Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

The effect of intracortical competition on the formation of topographic maps in models of Hebbian learning

Correlation-based learning (CBL) models and self-organizing maps (SOM) are two classes of Hebbian models that have both been proposed to explain the activity-driven formation of cortical maps. Both models differ significantly in the way lateral cortical interactions are treated, leading to different predictions for the formation of receptive fields. The linear CBL models predict that receptive field profiles are determined by the average values and the spatial correlations of the second order of the afferent activity patterns, wheras SOM models map stimulus features. Here, we investigate a class of models which are characterized by a variable degree of lateral competition and which have the CBL and SOM models as limit cases. We show that there exists a critical value for intracortical competition below which the model exhibits CBL properties and above which feature mapping sets in. The class of models is then analyzed with respect to the formation of topographic maps between two layers of neurons. For Gaussian input stimuli we find that localized receptive fields and topographic maps emerge above the critical value for intracortical competition, and we calculate this value as a function of the size of the input stimuli and the range of the lateral interaction function. Additionally, we show that the learning rule can be derived via the optimization of a global cost function in a framework of probabilistic output neurons which represent a set of input stimuli by a sparse code. Received: 23 June 1999 / Accepted in revised form: 05 November 1999     

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119–138, 2006).     

An incremental Hebbian learning model of the primary visual cortex with lateral plasticity and real input patterns

We present a simplified binocular neural network model of the primary visual cortex with separate ON/OFF-pathways and modifiable afferent as well as intracortical synaptic couplings. Random as well as natural image stimuli drive the weight adaptation which follows Hebbian learning rules stabilized with constant norm and constant sum constraints. The simulations consider the development of orientation and ocular dominance maps under different conditions concerning stimulus patterns and lateral couplings. With random input patterns realistic orientation maps with +/- 1/2-vortices mostly develop and plastic lateral couplings self-organize into mexican hat type structures on average. Using natural greyscale images as input patterns, realistic orientation maps develop as well and the lateral coupling profiles of the cortical neurons represent the two point correlations of the input image used.     

Development and regeneration of the retinotectal map in goldfish: a computational study

We present a simple computational model to study the interplay of activity-dependent and intrinsic processes thought to be involved in the formation of topographic neural projections. Our model consists of two input layers which project to one target layer. The connections between layers are described by a set of synaptic weights. These weights develop according to three interacting developmental rules: (i) an intrinsic fibre-target interaction which generates chemospecific adhesion between afferent fibres and target cells; (ii) an intrinsic fibre-fibre interaction which generates mutual selective adhesion between the afferent fibres; and (iii) an activity-dependent fibre-fibre interaction which implements Hebbian learning. Additionally, constraints are imposed to keep synaptic weights finite. The model is applied to a set of eleven experiments on the regeneration of the retinotectal projection in goldfish. We find that the model is able to reproduce the outcome of an unprecedented range of experiments with the same set of model parameters, including details of the size of receptive and projective fields. We expect this mathematical framework to be a useful tool for the analysis of developmental processes in general. <br>     

Origin of orientation tuning in the visual cortex.

The results of recent experiments have thrown new light on the neuronal connections underlying orientation-selective responses in the primary visual cortex of adult animals. The pattern of afferent input from the lateral geniculate nucleus to the cortex appears to be specific for orientation, while intracortical inhibitory connections appear to be non-specific in this respect. Experimental and theoretical studies have suggested that the development of cortical cell orientation tuning is an activity-dependent process.     

A Proto-Architecture for Innate Directionally Selective Visual Maps

Self-organizing artificial neural networks are a popular tool for studying visual system development, in particular the cortical feature maps present in real systems that represent properties such as ocular dominance (OD), orientation-selectivity (OR) and direction selectivity (DS). They are also potentially useful in artificial systems, for example robotics, where the ability to extract and learn features from the environment in an unsupervised way is important. In this computational study we explore a DS map that is already latent in a simple artificial network. This latent selectivity arises purely from the cortical architecture without any explicit coding for DS and prior to any self-organising process facilitated by spontaneous activity or training. We find DS maps with local patchy regions that exhibit features similar to maps derived experimentally and from previous modeling studies. We explore the consequences of changes to the afferent and lateral connectivity to establish the key features of this proto-architecture that support DS.     

