We introduce a computational design workflow based on training examples: Generative Embedded Mapping Systems (GEMS). GEMS enable a designer to leverage embedded spaces to provide parametric systems with automatic mappings to future input data. Instead of specifying a rule-based system for mapping data based on predefined attributes, designers provide parameter values across a set of training examples. These training values serve as anchor points bridging a parameter and embedding space. Settings for new data can then be extrapolated from known pairs. A Neural Caricature application is examined as an example implementation of this workflow. The Neural Caricature architecture is more modular, upgradable, and can capture more nuance than systems using more traditional representation based mappings.