Restoring Network Evolution from Static Structure

TL;DR

This paper introduces a machine learning framework combining graph neural networks and transformers to infer the evolutionary history of complex networks from a single static snapshot, revealing hidden temporal dynamics.

Contribution

The authors develop a transferable, neural network-based method that predicts network evolution solely from static topology, applicable across diverse domains.

Findings

Achieves up to 95.3% transfer accuracy in various datasets.

Restores formation times of over 2.6 million neural connections.

Reveals links between connection age and functional roles in neural systems.

Abstract

The dynamical evolution of complex networks underpins the structure-function relationships in natural and artificial systems. Yet, restoring a network's formation from a single static snapshot remains challenging. Here, we present a transferable machine learning framework that infers network evolutionary trajectories solely from present topology. By integrating graph neural networks with transformers, our approach unlocks a latent temporal dimension directly from the static topology. Evaluated across diverse domains, the framework achieves high transfer accuracy of up to 95.3%, demonstrating its robustness and transferability. Applied to the Drosophila brain connectome, it restores the formation times of over 2.6 million neural connections, revealing that early-forming links support essential behaviors such as mating and foraging, whereas later-forming connections underpin complex sensory and social functions. These results demonstrate that a substantial fraction of evolutionary information is encoded within static network architecture, offering a powerful, general tool for elucidating the hidden temporal dynamics of complex systems.