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     

Intrinsic versus extrinsic influences in the development of neuronal maps

Accumulating evidence suggests that the plasticity of extrinsic thalamocortical inputs in cortical layer IV may be guided or instructed by earlier plasticity events in the intrinsic, horizontal connections within the extragranular cortical layers. We analyse a rate-based model of the plasticity of a set of extrinsic afferents in the presence of a pre-existing (and fixed) plexus of intrinsic, overall excitatory horizontal connections between a set of target neurons. We determine conditions under which afferent synaptic pattern formation respects this pre-existing lateral structure. We find three broad regimes under which extrinsic afferent plasticity may violate this structure: the initial pattern of extrinsic afferent innervation of the target cells is far from balanced; the gain of the extrinsic afferents greatly exceeds the overall scale of the strength of lateral excitation; the target cell horizontal coupling matrix is sparse. If none of these conditions is satisfied, then extrinsic afferent plasticity respects the pre-existing lateral connectivity, so that afferent synaptic pattern formation conforms to the pattern of lateral excitation.     

Bayesian inference in populations of cortical neurons: a model of motion integration and segmentation in area MT

A major issue in cortical physiology and computational neuroscience is understanding the interaction between extrinsic signals from feedforward connections and intracortical signals from lateral connections. We propose here a computational model for motion perception based on the assumption that the local cortical circuits in the medio-temporal area (area MT) implement a Bayesian inference principle. This approach establishes a functional balance between feedforward and lateral, excitatory and inhibitory, inputs. The model reproduces most of the known properties of the neurons in area MT in response to moving stimuli. It accounts for important motion perception phenomena including motion transparency, spatial and temporal integration/segmentation. While integrating several properties of previously proposed models, it makes specific testable predictions concerning, in particular, temporal properties of neurons and the architecture of lateral connections in area MT. In addition, the proposed mechanism is consistent with the known properties of local cortical circuits in area V1. This suggests that Bayesian inference may be a general feature of information processing in cortical neuron populations. Received: 3 December 1997 / Accepted in revised form: 21 July 1998     

Mathematical model for self-organization of direction columns in the primate middle temporal area

We attempted to reproduce modular structures for direction selectivity characteristic of the primate middle temporal area (MT) based on our thermodynamic model for the activity-dependent self-organization of neural networks. We assumed that excitatory afferent input to MT neurons arises from V1 and/or V2 neurons which are selective to both orientation of a visual stimulus and direction of its motion, and that such input is modifiable and becomes selectively connected through the process of self-organization. By contrast, local circuit connections within MT are unmodifiable and remain nonselectively connected (isotropic). The present simulations reproduced characteristic patterns of organization in the cortex of MT in that: (1) preferred directions of the afferent input gradually shifted, except for singularity lines where direction abruptly changed by 180°; (2) model MT neurons located between the singularity lines responded to unidirectionally moving stimuli, closely reflecting preferred direction of the afferent input; (3) neurons responding to stimuli moving in two opposite directions were located along the singularity lines; and (4) neurons responding to stimuli moving in any direction were clustered at the ends of the singularity lines. When the strength of the lateral inhibition was decreased, direction selectivity of MT neurons was reduced. Therefore, the lateral inhibition, even if isotropic, strengthens the direction selectivity of MT neurons. Expression of singularities changed depending on a parameter that represents the relative dominance of the direction selectivity to the orientation selectivity of the afferent input. When the direction selectivity was predominant, singularity points were formed, while when the orientation selectivity prevailed, the MT was covered by two-dimensional singularity networks. Line singularities similar to those experimentally observed were reproduced when these two types of selectivity were in balance. Received: 15 October 1992/Accepted in revised form: 27 June 1993     

Development of spatiotemporal receptive fields of simple cells: II. Simulation and analysis

