Models of associative memory with discrete state synapses learn new memories by forgetting old ones. In contrast to non-integrative models of synaptic plasticity, models with integrative, filter-based synapses exhibit an initial rise in the fidelity of recall of stored memories. This rise to a peak is driven by a transient process and is then followed by a return to equilibrium. In a series of papers, we have employed a first passage time (FPT) approach to define and study memory lifetimes, incrementally developing our methods, from both simple and complex binary-strength synapses to simple multistate synapses. Here, we complete this work by analyzing FPT memory lifetimes in multistate, filter-based synapses. To achieve this, we integrate out the internal filter states so that we can work with transitions only in synaptic strength. We then generalize results on polysynaptic generating functions from binary strength to multistate synapses, allowing us to examine the dynamics of synaptic strength changes in an ensemble of synapses rather than just a single synapse. To derive analytical results for FPT memory lifetimes, we partition the synaptic dynamics into two distinct phases: the first, pre-peak phase studied with a drift-only approximation, and the second, post-peak phase studied with approximations to the full strength transition probabilities. These approximations capture the underlying dynamics very well, as demonstrated by the extremely good agreement between results obtained by simulating our model and results obtained from the Fokker-Planck or integral equation approaches to FPT processes.

中文翻译：

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多状态、基于过滤器的突触的首次通过时间记忆寿命

具有离散状态突触的联想记忆模型通过忘记旧记忆来学习新记忆。与突触可塑性的非整合模型相比，具有整合的、基于过滤器的突触的模型表现出存储记忆回忆保真度的初始上升。这种上升到峰值是由一个瞬态过程驱动的，然后又回到平衡状态。在一系列论文中，我们采用了首次通过时间 (FPT) 方法来定义和研究记忆寿命，逐步开发我们的方法，从简单和复杂的二元强度突触到简单的多态突触。在这里，我们通过分析多状态、基于过滤器的突触中的 FPT 内存寿命来完成这项工作。为了实现这一点，我们整合了内部过滤器状态，以便我们只能在突触强度中处理转换。然后，我们将多突触生成函数的结果从二元强度推广到多状态突触，使我们能够检查突触集合中突触强度变化的动态，而不仅仅是单个突触。为了获得 FPT 记忆寿命的分析结果，我们将突触动力学划分为两个不同的阶段：第一个，峰值前阶段，仅使用漂移近似研究，第二个，峰值后阶段，使用全强度过渡的近似值研究概率。这些近似值很好地捕捉了潜在的动力学，正如通过模拟我们的模型获得的结果与从 Fokker-Planck 或 FPT 过程的积分方程方法获得的结果之间的极好的一致性所证明的。