Effective modeling of human interactions is of utmost importance when forecasting behaviors such as future trajectories. Each individual, with its motion, influences surrounding agents since everyone obeys to social non-written rules such as collision avoidance or group following. In this paper we model such interactions, which constantly evolve through time, by looking at the problem from an algorithmic point of view, i.e., as a data manipulation task. We present a neural network based on an end-to-end trainable working memory, which acts as an external storage where information about each agent can be continuously written, updated and recalled. We show that our method is capable of learning explainable cause-effect relationships between motions of different agents, obtaining state-of-the-art results on multiple trajectory forecasting datasets.