Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. Such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.

翻译：认知的数学模型通常是无记忆的，并忽略其参数可能存在的波动。然而，人类认知本质上是动态的。因此，我们提出从超统计视角，为机械性认知模型赋予时间维度，并估计由此产生的动态过程。此类模型在低层观测模型与高层转移模型之间形成层级结构：观测模型描述系统的局部行为，转移模型则规定观测模型参数随时间演化的方式。为克服超统计模型复杂性所带来的估计难题，我们开发并验证了一种基于仿真的深度学习方法用于贝叶斯推断，该方法能够同时恢复时变参数与时不变参数。我们首先将所提方法与两种现有可估计时变参数的框架进行基准测试，随后将其应用于拟合扩散决策模型的动态版本至人类反应时数据的长时序数据。结果表明，深度学习方法在捕捉模型时间动态方面非常高效。此外，我们证明，假设参数为静态或同质的错误做法将掩盖重要的时间信息。