In part I of this article a correlation based model for the developmental process of spatiotemporal receptive fields has been introduced. In this model the development is described as an activity-dependent competition between four types of input from the lateral geniculate nucleus onto a cortical cell, viz. non-lagged ON and OFF and lagged ON and OFF inputs. In the present paper simulation results and a first analysis are presented for this model. We study the developmental process both before and after eye-opening and compare the results with experimental data from reverse correlation measurements. The outcome of the developmental process is determined mainly by the spatial and the temporal correlations between the different inputs. In particular, if the mean correlation between non-lagged and lagged inputs is weak, receptive fields with a widely varying degree of direction selectivity emerge. However, spatiotemporal receptive fields may show rotation of their preferred orientation as a function of response delay. Even if the mean correlation between two types of temporal input is not weak, direction-selective receptive fields may emerge because of an intracortical interaction between different cortical maps. In an environment of moving lines or gratings, direction-selective receptive fields develop only if the distribution of the directions of motion presented during development shows some anisotropy. In this case, a continuous map of preferred direction is also shown to develop. Received: 18 June 1997 / Accepted: 16 September 1997     

Lateral spike conduction velocity in the visual cortex affects spatial range of synchronization and receptive field size without visual experience: a learning model with spiking neurons

Classical receptive fields (cRF) increase in size from the retina to higher visual centers. The present work shows how temporal properties, in particular lateral spike velocity and spike input correlation, can affect cRF size and position without visual experience. We demonstrate how these properties are related to the spatial range of cortical synchronization if Hebbian learning dominates early development. For this, a largely reduced model of two successive levels of the visual cortex is developed (e.g., areas V1 and V2). It consists of retinotopic networks of spiking neurons with constant spike velocity in lateral connections. Feedforward connections between level 1 and 2 are additive and determine cRF size and shape, while lateral connections within level 1 are modulatory and affect the cortical range of synchronization. Input during development is mimicked by spike trains with spatially homogeneous properties and a confined temporal correlation width. During learning, the homogeneous lateral coupling shrinks to limited coupling structures defining synchronization and related association fields (AF). The size of level-1 synchronization fields determines the lateral coupling range of developing level-1-to-2 connections and, thus, the size of level-2 cRFs, even if the feedforward connections have distance-independent delays. AFs and cRFs increase with spike velocity in the lateral network and temporal correlation width of the input. Our results suggest that AF size of V1 and cRF size of V2 neurons are confined during learning by the temporal width of input correlations and the spike velocity in lateral connections without the need of visual experience. During learning from visual experience, a similar influence of AF size on the cRF size may be operative at successive levels of processing, including other parts of the visual system.     

A reaction-diffusion model to capture disparity selectivity in primary visual cortex

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.     

The functional logic of cortico-pulvinar connections

The pulvinar is an 'associative' thalamic nucleus, meaning that most of its input and output relationships are formed with the cerebral cortex. The function of this circuitry is little understood and its anatomy, though much investigated, is notably recondite. This is because pulvinar connection patterns disrespect the architectural subunits (anterior, medial, lateral and inferior pulvinar nuclei) that have been the traditional reference system. This article presents a simplified, global model of the organization of cortico-pulvinar connections so as to pursue their structure-function relationships. Connections between the cortex and pulvinar are topographically organized, and as a result the pulvinar contains a 'map' of the cortical sheet. However, the topography is very blurred. Hence the pulvinar connection zones of nearby cortical areas overlap, allowing indirect transcortical communication via the pulvinar. A general observation is that indirect cortico-pulvino-cortical circuits tend to mimic direct cortico-cortical pathways: this is termed 'the replication principle'. It is equally apt for certain pairs (or groups) of nearby cortical areas that happen not to connect with each other. The 'replication' of this non-connection is achieved by discontinuities and dislocations of the cortical topography within the pulvinar, such that the associated pair of connection zones do not overlap. Certain of these deformations can be used to divide the global cortical topography into specific sub-domains, which form the natural units of a connectional subdivision of the pulvinar. A substantial part of the pulvinar also expresses visual topography, reflecting visual maps in occipital cortex. There are just two well-ordered visual maps in the pulvinar, that both receive projections from area V1, and several other occipital areas; the resulting duplication of cortical topography means that each visual map also acts as a separate connection domain. In summary, the model identifies four topographically ordered connection domains, and reconciles the coexistence of visual and cortical maps in two of them. The replication principle operates at and below the level of domain structure. It is argued that cortico-pulvinar circuitry replicates the pattern of cortical circuitry but not its function, playing a more regulatory role instead. Thalamic neurons differ from cortical neurons in their inherent rhythmicity, and the pattern of cortico-thalamic connections must govern the formation of specific resonant circuits. The broad implication is that the pulvinar acts to coordinate cortical information processing by facilitating and sustaining the formation of synchronized trans-areal assemblies; a more pointed suggestion is that, owing to the considerable blurring of cortical topography in the pulvinar, rival cortical assemblies may be in competition to recruit thalamic elements in order to outlast each other in activity.     

