Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics

[2211.11346] Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantitative Biology > Neurons and Cognition arXiv:2211.11346 (q-bio) [Submitted on 21 Nov 2022 ( v1 ), last revised 15 Apr 2026 (this version, v2)] Title: Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics Authors: Kazuyoshi Tsutsumi , Ernst Niebur View a PDF of the paper titled Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics, by Kazuyoshi Tsutsumi and Ernst Niebur View PDF HTML (experimental) Abstract: We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are connected with a layered internetwork that consists of a pair of forward and backward subnets composed of static neurons (with an instantaneous time-course). Dynamical neurons with large time constants in the internal space determine the overall time-course. The model offers a framework in which state variables in the network relax in a warped space, due to the cooperation between dynamic and static neurons. We assume that the system operates in either a learning or an association mode, depending on the presence or absence of feedback paths and input ports. In the learning mode, synaptic weights in the internetwork are modified by strong inputs corresponding to repetitive neuronal bursting, which represents sinusoidal or quasi-sinusoidal waves in the short-term average density of nerve impulses or in the membrane potential. A two-dimensional mapping relationship can be formed by employing signals with different frequencies based on the same mechanism as Lissajous curves. In the association mode, the speed of convergence to a goal point greatly varies with the mapping relationship of the previously trained internetwork, and owing to this property, the convergence trajectory in the two-dimensional model with the non-linear mapping internetwork cannot go straight but instead must curve. We further introduce a constrained association mode with a given target trajectory and elucidate that in the internal space, an output trajectory is generated, which is mapped from the external space according to the inverse of the mapping relationship of the forward subnet. Comments: 44 pages, 22 figures. v2: fixed typos and clarified phrasing Subjects: Neurons and Cognition (q-bio.NC) Cite as: arXiv:2211.11346 [q-bio.NC] (or arXiv:2211.11346v2 [q-bio.NC] for this version) https://doi.org/10.48550/arXiv.2211.11346 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kazuyoshi Tsutsumi [ view email ] [v1] Mon, 21 Nov 2022 10:53:46 UTC (3,442 KB) [v2] Wed, 15 Apr 2026 07:17:28 UTC (3,439 KB) Full-text links: Access Paper: View a PDF of the paper titled Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics, by Kazuyoshi Tsutsumi and Ernst Niebur View PDF HTML (experimental) TeX Source view license Current browse context: q-bio.NC < prev | next > new | recent | 2022-11 Change to browse by: q-bio References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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