Maoz Shamir

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.

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 n 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. We ask 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.

Cortical Discrimination of Complex Natural Stimuli: Can Single Neurons Match Behavior?

A central finding in many cortical areas is that single neurons can match behavioral performance in the discrimination of sensory stimuli. However, whether this is true for natural behaviors involving complex natural stimuli remains unknown. Here we use the model system of songbirds to address this problem. Specifically, we investigate whether neurons in field L, the homolog of primary auditory cortex, can match behavioral performance in the discrimination of conspecific songs. We use a classification framework based on the (dis)similarity between single spike trains to quantify neural discrimination. We use this framework to investigate the discriminability of single spike trains in field L in response to conspecific songs, testing different candidate neural codes underlying discrimination. We find that performance based on spike timing is significantly higher than performance based on spike rate and interspike intervals. We then assess the impact of temporal correlations in spike trains on discrimination. In contrast to widely discussed effects of correlations in limiting the accuracy of a population code, temporal correlations appear to improve the performance of single neurons in the majority of cases. Finally, we compare neural performance with behavioral performance. We find a diverse range of performance levels in field L, with neural performance matching behavioral accuracy only for the best neurons using a spike-timing-based code.

Balancing Feed-Forward Excitation and Inhibition via Hebbian Inhibitory Synaptic Plasticity

It has been suggested that excitatory and inhibitory inputs to cortical cells are balanced, and that this balance is important for the highly irregular firing observed in the cortex. There are two hypotheses as to the origin of this balance. One assumes that it results from a stable solution of the recurrent neuronal dynamics. This model can account for a balance of steady state excitation and inhibition without fine tuning of parameters, but not for transient inputs. The second hypothesis suggests that the feed forward excitatory and inhibitory inputs to a postsynaptic cell are already balanced. This latter hypothesis thus does account for the balance of transient inputs. However, it remains unclear what mechanism underlies the fine tuning required for balancing feed forward excitatory and inhibitory inputs. Here we investigated whether inhibitory synaptic plasticity is responsible for the balance of transient feed forward excitation and inhibition. We address this issue in the framework of a model characterizing the stochastic dynamics of temporally anti-symmetric Hebbian spike timing dependent plasticity of feed forward excitatory and inhibitory synaptic inputs to a single post-synaptic cell. Our analysis shows that inhibitory Hebbian plasticity generates ‘negative feedback’ that balances excitation and inhibition, which contrasts with the ‘positive feedback’ of excitatory Hebbian synaptic plasticity. As a result, this balance may increase the sensitivity of the learning dynamics to the correlation structure of the excitatory inputs.

Emerging principles of population coding: in search for the neural code

Population coding theory aims to provide quantitative tests for hypotheses concerning the neural code. Over the last two decades theory has focused on analyzing the ways in which various parameters that characterize neuronal responses to external stimuli affect the information content of these responses. This article reviews and provides an intuitive explanation for the major effects of noise correlations and neuronal heterogeneity, and discusses their implications for our ability to investigate the neural code. It is argued that to test neural code hypotheses further, additional constraints are required, including relating trial-to-trial variation in neuronal population responses to behavioral decisions and specifying how information is decoded by downstream networks.

Representation of time-varying stimuli by a network exhibiting oscillations on a faster time scale.

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp.

First Spike Latency Code for Interaural Phase Difference Discrimination in the Guinea Pig Inferior Colliculus

