Search Space Synthesis for Parametric Functions

We present a general framework for synthesizing search spaces of parametric functions, along with strategies for traversing these spaces to find optima. We formalize an algebraic theory for the categorical model of parametric functions in finite combinatory logic with predicates (FCLP). Based on a component-oriented synthesis framework for FCLP we automate composition from given components and search for parametric functions. Components are language-agnostic and may be instantiated as any implementation of parametric functions, e.g., as PyTorch modules. A proof-of-concept implementation demonstrates how to represent more specific concepts, such as neural architecture search and hyperparameter optimization, within the framework.