Humans can estimate the duration of intervals of time, and psychophysical experiments show that these estimations are subject to timing errors. According to standard theories of timing, these errors increase linearly with the interval to be estimated (Weber's law), and both at longer and shorter intervals, deviations from linearity are reported. This is not easily reconciled with the accumulation of neuronal noise, which would only lead to an increase with the square root of the interval. Here, we offer a neuronal model which explains the form of the error function as a result of a constrained optimization process. The model consists of a number of synfire chains with different transmission times, which project onto a set of readout neurons. We show that an increase in the transmission time corresponds to a superlinear increase of the timing errors. Under the assumption of a fixed chain length, the experimentally observed error function emerges from optimal selection of chains for each given interval. Furthermore, we show how this optimal selection could be implemented by competitive spike-timing dependent plasticity in the connections from the chains to the readout network, and discuss implications of our model on selective temporal learning and possible neural architectures of interval timing.

中文翻译：

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用于最佳时间处理的神经计算模型。

人类可以估计时间间隔的持续时间，心理物理学实验表明，这些估计会受到时间误差的影响。根据时间的标准理论，这些误差随着要估计的间隔（韦伯定律）线性增加，并且在更长和更短的间隔中，都会报告与线性的偏差。这不容易与神经元噪声的积累相协调，后者只会导致间隔的平方根增加。在这里，我们提供了一个神经元模型，它解释了作为约束优化过程的结果的误差函数的形式。该模型由许多具有不同传输时间的合成火链组成，它们投射到一组读出神经元上。我们表明传输时间的增加对应于定时误差的超线性增加。在固定链长的假设下，实验观察到的误差函数来自每个给定间隔的链的最佳选择。此外，我们展示了如何通过从链到读出网络的连接中的竞争性尖峰时间依赖可塑性来实现这种最佳选择，并讨论我们的模型对选择性时间学习和间隔时间可能的神经结构的影响。