Research Centre of Mathematics, University of Minho, Guimarães, Portugal.
Research Centre Algoritmi, University of Minho, Guimarães, Portugal.
Biol Cybern. 2021 Oct;115(5):451-471. doi: 10.1007/s00422-021-00893-7. Epub 2021 Aug 21.
The ability of neural systems to turn transient inputs into persistent changes in activity is thought to be a fundamental requirement for higher cognitive functions. In continuous attractor networks frequently used to model working memory or decision making tasks, the persistent activity settles to a stable pattern with the stereotyped shape of a "bump" independent of integration time or input strength. Here, we investigate a new bump attractor model in which the bump width and amplitude not only reflect qualitative and quantitative characteristics of a preceding input but also the continuous integration of evidence over longer timescales. The model is formalized by two coupled dynamic field equations of Amari-type which combine recurrent interactions mediated by a Mexican-hat connectivity with local feedback mechanisms that balance excitation and inhibition. We analyze the existence, stability and bifurcation structure of single and multi-bump solutions and discuss the relevance of their input dependence to modeling cognitive functions. We then systematically compare the pattern formation process of the two-field model with the classical Amari model. The results reveal that the balanced local feedback mechanisms facilitate the encoding and maintenance of multi-item memories. The existence of stable subthreshold bumps suggests that different to the Amari model, the suppression effect of neighboring bumps in the range of lateral competition may not lead to a complete loss of information. Moreover, bumps with larger amplitude are less vulnerable to noise-induced drifts and distance-dependent interaction effects resulting in more faithful memory representations over time.
神经系统将短暂输入转化为持久活动变化的能力被认为是更高认知功能的基本要求。在常用于模拟工作记忆或决策任务的连续吸引子网络中，持久活动稳定在一个稳定的模式中，具有刻板的“凸起”形状，与积分时间或输入强度无关。在这里，我们研究了一种新的凸起吸引子模型，其中凸起的宽度和幅度不仅反映了先前输入的定性和定量特征，而且还反映了更长时间尺度上证据的连续积分。该模型通过两个耦合的 Amari 型动态场方程来形式化，这些方程结合了由墨西哥帽连接介导的递归相互作用与平衡兴奋和抑制的局部反馈机制。我们分析了单峰和多峰解的存在、稳定性和分岔结构，并讨论了它们对输入的依赖性与建模认知功能的相关性。然后，我们系统地比较了双场模型与经典 Amari 模型的模式形成过程。结果表明，平衡的局部反馈机制有助于多项目记忆的编码和维持。亚阈值凸起的存在表明，与 Amari 模型不同，在侧向竞争范围内相邻凸起的抑制作用可能不会导致信息的完全丢失。此外，幅度较大的凸起受噪声诱导漂移和距离相关相互作用效应的影响较小，因此随着时间的推移，记忆表示更忠实。
