Working Paper: Towards Schema-based Learning from a Category-Theoretic Perspective
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 $\mathbf{KL(G)}$, prov...
| Authors | Pablo de los Riscos, Fernando J. Corbacho, Michael A. Arbib |
|---|---|
| Primary category | cs.AI |
| Published | 12 April 2026 |
| Last updated at source | 12 April 2026 |
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