Title: AlignNet: Self-supervised Alignment Module. Abstract: The natural world consists of objects that we perceive as persistent in space and time, even though these objects appear, disappear and reappear in our field of view as we move. This can be attributed to our notion of object persistence -- our knowledge that objects typically continue to exist, even if we can no longer see them -- and our ability to track objects. Drawing inspiration from the psychology literature on `sticky indices', we propose the AlignNet, a model that learns to assign unique indices to new objects when they first appear and reassign the index to subsequent instances of that object. By introducing a persistent object-based memory, the AlignNet may be used to keep track of objects across time, even if they disappear and reappear later. We implement the AlignNet as a graph network applied to a bipartite graph, in which the input nodes are objects from two sets that we wish to align. The network is trained to predict the edges which connect two instances of the same object across sets. The model is also capable of identifying when there are no matches and dealing with these cases. We perform experiments to show the model's ability to deal with the appearance, disappearance and reappearance of objects. Additionally, we demonstrate how a persistent object-based memory can help solve question-answering problems in a partially observable environment.