The purpose of this study was to take a new approach in showing how the central nervous system might encode time at the supra-second level using recurrent neural nets (RNNs). This approach utilizes units with a delayed feedback, whose feedback weight determines the temporal properties of specific neurons in the network architecture. When these feedback neurons are coupled, they form a multilayered dynamical system that can be used to model temporal responses to steps of input in multidimensional systems. The timing network was implemented using separate recurrent "Go" and "No-Go" neural processing units to process an individual stimulus indicating the time of reward availability. Outputs from these distinct units on each time step are converted to a pulse reflecting a weighted sum of the separate Go and No-Go signals. This output pulse then drives an integrator unit, whose feedback weight and input weights shape the pulse distribution. This system was used to model empirical data from rodents performing in an instrumental "peak interval timing" task for two stimuli, Tone and Flash. For each of these stimuli, reward availability was signaled after different times from stimulus onset during training. Rodent performance was assessed on non-rewarded trials, following training, with each stimulus tested individually and simultaneously in a stimulus compound. The associated weights in the Go/No-Go network were trained using experimental data showing the mean distribution of bar press rates across an 80 s period in which a tone stimulus signaled reward after 5 s and a flash stimulus after 30 s from stimulus onset. Different Go/No-Go systems were used for each stimulus, but the weighted output of each fed into a final recurrent integrator unit, whose weights were unmodifiable. The recurrent neural net (RNN) model was implemented using Matlab and Matlab's machine learning tools were utilized to train the network using the data from non-rewarded trials. The neural net output accurately fit the temporal distribution of tone and flash-initiated bar press data. Furthermore, a "Temporal Averaging" effect was also obtained when the flash and tone stimuli were combined. These results indicated that the system combining tone and flash responses were not superposed as in a linear system, but that there was a non-linearity, which interacted between tone and flash. In order to achieve an accurate fit to the empirical averaging data it was necessary to implement non-linear "saliency functions" that limited the output signal of each stimulus to the final integrator when the other was co-present. The model suggests that the central nervous system encodes timing generation as a dynamical system whose timing properties are embedded in the connection weights of the system. In this way, event timing is coded similar to the way other sensory-motor systems, such as the vestibulo-ocular and optokinetic systems, which combine sensory inputs from the vestibular and visual systems to generate the temporal aspects of compensatory eye movements.

中文翻译：

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通过递归神经网络建模时间间隔。

这项研究的目的是采用一种新的方法来展示中枢神经系统如何使用递归神经网络（RNN）在超秒级别编码时间。这种方法利用具有延迟反馈的单元，其反馈权重决定了网络体系结构中特定神经元的时间特性。当这些反馈神经元耦合时，它们形成了多层动力学系统，可以用来对多维系统中输入步骤的时间响应进行建模。使用单独的循环“执行”和“不执行”神经处理单元来实现计时网络，以处理指示奖励可用性时间的单个刺激。每个时间步长上来自这些不同单元的输出将转换为反映单独的Go和No-Go信号的加权和的脉冲。然后，该输出脉冲驱动积分器单元，积分器单元的反馈权重和输入权重决定了脉冲分布。该系统用于对来自啮齿动物的经验数据进行建模，该啮齿动物在仪器的“峰值间隔计时”任务中对两种刺激（音调和闪光）进行测试。对于这些刺激中的每一个，从训练过程中的刺激发作开始，经过不同的时间后都会发出奖励可用性信号。训练后，在非奖励性试验中对啮齿动物的表现进行了评估，每种刺激都单独且同时在刺激化合物中进行了测试。使用实验数据来训练“通过/不通过”网络中的相关权重，这些数据显示了在80 s周期内杠铃按压速率的平均分布，其中音调刺激在5 s后开始表示奖励，而闪光刺激在刺激开始30 s后进行了奖励。每种刺激使用不同的Go / No-Go系统，但是每种的加权输出被馈送到最终的循环积分器单元，该单元的权重不可更改。递归神经网络（RNN）模型是使用Matlab实现的，而Matlab的机器学习工具则利用来自非奖励试验的数据来训练网络。神经网络输出准确地拟合了音调和闪光灯启动的压条数据的时间分布。此外，当闪光和音调刺激相结合时，也获得了“时间平均”效果。这些结果表明，结合了音调和闪光响应的系统没有像线性系统那样叠加，但是存在非线性，它在音调和闪光之间相互作用。为了实现对经验平均数据的精确拟合，有必要实现非线性“显着性函数”，该非线性“显着性函数”将每个激励的输出信号限制在最终存在的积分器中。该模型表明，中枢神经系统将时序生成编码为动态系统，其时序属性嵌入到系统的连接权重中。这样，事件计时的编码方式类似于其他感觉运动系统（例如前庭眼和视动系统），它们结合了前庭和视觉系统的感觉输入以生成代偿性眼动的时间方面。该模型表明，中枢神经系统将时序生成编码为动态系统，其时序属性嵌入到系统的连接权重中。这样，事件计时的编码方式类似于其他感觉运动系统（例如前庭眼和视动系统），它们结合了前庭和视觉系统的感觉输入以生成代偿性眼动的时间方面。该模型表明，中枢神经系统将时序生成编码为动态系统，其时序属性嵌入到系统的连接权重中。这样，事件计时的编码方式类似于其他感觉运动系统（例如前庭眼和视动系统），它们结合了前庭和视觉系统的感觉输入以生成代偿性眼动的时间方面。