Biomedical subjects

Haim Sompolinsky

Publications and source records attributed to Haim Sompolinsky.

15 recordsLinked to original sources

PubMed2006

The tempotron: a neuron that learns spike timing-based decisions.

The timing of action potentials in sensory neurons contains substantial information about the eliciting stimuli. Although the computational advantages of spike timing-based neuronal codes have long been recognized, it is unclear whether, and if so how, neurons can learn to read out such representations. We propose a new, biologically plausible supervised synaptic learning rule that enables neurons to efficiently learn a broad range of decision rules, even when information is embedded in the spatiotemporal structure of spike patterns rather than in mean firing rates. The number of categorizations of random spatiotemporal patterns that a neuron can implement is several times larger than the number of its synapses. The underlying nonlinear temporal computation allows neurons to access information beyond single-neuron statistics and to discriminate between inputs on the basis of multineuronal spike statistics. Our work demonstrates the high capacity of neural systems to learn to decode information embedded in distributed patterns of spike synchrony.

Action Potentials↗

PubMed2006

Implications of neuronal diversity on population coding.

In many cortical and subcortical areas, neurons are known to modulate their average firing rate in response to certain external stimulus features. It is widely believed that information about the stimulus features is coded by a weighted average of the neural responses. Recent theoretical studies have shown that the information capacity of such a coding scheme is very limited in the presence of the experimentally observed pairwise correlations. However, central to the analysis of these studies was the assumption of a homogeneous population of neurons. Experimental findings show a considerable measure of heterogeneity in the response properties of different neurons. In this study, we investigate the effect of neuronal heterogeneity on the information capacity of a correlated population of neurons. We show that information capacity of a heterogeneous network is not limited by the correlated noise, but scales linearly with the number of cells in the population. This information cannot be extracted by the population vector readout, whose accuracy is greatly suppressed by the correlated noise. On the other hand, we show that an optimal linear readout that takes into account the neuronal heterogeneity can extract most of this information. We study analytically the nature of the dependence of the optimal linear readout weights on the neuronal diversity. We show that simple online learning can generate readout weights with the appropriate dependence on the neuronal diversity, thereby yielding efficient readout.

Action Potentials↗

PubMed2005

Adaptation without parameter change: Dynamic gain control in motion detection.

Many sensory systems adapt their input-output relationship to changes in the statistics of the ambient stimulus. Such adaptive behavior has been measured in a motion detection sensitive neuron of the fly visual system, H1. The rapid adaptation of the velocity response gain has been interpreted as evidence of optimal matching of the H1 response to the dynamic range of the stimulus, thereby maximizing its information transmission. Here, we show that correlation-type motion detectors, which are commonly thought to underlie fly motion vision, intrinsically possess adaptive properties. Increasing the amplitude of the velocity fluctuations leads to a decrease of the effective gain and the time constant of the velocity response without any change in the parameters of these detectors. The seemingly complex property of this adaptation turns out to be a straightforward consequence of the multidimensionality of the stimulus and the nonlinear nature of the system.

Adaptation, Physiological↗

PubMed2005

Bistability of cerebellar Purkinje cells modulated by sensory stimulation.

A persistent change in neuronal activity after brief stimuli is a common feature of many neuronal microcircuits. This persistent activity can be sustained by ongoing reverberant network activity or by the intrinsic biophysical properties of individual cells. Here we demonstrate that rat and guinea pig cerebellar Purkinje cells in vivo show bistability of membrane potential and spike output on the time scale of seconds. The transition between membrane potential states can be bidirectionally triggered by the same brief current pulses. We also show that sensory activation of the climbing fiber input can switch Purkinje cells between the two states. The intrinsic nature of Purkinje cell bistability and its control by sensory input can be explained by a simple biophysical model. Purkinje cell bistability may have a key role in the short-term processing and storage of sensory information in the cerebellar cortex.

Action Potentials↗

PubMed2004

Patterns of ongoing activity and the functional architecture of the primary visual cortex.

Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple "attractor" states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feed-forward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.

Action Potentials↗

PubMed2004

Information tuning of populations of neurons in primary visual cortex.

Neurons in macaque primary visual cortex (V1) show a diversity of orientation tuning properties, exhibiting a broad distribution of tuning width, baseline activity, peak response, and circular variance (CV). Here, we studied how the different tuning features affect the performance of these cells in discriminating between stimuli with different orientations. Previous studies of the orientation discrimination power of neurons in V1 focused on resolving two nearby orientations close to the psychophysical threshold of orientation discrimination. Here, we developed a theoretical framework, the information tuning curve, that measures the discrimination power of cells as a function of the orientation difference, deltatheta, of the two stimuli. This tuning curve also represents the mutual information between the neuronal responses and the stimulus orientation. We studied theoretically the dependence of the information tuning curve on the orientation tuning width, baseline, and peak responses. Of main interest is the finding that narrow orientation tuning is not necessarily optimal for all angular discrimination tasks. Instead, the optimal tuning width depends linearly on deltatheta. We applied our theory to study the discrimination performance of a population of 490 neurons in macaque V1. We found that a significant fraction of the neuronal population exhibits favorable tuning properties for large deltatheta. We also studied how the discrimination capability of neurons is distributed and compared several other measures of the orientation tuning such as CV with Chernoff distances for normalized tuning curves.

