- Abstract: Recommender systems can be formulated as a matrix completion problem, where the goal is to estimate missing ratings. A popular matrix completion algorithm is matrix factorization, where ratings are predicted from combining learned user and item parameter vectors. As dataset sizes increase many matrix factorization models suffer from slow rates of convergence, linear parameter scaling and a need to be retrained when new users or items are added. We develop a novel approach to generate user and item vectors on demand from the ratings matrix itself and a fixed pool of parameters. In our approach, each vector is generated using chains of evidence that link them to a small set of learned prototypical user and item latent vectors. We demonstrate that our approach has a number of desirable scaling properties, such as having a constant rate of convergence to a competitive RMSE, requiring the optimization of only a constant number of parameters.