Robots can use auditory, visual, or haptic interfaces to convey information to human users. The way these interfaces select signals is typically pre-defined by the designer: for instance, a haptic wristband might vibrate when the robot is moving and squeeze when the robot stops. But different people interpret the same signals in different ways, so that what makes sense to one person might be confusing or unintuitive to another. In this paper we introduce a unified algorithmic formalism for learning co-adaptive interfaces from scratch. Our method does not need to know the human's task (i.e., what the human is using these signals for). Instead, our insight is that interpretable interfaces should select signals that maximize correlation between the human's actions and the information the interface is trying to convey. Applying this insight we develop LIMIT: Learning Interfaces to Maximize Information Transfer. LIMIT optimizes a tractable, real-time proxy of information gain in continuous spaces. The first time a person works with our system the signals may appear random; but over repeated interactions the interface learns a one-to-one mapping between displayed signals and human responses. Our resulting approach is both personalized to the current user and not tied to any specific interface modality. We compare LIMIT to state-of-the-art baselines across controlled simulations, an online survey, and an in-person user study with auditory, visual, and haptic interfaces. Overall, our results suggest that LIMIT learns interfaces that enable users to complete the task more quickly and efficiently, and users subjectively prefer LIMIT to the alternatives. See videos here: https://youtu.be/IvQ3TM1_2fA