First spike latency has been suggested as a source of the information required for fast discrimination tasks. However, the accuracy of such a mechanism has not been analyzed rigorously. Here, we investigate the utility of first spike latency for encoding information about the location of a sound source, based on the responses of inferior colliculus (IC) neurons in the guinea pig to interaural phase differences (IPDs). First spike latencies of many cells in the guinea pig IC show unimodal tuning to stimulus IPD. We investigated the discrimination accuracy of a simple latency code that estimates stimulus IPD from the preferred IPD of the single cell that fired first. Surprisingly, despite being based on only a single spike, the accuracy of the latency code is comparable to that of a conventional rate code computed over the entire response. We show that spontaneous firing limits the capacity of the latency code to accumulate information from large neural populations. This detrimental effect can be overcome by generalizing the latency code to estimate the stimulus IPD from the preferred IPDs of the population of cells that fired the first n spikes. In addition, we show that a good estimate of the neural response time to the stimulus, which can be obtained from the responses of the cells whose response latency is invariant to stimulus identity, limits the detrimental effect of spontaneous firing. Thus, a latency code may provide great improvement in response speed at a small cost to the accuracy of the decision.

Coding "what" and "when" in the Archer fish retina.

Traditionally, the information content of the neural response is quantified using statistics of the responses relative to stimulus onset time with the assumption that the brain uses onset time to infer stimulus identity. However, stimulus onset time must also be estimated by the brain, making the utility of such an approach questionable. How can stimulus onset be estimated from the neural responses with sufficient accuracy to ensure reliable stimulus identification? We address this question using the framework of colour coding by the archer fish retinal ganglion cell. We found that stimulus identity, “what”, can be estimated from the responses of best single cells with an accuracy comparable to that of the animals psychophysical estimation. However, to extract this information, an accurate estimation of stimulus onset is essential. We show that stimulus onset time, “when”, can be estimated using a linear-nonlinear readout mechanism that requires the response of a population of 100 cells. Thus, stimulus onset time can be estimated using a relatively simple readout. However, large nerve cell populations are required to achieve sufficient accuracy.

Fast Coding of Orientation in Primary Visual Cortex

Understanding how populations of neurons encode sensory information is a major goal of systems neuroscience. Attempts to answer this question have focused on responses measured over several hundred milliseconds, a duration much longer than that frequently used by animals to make decisions about the environment. How reliably sensory information is encoded on briefer time scales, and how best to extract this information, is unknown. Although it has been proposed that neuronal response latency provides a major cue for fast decisions in the visual system, this hypothesis has not been tested systematically and in a quantitative manner. Here we use a simple ‘race to threshold’ readout mechanism to quantify the information content of spike time latency of primary visual (V1) cortical cells to stimulus orientation. We find that many V1 cells show pronounced tuning of their spike latency to stimulus orientation and that almost as much information can be extracted from spike latencies as from firing rates measured over much longer durations. To extract this information, stimulus onset must be estimated accurately. We show that the responses of cells with weak tuning of spike latency can provide a reliable onset detector. We find that spike latency information can be pooled from a large neuronal population, provided that the decision threshold is scaled linearly with the population size, yielding a processing time of the order of a few tens of milliseconds. Our results provide a novel mechanism for extracting information from neuronal populations over the very brief time scales in which behavioral judgments must sometimes be made.

Archer fish fast hunting maneuver may be guided by directionally selective retinal ganglion cells.

Archer fish are known for their unique hunting method, where one fish in a group shoots down an insect with a jet of water while all the other fish are observing the prey’s motion. To reap its reward, the archer fish must reach the prey before its competitors. This requires fast computation of the direction of motion of the prey, which enables the fish to initiate a turn towards the prey with an accuracy of 99%, at about 100 ms after the prey is shot. We explored the hypothesis that direction‐selective retinal ganglion cells may underlie this rapid processing. We quantified the degree of directional selectivity of ganglion cells in the archer fish retina. The cells could be categorized into three groups: sharply (5%), broadly (37%) and non‐tuned (58%) directionally selective cells. To relate the electrophysiological data to the behavioral results we studied a computational model and estimated the time required to accumulate sufficient directional information to match the decision accuracy of the fish. The computational model is based on two direction‐selective populations that race against each other until one reaches the threshold and drives the decision. We found that this competition model can account for the observed response time at the required accuracy. Thus, our results are consistent with the hypothesis that the fast response behavior of the archer fish relies on retinal identification of movement direction.