Weight geometry governs functional memory in complex systems

2026-06-24

AI Summary

In complex systems, topological structure alone is insufficient to fully account for functional memory behavior. This work proposes a thermodynamics-based multiscale information flow framework that integrates weighted network null models, path length distributions, and structural perturbation sensitivity analyses to systematically dissect how weight geometry, mesoscale organization, and directionality shape hierarchical memory. The study identifies weight geometry as the key determinant of functional memory depth and demonstrates that diverse memory behaviors can be reduced to four low-dimensional dynamical organizational motifs. Empirical validation across 34 real-world networks spanning multiple domains reveals that empirically observed weights significantly enhance memory depth compared to randomized counterparts, leading to an operational criterion for assessing whether network weights encode functionally relevant structure.

Abstract

Complex systems, from gene regulatory networks to neural circuits and transportation infrastructures, exhibit rich functional behaviour that topology alone does not capture. Here we show that functional memory exhibits a universal organisational regularity: in every biological, ecological, social, and technological domain studied, real interaction strengths organise memory at greater hierarchical depth than random weight assignment on the same topology, across thirty-four networks spanning several orders of magnitude in size and density. Using a thermodynamic description of multiscale information flow, we quantify how memory is distributed across path lengths and show that functional memory organisation collapses onto four recurrent dynamical organisations, revealing an intrinsically low-dimensional structure. Comparing each network against null models that selectively perturb weighted transport geometry, mesoscale structure, and directionality reveals that these ingredients contribute distinct and non-equivalent roles: weight geometry systematically governs memory depth, mesoscale structure shapes memory organisation across scales, and directionality modulates the sensitivity of the cascade to structural perturbation. The same comparison provides an operational criterion for whether network weights encode genuine functional interaction structure. These results establish weighted transport geometry as a primary organiser of functional memory and show that weighted interactions carry dynamical structure that binary topology alone cannot recover.

Problem

• functional memory
• complex systems
• weight geometry
• network topology
• multiscale information flow

Innovation

• weight geometry
• functional memory
• multiscale information flow
• network dynamics
• null models