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.

中文翻译：

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神经信息网络的同伦理论和分类模型

在本文中，我们为神经信息网络的建模开发了一种新的数学形式，以资源分配的形式赋予附加结构，无论是计算资源还是代谢资源或信息资源。这种构造的起点是求和函子的概念和同伦理论中的 Segal 的 Gamma 空间。本文的主要结果包括并发/分布式计算架构和相关二进制代码到网络及其子系统的函数分配，Hopfield 网络动力学的一种分类形式，当应用于合适的加权代码类别时，它恢复了通常的 Hopfield 方程，对相应信息结构和信息上同调网络的函数分配，以及集成信息的上同调版本。