  In this paper, we propose GAIA, a generative AI architecture based on
category theory. GAIA is based on a hierarchical model where modules are
organized as a simplicial complex. Each simplicial complex updates its internal
parameters biased on information it receives from its superior simplices and in
turn relays updates to its subordinate sub-simplices. Parameter updates are
formulated in terms of lifting diagrams over simplicial sets, where inner and
outer horn extensions correspond to different types of learning problems.
Backpropagation is modeled as an endofunctor over the category of parameters,
leading to a coalgebraic formulation of deep learning.
