The performance of deep learning models is dependent on the precise configuration of many layers and parameters. However, there are currently few systematic guidelines for how to configure a successful model. This means model builders often have to experiment with different configurations by manually programming different architectures (which is tedious and time consuming) or rely on purely automated approaches to generate and train the architectures (which is expensive). In this paper, we present Rapid Exploration of Model Architectures and Parameters, or REMAP, a visual analytics tool that allows a model builder to discover a deep learning model quickly via exploration and rapid experimentation of neural network architectures. In REMAP, the user explores the large and complex parameter space for neural network architectures using a combination of global inspection and local experimentation. Through a visual overview of a set of models, the user identifies interesting clusters of architectures. Based on their findings, the user can run ablation and variation experiments to identify the effects of adding, removing, or replacing layers in a given architecture and generate new models accordingly. They can also handcraft new models using a simple graphical interface. As a result, a model builder can build deep learning models quickly, efficiently, and without manual programming. We inform the design of REMAP through a design study with four deep learning model builders. Through a use case, we demonstrate that REMAP allows users to discover performant neural network architectures efficiently using visual exploration and user-defined semi-automated searches through the model space.