Nonlinear Population Codes

Shamir, Maoz; Sompolinsky, Haim

doi:10.1162/089976604773717559

Cited by 133 publications

(125 citation statements)

References 20 publications

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“…The accuracy of the code decreases if similarly tuned neurons are correlated more strongly than dissimilar cells, as we find. For some algorithms for reading population codes, however, stimulus-dependent correlation can improve markedly the accuracy of the population code (Shamir and Sompolinsky, 2004). The net effect of the V1 correlation we report will thus depend on the degree to which subsequent stages of cortical processing can read out stimulus dependent correlation.…”

Section: Functional Implicationsmentioning

confidence: 80%

“…For instance, understanding the stimulus dependence of synchrony is necessary for evaluating its role in binding and for determining how it affects the maximal stimulus frequency that can be encoded in a population firing rate (Mazurek and Shadlen, 2002). In addition, theoretical studies suggest that capacity of a population rate code to encode information depends on the magnitude of correlated variability, its relationship to the tuning similarity of two neurons, and its dependence on stimulus drive (Abbott and Dayan, 1999;Sompolinsky et al, 2001;Shamir and Sompolinsky, 2004). Finally, measuring correlation provides a way to test current models for reading out noisy population codes (Pouget et al, 1998), because these make testable predictions about the stimulus dependence of correlation.…”

Section: Introductionmentioning

confidence: 99%

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Stimulus Dependence of Neuronal Correlation in Primary Visual Cortex of the Macaque

Kohn¹,

Ma²

2005

J. Neurosci.

512

584

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Nearby cortical neurons often have correlated trial-to-trial response variability, and a significant fraction of their spikes occur synchronously. These two forms of correlation are both believed to arise from common synaptic input, but the origin of this input is unclear. We investigated the source of correlated responsivity by recording from pairs of single neurons in primary visual cortex of anesthetized macaque monkeys and comparing correlated variability and synchrony for spontaneous activity and activity evoked by stimuli of different orientations and contrasts. These two stimulus manipulations would be expected to have different effects on the cortical pool providing input to the recorded pair: changing stimulus orientation should recruit different populations of cells, whereas changing stimulus contrast affects primarily the relative strength of sensory drive and ongoing cortical activity. Consistent with this predicted difference, we found that correlation was affected by these stimulus manipulations in different ways. Synchrony was significantly stronger for orientations that drove both neurons well than for those that did not, but correlation on longer time scales was orientation independent. Reducing stimulus contrast resulted in a decrease in the temporal precision of synchronous firing and an enhancement of correlated response variability on longer time scales. Our results thus suggest that correlated responsivity arises from mechanisms operating at two distinct timescales: one that is orientation tuned and that determines the strength of temporally precise synchrony, and a second that is contrast sensitive, of low temporal frequency, and present in ongoing cortical activity.

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Section: Functional Implicationsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Stimulus Dependence of Neuronal Correlation in Primary Visual Cortex of the Macaque

Kohn¹,

Ma²

2005

J. Neurosci.

512

584

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“…Here, we provide experimental evidence suggesting that stimulusdependent correlations might be used to transmit information. However, information readout from the covariance structure is nontrivial and requires nonlinear schemes (45), and it remains to be determined whether and how they are implemented by neural systems in vivo.…”

Section: Discussionmentioning

confidence: 99%

Stimulus-dependent variability and noise correlations in cortical MT neurons

Ponce‐Alvarez

Thiele

Albright

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

124

152

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Population codes assume that neural systems represent sensory inputs through the firing rates of populations of differently tuned neurons. However, trial-by-trial variability and noise correlations are known to affect the information capacity of neural codes. Although recent studies have shown that stimulus presentation reduces both variability and rate correlations with respect to their spontaneous level, possibly improving the encoding accuracy, whether these second order statistics are tuned is unknown. If so, second-order statistics could themselves carry information, rather than being invariably detrimental. Here we show that rate variability and noise correlation vary systematically with stimulus direction in directionally selective middle temporal (MT) neurons, leading to characteristic tuning curves. We show that such tuning emerges in a stochastic recurrent network, for a set of connectivity parameters that overlaps with a single-state scenario and multistability. Information theoretic analysis shows that second-order statistics carry information that can improve the accuracy of the population code.C ortical activity is highly variable during spontaneous activity (1-4) and even when tested under constant experimental conditions (5-8). This variability is thought to limit the capacity of individual neurons to transmit information (9). Furthermore, variability is often correlated among neurons, and thus, it cannot be completely removed by averaging the population response (9-12). Recent experimental studies have examined the secondorder statistics of neural responses across a variety of species, cortical areas, tasks, and stimulus and/or attentional conditions (13-17). In particular, it has been shown that the Fano factor (FF)-that is, the ratio between the variance of the spike counts over trials and its mean-is reduced when a stimulus is applied (16), thus improving the encoding of the stimulus. Importantly, both preferred and nonpreferred stimuli reduced the FF. In addition, the evoked noise correlation-that is, the trial-to-trial covariance of stimulus induced activity between two simultaneously recorded neurons-is also reduced upon stimulus presentation (18), after stimulus adaptation (19) or perceptual learning (20), and under attention (14, 21), an effect that could, under certain conditions, lead to more reliable estimates of the mean population activity (22). Hence, there is a growing body of evidence suggesting that the encoding of a signal through cortical activity may be improved by minimizing both trialby-trial variability and noise correlations. However, it remains an open experimental and theoretical question, whether these statistics are themselves tuned to different stimulus features, an aspect that may be overlooked when only analyzing preferred and nonpreferred stimuli.Here, we examined the statistics of responses of area-middle temporal (MT) neurons in awake, fixating primates, to moving gratings and different plaid patterns of different directions, as well as moving gratings of differ...

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“…For instance, when p(y|s) is a multivariate gaussian distribution, there is a second term, the so-called trace term, that reflects the information content that results from a stimulus-dependent covariance matrix under the gaussian assumption. In theory, this term can contain a large fraction of the information, particularly when the covariance matrix depends on the stimulus (Shamir & Sompolinsky, 2004). Nonetheless, we chose to focus on the linear term because it provides a tight bound on total Fisher information in both simulations (Seriès et al, 2004) and in vivo (Averbeck et al, 2006).…”

Section: Linear Fisher Informationmentioning

confidence: 99%

Insights from a Simple Expression for Linear Fisher Information in a Recurrently Connected Population of Spiking Neurons

2011

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A simple expression for a lower bound of Fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise-perturbed steady state. We call this lower bound linear Fisher information, as it corresponds to the Fisher information that can be recovered by a locally optimal linear estimator. Unlike recent similar calculations, the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network. Here, this expression is used to (1) compute the optimal (i.e., informationmaximizing) firing rate of a neuron, (2) demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea, (3) show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss, and (4) show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network.

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Nonlinear Population Codes

Cited by 133 publications

References 20 publications

Stimulus Dependence of Neuronal Correlation in Primary Visual Cortex of the Macaque

Stimulus Dependence of Neuronal Correlation in Primary Visual Cortex of the Macaque

Stimulus-dependent variability and noise correlations in cortical MT neurons

Insights from a Simple Expression for Linear Fisher Information in a Recurrently Connected Population of Spiking Neurons

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