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Haim Sompolinsky

Publications and source records attributed to Haim Sompolinsky.

6 recordsLinked to original sources

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↗

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↗

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↗

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↗

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↗

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↗