  Human-AI coevolution, defined as a process in which humans and AI algorithms
continuously influence each other, increasingly characterises our society, but
is understudied in artificial intelligence and complexity science literature.
Recommender systems and assistants play a prominent role in human-AI
coevolution, as they permeate many facets of daily life and influence human
choices on online platforms. The interaction between users and AI results in a
potentially endless feedback loop, wherein users' choices generate data to
train AI models, which, in turn, shape subsequent user preferences. This
human-AI feedback loop has peculiar characteristics compared to traditional
human-machine interaction and gives rise to complex and often ``unintended''
social outcomes. This paper introduces Coevolution AI as the cornerstone for a
new field of study at the intersection between AI and complexity science
focused on the theoretical, empirical, and mathematical investigation of the
human-AI feedback loop. In doing so, we: (i) outline the pros and cons of
existing methodologies and highlight shortcomings and potential ways for
capturing feedback loop mechanisms; (ii) propose a reflection at the
intersection between complexity science, AI and society; (iii) provide
real-world examples for different human-AI ecosystems; and (iv) illustrate
challenges to the creation of such a field of study, conceptualising them at
increasing levels of abstraction, i.e., technical, epistemological, legal and
socio-political.
