Learning Functions in Large Networks requires Modularity and produces Multi-Agent Dynamics

TL;DR

This paper investigates the limits of learning large functional motifs in biological networks, revealing a size threshold due to stability issues, and highlights the importance of modularity and team learning in network organization.

Contribution

It introduces a machine learning and genetic algorithm approach to identify large network motifs and demonstrates a size limit linked to stability, emphasizing modularity in biological networks.

Findings

Learning breaks down beyond ~20 nodes due to stability issues.

Negative eigenvalues of the Jacobian decrease with size, indicating instability.

Unconstrained middle components can still learn functions, showing team learning.

Abstract

Networks are abundant in biological systems. Small sized over-represented network motifs have been discovered, and it has been suggested that these constitute functional building blocks. We ask whether larger dynamical network motifs exist in biological networks, thus contributing to the higher-order organization of a network. To end this, we introduce a gradient descent machine learning (ML) approach and genetic algorithms to learn larger functional motifs in contrast to an (unfeasible) exhaustive search. We use the French Flag (FF) and Switch functional motif as case studies motivated from biology. While our algorithm successfully learns large functional motifs, we identify a threshold size of approximately 20 nodes beyond which learning breaks down. Therefore we investigate the stability of the motifs. We find that the size of the real negative eigenvalues of the Jacobian decreases with increasing system size, thus conferring instability. Finally, without imposing learning an input-output for all the components of the network, we observe that unconstrained middle components of the network still learn the desired function, a form of homogeneous team learning. We conclude that the size limitation of learnability, most likely due to stability constraints, impose a definite requirement for modularity in networked systems while enabling team learning within unconstrained parts of the module. Thus, the observation that community structures and modularity are abundant in biological networks could be accounted for by a computational compositional network structure.