This paper presents a novel approach to advancing artificial intelligence (AI) through the development of the Complex Recurrent Spectral Network ($\mathbb{C}$-RSN), an innovative variant of the Recurrent Spectral Network (RSN) model. The $\mathbb{C}$-RSN is designed to address a critical limitation in existing neural network models: their inability to emulate the complex processes of biological neural networks dynamically and accurately. By integrating key concepts from dynamical systems theory and leveraging principles from statistical mechanics, the $\mathbb{C}$-RSN model introduces localized non-linearity, complex fixed eigenvalues, and a distinct separation of memory and input processing functionalities. These features collectively enable the $\mathbb{C}$-RSN evolving towards a dynamic, oscillating final state that more closely mirrors biological cognition. Central to this work is the exploration of how the $\mathbb{C}$-RSN manages to capture the rhythmic, oscillatory dynamics intrinsic to biological systems, thanks to its complex eigenvalue structure and the innovative segregation of its linear and non-linear components. The model's ability to classify data through a time-dependent function, and the localization of information processing, is demonstrated with an empirical evaluation using the MNIST dataset. Remarkably, distinct items supplied as a sequential input yield patterns in time which bear the indirect imprint of the insertion order (and of the time of separation between contiguous insertions).

翻译：本文提出了一种推动人工智能（AI）发展的新方法，即开发复杂循环谱网络（$\mathbb{C}$-RSN），这是循环谱网络（RSN）模型的一种创新变体。$\mathbb{C}$-RSN旨在解决现有神经网络模型的一个关键局限性：它们无法动态且精确地模拟生物神经网络的复杂过程。通过整合动力系统理论的核心概念并利用统计力学的原理，$\mathbb{C}$-RSN模型引入了局部非线性、复杂固定特征值，以及记忆与输入处理功能的明确分离。这些特征共同使$\mathbb{C}$-RSN能够演化至一种动态振荡的最终状态，更紧密地模拟生物认知。本工作的核心在于探讨$\mathbb{C}$-RSN如何凭借其复杂特征值结构以及线性和非线性组分的创新分离，捕捉生物系统固有的节律性振荡动力学。该模型通过时间依赖函数进行数据分类的能力以及信息处理的局部化，通过使用MNIST数据集进行的实证评估得到了验证。值得注意的是，作为序列输入提供的不相同项目会在时间上产生模式，这些模式间接保留了插入顺序（以及连续插入之间的时间间隔）的痕迹。