RUI: A Proposal for Research on Computing with Neural Models of Computation

在过去的二十年里，研究各种计算的神经模型的兴趣重新抬头。来自数学、计算机科学、认知科学和生物学等各个领域的研究人员要么试图分析各种神经模型的能力和局限性，要么提出对现有神经模型的扩展或修改，以使这些模型与生物学、控制理论、模式识别等相关领域的应用更加一致。近年来先进的数学技术利用半代数集的结果、模型论、统计方法和实数理论，使研究人员能够回答许多以前开放的关于神经模型的理论问题。这个项目继续进一步研究各种神经模型的能力和局限性，无论是从理论的角度来看，使用参考文献中提到的一些先进的数学技术，还是从实验的角度来看。最终的目标是能够提供对这些模型的工作机制的进一步了解，并在适当的时候修改或扩展现有的模型。本课题所进行的理论研究对神经模型的各种实际应用也有一定的价值。这个项目涉及与本科生的互动，为他们可能在数学、计算机科学和理论生物学方面的研究生学习做准备。

The last two decades have seen a resurgence in the interest of investigating various neural models of computation. Researchers from various fields such as mathematics, computer science, cognitive science and biology are either trying to analyze the capabilities and limitations of various neural models, or proposing extensions or modifications of current neural models to make these models more consistent with applications in biology, control theory, pattern recognition and other related areas. Recent advanced mathematical techniques using results on semi- algebraic sets, model theory, statistical methods and theory of real numbers have enabled researchers to answer many theoretical questions about neural models which were previously open. This project continues further investigation of the capabilities and limitations of various neural models, either from a theoretical point of view using some of the advanced mathematical techniques mentioned in the references, or from an experimental point of view. The ultimate objective is to be able to provide further insight into the working mechanisms of these models, and to modify or extend existing models whenever appropriate. The theoretical investigations to be carried out in this project will also be valuable in various practical application of neural models. This project involves interaction with undergraduate students which should prepare them for possible graduate studies in mathematics, computer science and theoretical biology.