Title: Distance-based Composable Representations with Neural Networks. Abstract: We introduce a new deep learning technique that builds individual and class representations based on distance estimates to randomly generated contextual dimensions for different modalities. Recent works have demonstrated advantages to creating representations from probability distributions over their contexts rather than single points in a low-dimensional Euclidean vector space. These methods, however, rely on pre-existing features and are limited to textual information. In this work, we obtain generic template representations that are vectors containing the average distance of a class to randomly generated contextual information. These representations have the benefit of being both interpretable and composable. They are initially learned by estimating the Wasserstein distance for different data subsets with deep neural networks. Individual samples or instances can then be compared to the generic class representations, which we call templates, to determine their similarity and thus class membership. We show that this technique, which we call WDVec, delivers good results for multi-label image classification. Additionally, we illustrate the benefit of templates and their composability by performing retrieval with complex queries where we modify the information content in the representations. Our method can be used in conjunction with any existing neural network and create theoretically infinitely large feature maps.