Using analogical reasoning to build transferable models

Humans use analogical reasoning to connect understanding of one system to another. Can machines use similar abstractions to transfer their learning from training data to other regimes? The Manifold Boundary Approximation Method constructs simple, reduced models of target phenomena in a data-driven way. We consider the set of all such reduced models and use the topological relationships among them to reason about model selection for new, unobserved phenomena. Given minimal models for several target behaviors, we introduce the supremum principle as a criterion for selecting a new, transferable model. The supremum principle shares connections with the theory of analogical reasoning in cognitive psychology. Having unified the relevant mechanisms, the supremal model, i.e., the least upper bound, is the simplest model that reduces to each of the target behaviors. Describing multiple behavioral regimes, the supremal model provides a controller to move between various states of interest, e.g., sick and healthy cells in systems biology. Additionally, the supremal model transfers to domains outside of the training data, allowing it to describe new, emergent behaviors. We present a general algorithm for constructing a supremal model and demonstrate with examples from various disciplines.