Origin of information-limiting noise correlations

The ability to discriminate between similar sensory stimuli relies on the amount of information encoded in sensory neuronal populations. Such information can be substantially reduced by correlated trial-to-trial variability. Noise correlations have been measured across a wide range of areas in the brain, but their origin is still far from clear. Here we show analytically and with simulations that optimal computation on inputs with limited information creates patterns of noise correlations that account for a broad range of experimental observations while at same time causing information to saturate in large neural populations. With the example of a network of V1 neurons extracting orientation from a noisy image, we illustrate to our knowledge the first generative model of noise correlations that is consistent both with neurophysiology and with behavioral thresholds, without invoking suboptimal encoding or decoding or internal sources of variability such as stochastic network dynamics or cortical state fluctuations. We further show that when information is limited at the input, both suboptimal connectivity and internal fluctuations could similarly reduce the asymptotic information, but they have qualitatively different effects on correlations leading to specific experimental predictions. Our study indicates that noise at the sensory periphery could have a major effect on cortical representations in widely studied discrimination tasks. It also provides an analytical framework to understand the functional relevance of different sources of experimentally measured correlations.The response of cortical neurons to an identical stimulus varies from trial to trial. Moreover, this variability tends to be correlated among pairs of nearby neurons. These correlations, known as noise correlations, have been the subject of numerous experimental as well as theoretical studies because they can have a profound impact on behavioral performance (1–7). Indeed, behavioral performance in discrimination tasks is inversely proportional to the Fisher information available in the neural responses, which itself is strongly dependent on the pattern of correlations. In particular, correlations can strongly limit information in the sense that some patterns of correlations can lead information to saturate to a finite value in large populations, in sharp contrast to the case of independent neurons for which information grows proportionally to the number of neurons. However, the saturation is observed for only one type of correlations known as differential correlations. If the correlation pattern slightly deviates from differential correlations, information typically scales with the number of neurons, just like it does for independent neurons (7). These previous results clarify how correlations impact information and consequently behavioral performance but fail to address another fundamental question, namely, Where do noise correlations, and in particular information-limiting differential correlation, come from? Understanding the origin of information-limiting correlation is a key step toward understanding how neural circuits can increase information transfer, thereby improving behavioral performance, via either perceptual learning or attentional selection.Several groups have started to investigate sources of noise correlations such as shared connectivity (2), feedback signals (8), internal dynamics (9–11), or global fluctuations in the excitability of cortical circuits (12–16). Global fluctuations have received a lot of attention recently as they appear to account for a large fraction of the measured correlations in the primary visual cortex. Correlations induced by global fluctuations, however, do not limit information in most discrimination tasks (with the possible exception of contrast discrimination for visual stimuli). Therefore, if cortex indeed operates at information saturation, the source of information-limiting correlations is still very much unclear.In this paper, we focus on correlations induced by feedforward processing of stimuli whose information content is small compared with the information capacity of neural circuits. Using orientation selectivity as a case study, we find that feedforward processing induces correlations that share many properties of the correlations observed in vivo. Moreover, we also show feedforward processing leads to information-limiting correlations as a direct consequence of the data processing inequality. Interestingly, these information-limiting correlations represent only a small fraction of the overall correlations induced by feedforward processing, making them difficult to detect through direct measurements of correlations. Finally, we demonstrate that correlations induced by global fluctuations cannot limit information on their own, but can reduce the level at which information saturates in the presence of information-limiting correlations. Despite our focus on orientation selectivity, our results can be generalized to other modalities, stimuli, and brain areas.In summary, this work identifies a major source of noise correlations and, importantly, a source of information-limiting noise correlations, while clarifying the interactions between information-limiting correlations and correlations induced by global fluctuations.