  We present a unified formalism for structure discovery of causal models and
predictive state representation (PSR) models in reinforcement learning (RL)
using higher-order category theory. Specifically, we model structure discovery
in both settings using simplicial objects, contravariant functors from the
category of ordinal numbers into any category. Fragments of causal models that
are equivalent under conditional independence -- defined as causal horns -- as
well as subsequences of potential tests in a predictive state representation --
defined as predictive horns -- are both special cases of horns of a simplicial
object, subsets resulting from the removal of the interior and the face
opposite a particular vertex. Latent structure discovery in both settings
involve the same fundamental mathematical problem of finding extensions of
horns of simplicial objects through solving lifting problems in commutative
diagrams, and exploiting weak homotopies that define higher-order symmetries.
Solutions to the problem of filling "inner" vs "outer" horns leads to various
notions of higher-order categories, including weak Kan complexes and
quasicategories. We define the abstract problem of structure discovery in both
settings in terms of adjoint functors between the category of universal causal
models or universal decision models and its simplicial object representation.

Artificial Intelligence;Category Theory