Existing frameworks for transfer learning are incomplete from a systems theoretic perspective. They place emphasis on notions of domain and task, and neglect notions of structure and behavior. In doing so, they limit the extent to which formalism can be carried through into the elaboration of their frameworks. Herein, we use Mesarovician systems theory to define transfer learning as a relation on sets and subsequently characterize the general nature of transfer learning as a mathematical construct. We interpret existing frameworks in terms of ours and go beyond existing frameworks to define notions of transferability, transfer roughness, and transfer distance. Importantly, despite its formalism, our framework avoids the detailed mathematics of learning theory or machine learning solution methods without excluding their consideration. As such, we provide a formal, general systems framework for modeling transfer learning that offers a rigorous foundation for system design and analysis.
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