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Scaling of perceptual errors can predict the shape of neural tuning curves.

ABSTRACT: Weber's law, first characterized in the 19th century, states that errors estimating the magnitude of perceptual stimuli scale linearly with stimulus intensity. This linear relationship is found in most sensory modalities, generalizes to temporal interval estimation, and even applies to some abstract variables. Despite its generality and long experimental history, the neural basis of Weber's law remains unknown. This work presents a simple theory explaining the conditions under which Weber's law can result from neural variability and predicts that the tuning curves of neural populations which adhere to Weber's law will have a log-power form with parameters that depend on spike-count statistics. The prevalence of Weber's law suggests that it might be optimal in some sense. We examine this possibility, using variational calculus, and show that Weber's law is optimal only when observed real-world variables exhibit power-law statistics with a specific exponent. Our theory explains how physiology gives rise to the behaviorally characterized Weber's law and may represent a general governing principle relating perception to neural activity.

SUBMITTER: Shouval HZ

PROVIDER: S-EPMC3968685 | biostudies-literature | 2013 Apr

REPOSITORIES: biostudies-literature

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Scaling of perceptual errors can predict the shape of neural tuning curves.

Shouval Harel Z HZ Agarwal Animesh A Gavornik Jeffrey P JP

Physical review letters 20130416 16

Weber's law, first characterized in the 19th century, states that errors estimating the magnitude of perceptual stimuli scale linearly with stimulus intensity. This linear relationship is found in most sensory modalities, generalizes to temporal interval estimation, and even applies to some abstract variables. Despite its generality and long experimental history, the neural basis of Weber's law remains unknown. This work presents a simple theory explaining the conditions under which Weber's law ...[more]

PMID: 23679640

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Project description:Tuning curves characterizing the response selectivities of biological neurons can exhibit large degrees of irregularity and diversity across neurons. Theoretical network models that feature heterogeneous cell populations or partially random connectivity also give rise to diverse tuning curves. Empirical tuning curve distributions can thus be utilized to make model-based inferences about the statistics of single-cell parameters and network connectivity. However, a general framework for such an inference or fitting procedure is lacking. We address this problem by proposing to view mechanistic network models as implicit generative models whose parameters can be optimized to fit the distribution of experimentally measured tuning curves. A major obstacle for fitting such models is that their likelihood function is not explicitly available or is highly intractable. Recent advances in machine learning provide ways for fitting implicit generative models without the need to evaluate the likelihood and its gradient. Generative Adversarial Networks (GANs) provide one such framework which has been successful in traditional machine learning tasks. We apply this approach in two separate experiments, showing how GANs can be used to fit commonly used mechanistic circuit models in theoretical neuroscience to datasets of tuning curves. This fitting procedure avoids the computationally expensive step of inferring latent variables, such as the biophysical parameters of, or synaptic connections between, particular recorded cells. Instead, it directly learns generalizable model parameters characterizing the network's statistical structure such as the statistics of strength and spatial range of connections between different cell types. Another strength of this approach is that it fits the joint high-dimensional distribution of tuning curves, instead of matching a few summary statistics picked a priori by the user, resulting in a more accurate inference of circuit properties. More generally, this framework opens the door to direct model-based inference of circuit structure from data beyond single-cell tuning curves, such as simultaneous population recordings.

Dataset Information

Scaling of perceptual errors can predict the shape of neural tuning curves.

Publications

Scaling of perceptual errors can predict the shape of neural tuning curves.

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