Adjacent Possible Innovation Dynamics on Local Optima Networks

TL;DR

This paper introduces Local Optima Networks (LONs) as a formal framework to model innovation dynamics, capturing empirical regularities and bridging different innovation modeling traditions.

Contribution

It presents a novel LON framework that models innovation as stochastic exploration on a network, unifying discovery-process and adaptive-search approaches.

Findings

LONs reproduce empirical regularities like Heaps' law and Zipf's law.

Exponents are within observed ranges and constrained by LON topology.

Communities in LONs define technological paradigms based on basin accessibility.

Abstract

We propose Local Optima Networks (LONs) as a formal framework for modeling innovation dynamics. A LON is a directed weighted graph in which nodes represent locally stable technological configurations and edges encode transition probabilities between their basins of attraction. We construct LONs from fitness landscapes and model innovating agents as stochastic walkers exploring the adjacent possible on the resulting network. We show that this model simultaneously generates the four main empirical regularities of the discovery-process tradition: sublinear novelty growth (Heaps' law), heavy-tailed frequency distributions (Zipf's law), anomalous fluctuation scaling (Taylor's law), and power-law distributed inter-event times. The exponents fall within empirically observed ranges and are jointly constrained by LON topology. Communities in the LON provide an operational definition of technological paradigms grounded in basin-level accessibility. The LON framework thus bridges the discovery-process and adaptive-search traditions of innovation modeling within a single, parsimonious, and empirically testable representation.