Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies

[2509.18758] Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies Skip to main content Search Submit Donate Log in Quantitative Biology > Neurons and Cognition arXiv:2509.18758 (q-bio) [Submitted on 23 Sep 2025] Title: Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies Authors: Marco Cafiso , Paolo Paradisi View PDF HTML (experimental) Abstract: Neural network models capable of storing memory have been extensively studied in computer science and computational neuroscience. The Hopfield network is a prototypical example of a model designed for associative, or content-addressable, memory and has been analyzed in many forms. Further, ideas and methods from complex network theory have been incorporated into artificial neural networks and learning, emphasizing their structural properties. Nevertheless, the temporal dynamics also play a vital role in biological neural networks, whose temporal structure is a crucial feature to examine. Biological neural networks display complex intermittency and, thus, can be studied through the lens of the temporal complexity (TC) theory. The TC approach look at the metastability of self-organized states, characterized by a power-law decay in the inter-event time distribution and in the total activity distribution or a scaling behavior in the corresponding event-driven diffusion processes. In this study, we present a temporal complexity (TC) analysis of a biologically-inspired Hopfield-type neural network model. We conducted a comparative assessment between scale-free and random network topologies, with particular emphasis on their global activation patterns. Our parametric analysis revealed comparable dynamical behaviors across both neural network architectures. Furthermore, our investigation into temporal complexity characteristics uncovered that seemingly distinct dynamical patterns exhibit similar temporal complexity behaviors. In particular, similar power-law decay in the activity distribution and similar complexity levels are observed in both topologies, but with a much reduced noise in the scale-free topology. Notably, most of the complex dynamical profiles were consistently observed in scale-free network configurations, thus confirming the crucial role of hubs in neural network dynamics. Subjects: Neurons and Cognition (q-bio.NC) ; Artificial Intelligence (cs.AI); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph) Cite as: arXiv:2509.18758 [q-bio.NC] (or arXiv:2509.18758v1 [q-bio.NC] for this version) https://doi.org/10.48550/arXiv.2509.18758 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Studies in Computational Intelligence, vol 1284, 2026 Related DOI : https://doi.org/10.1007/978-3-032-22633-4_11 Focus to learn more DOI(s) linking to related resources Submission history From: Marco Cafiso [ view email ] [v1] Tue, 23 Sep 2025 07:53:27 UTC (1,920 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: q-bio.NC < prev | next > new | recent | 2025-09 Change to browse by: cs cs.AI nlin nlin.AO physics physics.bio-ph q-bio References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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