  Category theory has been successfully applied in various domains of science,
shedding light on universal principles unifying diverse phenomena and thereby
enabling knowledge transfer between them. Applications to machine learning have
been pursued recently, and yet there is still a gap between abstract
mathematical foundations and concrete applications to machine learning tasks.
In this paper we introduce DisCoPyro as a categorical structure learning
framework, which combines categorical structures (such as symmetric monoidal
categories and operads) with amortized variational inference, and can be
applied, e.g., in program learning for variational autoencoders. We provide
both mathematical foundations and concrete applications together with
comparison of experimental performance with other models (e.g., neuro-symbolic
models). We speculate that DisCoPyro could ultimately contribute to the
development of artificial general intelligence.
