论文标题
神经信息网络的理论和分类模型
Homotopy Theoretic and Categorical Models of Neural Information Networks
论文作者
论文摘要
在本文中，我们开发了一种新颖的数学形式主义，以建模神经信息网络，并以资源或代谢或信息性的资源分配形式赋予其他结构。这种构建的起点是在同型理论中求和函子和西加尔的伽马空间的概念。本文的主要结果包括并发/分布式计算体系结构的功能分配以及与网络及其子系统相关的二进制代码，这是Hopfield Network Network Dynamics的一种类别形式，当将通常的Hopfield方程式恢复到适当的加权编码类别时，将其应用于相应的信息结构和信息信息的网络，以及一个组合信息的网络，以及一个集合的信息。
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.
