Automation of tasks can have critical consequences when humans lose agency over decision processes. Deep learning models are particularly susceptible since current black-box approaches lack explainable reasoning. We argue that both the visual interface and model structure of deep learning systems need to take into account interaction design. We propose a framework of collaborative semantic inference (CSI) for the co-design of interactions and models to enable visual collaboration between humans and algorithms. The approach exposes the intermediate reasoning process of models which allows semantic interactions with the visual metaphors of a problem, which means that a user can both understand and control parts of the model reasoning process. We demonstrate the feasibility of CSI with a co-designed case study of a document summarization system.