Department of Neurobiology and Anatomy, University of Texas Medical School, Houston, Texas 77030, USA.
Phys Rev Lett. 2013 Apr 19;110(16):168102. doi: 10.1103/PhysRevLett.110.168102. Epub 2013 Apr 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 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.
韦伯定律于 19 世纪首次被描述，指出感知刺激的大小估计误差与刺激强度呈线性关系。这种线性关系在大多数感觉模式中都存在，也适用于时间间隔估计，甚至适用于一些抽象变量。尽管它具有普遍性和悠久的实验历史，但韦伯定律的神经基础仍然未知。这项工作提出了一个简单的理论，解释了在何种条件下，神经变异性会导致韦伯定律，并预测符合韦伯定律的神经群体的调谐曲线将具有对数幂形式，其参数取决于尖峰计数统计。韦伯定律的普遍性表明，从某种意义上说，它可能是最优的。我们使用变分法来检验这种可能性，并表明只有当观察到的现实世界变量表现出具有特定指数的幂律统计时，韦伯定律才是最优的。我们的理论解释了生理学如何产生行为特征的韦伯定律，并且可能代表了一种将感知与神经活动联系起来的普遍的控制原则。
