Fernando J. Corbacho

Pablo de los Riscos, Fernando J. Corbacho, Michael A. Arbib

AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition and only some empirical AGI benchmarking frameworks currently exist. The main purpose of this paper is to develop a general, algebraic and category theoretic framework for describing, comparing and analysing different possible AGI architectures. Thus, this Category theoretic formalization would also allow to compare different possible candidate AGI architectures, such as, RL, Universal AI, Active Inference, CRL, Schema based Learning, etc. It will allow to unambiguously expose their commonalities and differences, and what is even more important, expose areas for future research. From the applied Category theoretic point of view, we take as inspiration Machines in a Category to provide a modern view of AGI Architectures in a Category. More specifically, this first position paper provides, on one hand, a first exercise on RL, Causal RL and SBL Architectures in a Category, and on the other hand, it is a first step on a broader research program that seeks to provide a unified formal foundation for AGI systems, integrating architectural structure, informational organization, agent realization, agent and environment interaction, behavioural development over time, and the empirical evaluation of properties. This framework is also intended to support the definition of architectural properties, both syntactic and informational, as well as semantic properties of agents and their assessment in environments with explicitly characterized features. We claim that Category Theory and AGI will have a very symbiotic relation.

Pablo de los Riscos, Fernando J. Corbacho, Michael A. Arbib

We introduce a hierarchical categorical framework for Schema-Based Learning (SBL) structured across four interconnected levels. At the schema level, a free multicategory $Sch_{syn}$ encodes fundamental schemas and transformations. An implementation functor $\mathcal{I}$ maps syntactic schemas to representational languages, inducing via the Grothendieck construction the total category $Sch_{impl}$. Implemented schemas are mapped by a functor $Model$ into the Kleisli category $\mathbf{KL(G)}$ of the Giry monad, yielding probabilistic models, while an instances presheaf assigns evaluated instance spaces. A semantic category $Sch_{sem}$, defined as a full subcategory of $\mathbf{KL(G)}$, provides semantic grounding through an interpretation functor from $Sch_{impl}$. At the agent level, $Sch_{impl}$ is equipped with a duoidal structure $\mathcal{O}_{Sch}$ supporting schema-based workflows. A left duoidal action on the category $Mind$ enables workflow execution over mental objects, whose components include mental spaces, predictive models, and a cognitive kernel composed of memory and cognitive modules. Each module is specified by schema-typed interfaces, duoidal workflows, a success condition, and a logical signature. Memory is formalized categorically via memory subsystems, a presheaf $Data_M$, a monoidal operation category $Ops_M$, and read/write natural transformations. Together with the $Body$ category, Mind defines the embodied SBL agent. At higher levels, SBL is represented as an object of the agent architecture category $ArchCat$, enabling comparison with heterogeneous paradigms, while the $World$ category models multi-agent and agent-environment interactions. Altogether, the framework forms a weak hierarchical $n$-categorical structure linking schema semantics, cognition, embodiment, architectural abstraction, and world-level interaction.

Fernando J. Corbacho

Artificial Intelligence frameworks should allow for ever more autonomous and general systems in contrast to very narrow and restricted (human pre-defined) domain systems, in analogy to how the brain works. Self-constructive Artificial Intelligence ($SCAI$) is one such possible framework. We herein propose that $SCAI$ is based on three principles of organization: self-growing, self-experimental and self-repairing. Self-growing: the ability to autonomously and incrementally construct structures and functionality as needed to solve encountered (sub)problems. Self-experimental: the ability to internally simulate, anticipate and take decisions based on these expectations. Self-repairing: the ability to autonomously re-construct a previously successful functionality or pattern of interaction lost from a possible sub-component failure (damage). To implement these principles of organization, a constructive architecture capable of evolving adaptive autonomous agents is required. We present Schema-based learning as one such architecture capable of incrementally constructing a myriad of internal models of three kinds: predictive schemas, dual (inverse models) schemas and goal schemas as they are necessary to autonomously develop increasing functionality. We claim that artificial systems, whether in the digital or in the physical world, can benefit very much form this constructive architecture and should be organized around these principles of organization. To illustrate the generality of the proposed framework, we include several test cases in structural adaptive navigation in artificial intelligence systems in Paper II of this series, and resilient robot motor control in Paper III of this series. Paper IV of this series will also include $SCAI$ for problem structural discovery in predictive Business Intelligence.