Action Potentials↗

PubMed2004

Short-term memory in orthogonal neural networks.

We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.

Memory, Short-Term↗

PubMed2004

Nonlinear population codes.

Theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information. However, recent theoretical studies have investigated the effect of cross-correlations in the trial-to-trial fluctuations of the neuronal responses on the accuracy of the representation. Assuming that only the first-order statistics of the neuronal responses are tuned to the stimulus, these studies have shown that in the presence of correlations, similar to those observed experimentally in cortical ensembles of neurons, the amount of information in the population is limited, yielding nonzero error levels even in the limit of infinitely large populations of neurons. In this letter, we study correlated neuronal populations whose higher-order statistics, and in particular response variances, are also modulated by the stimulus. Weask two questions: Does the correlated noise limit the accuracy of the neuronal representation of the stimulus? and, How can a biological mechanism extract most of the information embedded in the higher-order statistics of the neuronal responses? Specifically, we address these questions in the context of a population of neurons coding an angular variable. We show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise. This information cannot be extracted by linear readout schemes, including the linear population vector. Instead, we propose a bilinear readout scheme that involves spatial decorrelation, quadratic nonlinearity, and population vector summation. We show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters, with an efficiency that grows linearly with the population size. This code can be implemented using biologically plausible neurons.

Brain↗

PubMed2003

Cortical representation of bimanual movements.

It is well established that the discharge of neurons in primate motor cortex is tuned to the movement direction of the contralateral arm. Interestingly, it has been found that these neurons exhibit a directional tuning to the ipsilateral arm as well and that the preferred directions to both arms tend to be similar. A recent study showed that motor cortex cells are also directionally selective to bimanual movements, but the relationship between the bimanual and unimanual representations remains unclear. To address this issue, we analyzed the responses of motor cortical neurons recorded from two macaque monkeys during unimanual and bimanual reaching movements. We decomposed the bimanual movement representation into contralateral and ipsilateral directionally tuned components. Our major finding is that the movement of the contralateral arm modifies the tuning of the cells to the ipsilateral arm such that: (1) the offset and modulation depth of the tuning are suppressed; and (2) the preferred directions are randomly shifted. Both these effects eliminate the correlation between the contralateral and ipsilateral representations during bimanual movements. We suggest that the modification of the ipsilateral arm representation is caused by the recruitment of local inhibition that conveys callosal inputs during bimanual movements. This hypothesis is supported by the analysis of a model of two motor cortical networks, coupled with sparse random interhemispheric projections that reproduce the main features observed in the data. Finally, we show that the modification of the ipsilateral arm representation reduces the interference between the movements of both arms.

Animals↗

PubMed2003

Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity.

Triggered by recent experimental results, temporally asymmetric Hebbian (TAH) plasticity is considered as a candidate model for the biological implementation of competitive synaptic learning, a key concept for the experience-based development of cortical circuitry. However, because of the well known positive feedback instability of correlation-based plasticity, the stability of the resulting learning process has remained a central problem. Plagued by either a runaway of the synaptic efficacies or a greatly reduced sensitivity to input correlations, the learning performance of current models is limited. Here we introduce a novel generalized nonlinear TAH learning rule that allows a balance between stability and sensitivity of learning. Using this rule, we study the capacity of the system to learn patterns of correlations between afferent spike trains. Specifically, we address the question of under which conditions learning induces spontaneous symmetry breaking and leads to inhomogeneous synaptic distributions that capture the structure of the input correlations. To study the efficiency of learning temporal relationships between afferent spike trains through TAH plasticity, we introduce a novel sensitivity measure that quantifies the amount of information about the correlation structure in the input, a learning rule capable of storing in the synaptic weights. We demonstrate that by adjusting the weight dependence of the synaptic changes in TAH plasticity, it is possible to enhance the synaptic representation of temporal input correlations while maintaining the system in a stable learning regime. Indeed, for a given distribution of inputs, the learning efficiency can be optimized.

Action Potentials↗

PubMed2003

On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance.

