The dynamics of higher-order novelties

TL;DR

This paper investigates higher-order novelties, defined as the first co-occurrence of multiple elements, introduces higher-order Heaps' exponents to measure their discovery rate, and models exploration as a dynamic network random walk.

Contribution

It introduces the concept of higher-order novelties and Heaps' exponents, and presents a dynamic network model to explain their empirical discovery patterns.

Findings

Processes with the same standard Heaps' exponent can differ at higher orders.

The proposed model reproduces empirical properties of higher-order novelties.

Network exploration changes over time, affecting novelty discovery.

Abstract

Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an element. However, novelties can also be generated by combining what is already known. We hence define higher-order novelties as the first time two or more elements appear together, and we introduce higher-order Heaps' exponents as a way to characterize their pace of discovery. Through extensive analysis of real-world data, we find that processes with the same pace of discovery, as measured by the standard Heaps' exponent, can instead differ at higher orders. We then propose to model an exploration process as a random walk on a network in which the possible connections between elements evolve in time. The model reproduces the empirical properties of higher-order novelties, revealing how the network we explore changes over time along with the exploration process.