Systematic algebraic encoding of algorithmic laws in hypergraph architectures

Develop a systematic method to express algorithmic theories—such as Bellman equations in reinforcement learning, Bayes rule in probabilistic inference, and dynamic programming recursions—as algebraic constraints within hypergraph categorical agent architectures by specifying equations over generated morphisms that implementation functors must satisfy.

Background

Beyond wiring structure, many AI paradigms are defined by characteristic algorithmic laws (e.g., Bellman equations, Bayes rule). The authors aim to incorporate such laws into their architectural presentations as equations over generated morphisms.

They note that, while this direction is motivated and partially outlined, creating a systematic and general mechanism to express these theories within the hypergraph categorical framework remains open.