Abstract
AbstractCortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool – Fisher information – can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information.
Highlights
Neuronal ensembles transmit information through their joint firing rate patterns [1]
A neurometric function shows how the discrimination error achieved by a population code depends on the difference between the two stimuli. We use it to revisit the question of optimal population coding with two goals: First, we show that optimal discrimination and optimal reconstruction lead to qualitatively similar results regarding the effect of tuning function width and of different noise correlation structures on coding accuracy; in contrast, Fisher information favors coding schemes which are severely suboptimal for both reconstruction and discrimination at low signal-to-noise ratio
Optimal tuning function width for individual neurons For all three measures (MASE, minimum mean squared error (MMSE) and integrated minimum discrimination error (IMDE)), we investigate how the coding quality of a population with 100 independent neurons with bell-shaped tuning functions depends on the tuning width of individual neurons at different time intervals available for decoding (10, 100, 500 and 1000 ms)
Summary
Neuronal ensembles transmit information through their joint firing rate patterns [1] This raises challenging theoretical questions on how the encoding accuracy of such population codes is affected by properties of individual neurons and correlations among them. A principled approach to define such a measure is to use the concept of a Bayesian ideal observer [2, 3]. This concept requires choosing a specific task: in a stimulus reconstruction task, we ask how well a Bayes-optimal decoder can estimate the true value of the presented stimulus based on the noisy neural response (Fig. 1A). In a stimulus discrimination task, we ask how well it is able to decide which of two stimuli was presented based on the response pattern (Fig. 1B)
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