Precise timing of spikes between different neurons has been found to convey reliable information beyond the spike count. In contrast, the role of small and variable spiking delays, as reported, for example, in the visual cortex, remains largely unclear. This issue becomes particularly important considering the high speed of neuronal information processing, which is assumed to be based on only a few milliseconds within each processing step. We investigate the role of small and variable spiking delays with a parsimonious stochastic spiking model that is strongly motivated by experimental observations. The model contains only two parameters for the response of a neuron to one stimulus, describing directly the rate and the delay, or phase. Within the theoretical model, we specifically investigate two quantities, the probability of correct stimulus detection and the probability of correct change point detection, as a function of these parameters and within short periods of time. Optimal combinations of the two parameters across stimuli are derived that maximize these probabilities and enable comparison of pure rate, pure phase, and combined codes. In particular, the gain in correct detection probability when adding small and variable spiking delays to pure rate coding increases with the number of stimuli. More interesting, small and variable spiking delays can considerably improve the process of detecting changes in the stimulus, while also decreasing the probability of false alarms and thus increasing robustness and speed of change point detection. The results are compared to empirical spike train recordings of neurons in the visual cortex reported earlier in response to a number of visual stimuli. The results suggest that near-optimal combinations of rate and phase parameters may be implemented in the brain and that adding phase information could particularly increase the quality of change point detection in cases of highly similar stimuli.

中文翻译：

---

用于研究刺激增加和变化点检测的模型，具有小的和可变的尖峰延迟

已发现不同神经元之间尖峰的精确计时可以传达超出尖峰计数的可靠信息。相比之下，小的和可变的尖峰延迟的作用，例如，在视觉皮层中的报道，在很大程度上仍不清楚。考虑到神经元信息处理的高速性，这个问题变得尤为重要，假设每个处理步骤中只有几毫秒。我们使用由实验观察强烈激发的简约随机尖峰模型来研究小而可变的尖峰延迟的作用。该模型仅包含用于神经元对一种刺激的响应的两个参数，直接描述速率和延迟或相位。在理论模型中，我们专门研究了两个量，正确刺激检测的概率和正确变化点检测的概率，作为这些参数的函数并且在短时间内。推导出跨刺激的两个参数的最佳组合，以最大化这些概率并能够比较纯速率、纯相位和组合代码。特别是，当向纯速率编码添加小的可变尖峰延迟时，正确检测概率的增益随着刺激的数量而增加。更有趣的是，小的和可变的尖峰延迟可以显着改善检测刺激变化的过程，同时也降低误报的概率，从而提高变化点检测的鲁棒性和速度。将结果与早先报告的视觉皮层神经元响应于许多视觉刺激的经验尖峰训练记录进行比较。结果表明，可以在大脑中实现速率和相位参数的近乎最佳组合，并且在高度相似的刺激的情况下，添加相位信息可以特别提高变化点检测的质量。