not rule out sparseness as a principle of neural coding per se: a mature network can perform sparse coding even if sparseness decreases somewhat during development. To make comparisons between model and physiological receptive fields, we introduce a new nonparametric method for comparing receptive field shapes using image registration techniques.     

Laminar distribution of neurons with different types of receptive fields in the rabbit visual cortex

Investigation of receptive fields of 232 primary visual cortical neurons in rabbits by the use of shaped visual stimuli showed that 21.1% are unselective for stimulus orientation, and 34.1% have simple, 16.4% complex, and 18.5% hypercomplex receptive fields, and 9.9% have other types. Neurons with different types of receptive fields also differed in spontaneous activity, selectivity for rate of stimulus movement, and acuteness of orientational selectivity. Neurons not selective to orientation were found more frequently in layer IV than in other layers, and very rarely in layer VI. Cells with simple receptive fields were numerous in all layers but predominated in layer VI. Neurons with complex receptive fields were rare in layer IV and more numerous in layers V and VI. Neurons with hypercomplex receptive fields were found frequently in layers II + III and IV, rarely in layers V and VI. Spontaneous unit activity in layer II + III was lowest on average, and highest in layer V. Acuteness or orientational selectivity of neurons with simple and complex receptive fields in layers II + III and V significantly exceeded the analogous parameter in layers IV and VI.A. N. Severtsov Institute of Evolutionary Morphology and Ecology of Animals, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 17, No. 1, pp. 19–27, January–February, 1985.     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.