Nested reentrant and recurrent computation in early vision: a Bayesian neuromorphic model applied to hyperacuity

 Hyperacuity is demonstrated in a neuromorphic model of the early visual system. The model incorporates Bayesian principles which are embodied in the dynamics of reentrant and recurrent feedback processes. Each retinotopically mapped area in the model represents a transformation of data from the visual field. Sensory information propagates in a bottom-up direction from one area to the next, while information based on Bayesian priors propagates in a top-down direction through reentrant connections. The ‘bottom-up’ and ‘top-down’ information maintain a separate existence in distinct layers of the model, but they interact through local connections within each area. Transformations between one area and the next are defined by the reentrant synaptic connections between areas, while local prior probability maps are defined by local recurrent connections within layers. The representation of hyperacuity is accomplished using a model of functional multiplicity: the large ratio of neurons in striate cortex compared with the number of afferent fibers projecting from the lateral geniculate nucleus. High functional multiplicity, in conjunction with hierarchical reentrant processing, allows the model to represent a fine-grained restoration of the line structure of visual input. Received : 26 April 1995 / Accepted in revised form : 27 July 1996     

Laminar specificity of extrinsic cortical connections studied in coculture preparations.

The formation of specific neural connections in the cerebral cortex was studied using organotypic coculture preparations composed of subcortical and cortical regions. Morphological and electrophysiological analysis indicated that several cortical efferent and afferent connections, such as the corticothalamic, thalamocortical, corticocortical, and corticotectal connections, were established in the cocultures with essentially the same laminar specificity as that found in the adult cerebral cortex, but without specificity of sensory modality. This suggests the existence of a cell-cell recognition system between cortical or subcortical neurons and their final targets. This interaction produces lamina-specific connections, but is probably insufficient for the formation of the modality-specific connections.     

Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene. Action Editor: Jonathan D. Victor     

Influences on the global structure of cortical maps.

Cortical maps often contain global spatial structure: however, theoretical accounts for their development have generally concentrated on reproducing only local structure. We show that the elastic net model of cortical map formation can closely approximate the global structure of the ocular dominance column map observed in macaque primary visual cortex. A key component is the assumption of spatially non-uniform and anisotropic correlations in the retina. This work shows how genetic and epigenetic effects could combine to establish characteristic global structure in cortical maps.     

The coordinated mapping of visual space and response features in visual cortex

Whether general principles can explain the layouts of cortical maps remains unresolved. In primary visual cortex of ferret, the relationships between the maps of visual space and response features are predicted by a "dimension-reduction" model. The representation of visual space is anisotropic, with the elevation and azimuth axes having different magnification. This anisotropy is reflected in the orientation, ocular dominance, and spatial frequency domains, which are elongated such that their directions of rapid change, or high-gradient axes, are orthogonal to the high-gradient axis of the visual map. The feature maps are also strongly interdependent-their high-gradient regions avoid one another and intersect orthogonally where essential, so that overlap is minimized. Our results demonstrate a clear influence of the visual map on each feature map. In turn, the local representation of visual space is smooth, as predicted when many features are mapped within a cortical area.