The capability of feedforward networks composed of multiple layers of integrate-and-fire neurons to transmit rate code was examined. Synaptic connections were made only from one layer to the next, and excitation was balanced by inhibition. When time is discrete and the synaptic potentials rise instantaneously, we show that, for random uncorrelated input to layer one, the mean rate of activity in deep layers is essentially independent of input firing rate. This implies that the input rate cannot be transmitted reliably in such feedforward networks because neurons in a given layer tend to synchronize partially with each other because of shared inputs. As a result of this synchronization, the average firing rate in deep layers will either decay to zero or reach a stable fixed point, depending on model parameters. When time is treated continuously and the synaptic potentials rise instantaneously, these effects develop slowly, and rate transmission over a limited number of layers is possible. However, the correlations among neurons at the same layer hamper reliable assessment of firing rate by averaging over 100 msec (or less). When the synaptic potentials develop gradually, as is the realistic case, transmission of rate code fails. In a network in which inhibition only balances the mean excitation but is not timed precisely with it, neurons in each layer fire together, and this volley successively propagates from layer to layer. We conclude that the transmission of rate code in feedforward networks is highly unlikely.

Animals↗

PubMed2003

Mexican hats and pinwheels in visual cortex.

Many models of cortical function assume that local lateral connections are specific with respect to the preferred features of the interacting cells and that they are organized in a Mexican-hat pattern with strong "center" excitation flanked by strong "surround" inhibition. However, anatomical data on primary visual cortex indicate that the local connections are isotropic and that inhibition has a shorter range than excitation. We address this issue in an analytical study of a neuronal network model of the local cortical circuit in primary visual cortex. In the model, the orientation columns specified by the convergent lateral geniculate nucleus inputs are arranged in a pinwheel architecture, whereas cortical connections are isotropic. We obtain a trade-off between the spatial range of inhibition and its time constant. If inhibition is fast, the network can operate in a Mexican-hat pattern with isotropic connections even with a spatially narrow inhibition. If inhibition is not fast, Mexican-hat operation requires a spatially broad inhibition. The Mexican-hat operation can generate a sharp orientation tuning, which is largely independent of the distance of the cell from the pinwheel center.

Animals↗

PubMed2003

Temporal integration by calcium dynamics in a model neuron.

The calculation and memory of position variables by temporal integration of velocity signals is essential for posture, the vestibulo-ocular reflex (VOR) and navigation. Integrator neurons exhibit persistent firing at multiple rates, which represent the values of memorized position variables. A widespread hypothesis is that temporal integration is the outcome of reverberating feedback loops within recurrent networks, but this hypothesis has not been proven experimentally. Here we present a single-cell model of a neural integrator. The nonlinear dynamics of calcium gives rise to propagating calcium wave-fronts along dendritic processes. The wave-front velocity is modulated by synaptic inputs such that the front location covaries with the temporal sum of its previous inputs. Calcium-dependent currents convert this information into concomitant persistent firing. Calcium dynamics in single neurons could thus be the physiological basis of the graded persistent activity and temporal integration observed in neurons during analog memory tasks.

Action Potentials↗

PubMed2003

Rate models for conductance-based cortical neuronal networks.

Population rate models provide powerful tools for investigating the principles that underlie the cooperative function of large neuronal systems. However, biophysical interpretations of these models have been ambiguous. Hence, their applicability to real neuronal systems and their experimental validation have been severely limited. In this work, we show that conductance-based models of large cortical neuronal networks can be described by simplified rate models, provided that the network state does not possess a high degree of synchrony. We first derive a precise mapping between the parameters of the rate equations and those of the conductance-based network models for time-independent inputs. This mapping is based on the assumption that the effect of increasing the cell's input conductance on its f-I curve is mainly subtractive. This assumption is confirmed by a single compartment Hodgkin-Huxley type model with a transient potassium A-current. This approach is applied to the study of a network model of a hypercolumn in primary visual cortex. We also explore extensions of the rate model to the dynamic domain by studying the firing-rate response of our conductance-based neuron to time-dependent noisy inputs. We show that the dynamics of this response can be approximated by a time-dependent second-order differential equation. This phenomenological single-cell rate model is used to calculate the response of a conductance-based network to time-dependent inputs.

Action Potentials↗

PubMed2002

Oscillations by symmetry breaking in homogeneous networks with electrical coupling.

In many biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. This work describes a dynamical mechanism in which the electrical coupling of identical nonoscillating cells destabilizes the homogeneous fixed point and leads to network oscillations via a Hopf bifurcation. Each cell is described by a passive membrane potential and additional internal variables. The dynamics of the internal variables, in isolation, is oscillatory, but their interaction with the membrane potential damps the oscillations and therefore constructs nonoscillatory cells. The electrical coupling reveals the oscillatory nature of the internal variables and generates network oscillations. This mechanism is analyzed near the bifurcation point, where the spatial structure of the membrane potential oscillations is determined by the network architecture and in the limit of strong coupling, where the membrane potentials of all cells oscillate in-phase and multiple cluster states dominate the dynamics. In particular, we have derived an asymptotic behavior for the spatial fluctuations in the limit of strong coupling in fully connected networks and in a one-dimensional lattice architecture.

Journal Article↗