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

2025-09-23

AI Summary

This study investigates the temporal complexity of activity patterns in biologically inspired Hopfield-type neural networks embedded in scale-free versus random topologies. Method: Integrating complex network theory with temporal complexity analysis, we systematically characterize inter-event interval distributions, power-law decay of total activation distributions, and scaling behavior of event-driven diffusion. Contribution/Results: Although both topologies exhibit similar power-law features and comparable overall complexity levels, scale-free networks demonstrate significantly enhanced dynamical stability and markedly reduced noise. Crucially, hub nodes are identified as key structural determinants governing robustness of temporal complexity and noise suppression. To our knowledge, this work establishes—for the first time within the Hopfield framework—the mechanistic role of topological heterogeneity in stabilizing temporal complexity. These findings provide a theoretical foundation for architecture design in brain-inspired computing systems.

Technology Category

Cognitive Modeling & Cognitive Systems: Neural Spike CodingPlanning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsSocial Networks and Social Media: Computational social scienceEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Analyzing temporal complexity in Hopfield networks with different topologies
• Comparing scale-free versus random network activation patterns and dynamics
• Investigating how network structure affects metastability and power-law behaviors

Innovation

• Analyzed temporal complexity in Hopfield networks
• Compared scale-free and random network topologies
• Found similar dynamics with reduced scale-free noise