The fact that the transmission and processing of visual information in the brain takes time presents a problem for the accurate real-time localization of a moving object. One way this problem might be solved is extrapolation: using an object’s past trajectory to predict its location in the present moment. Here, we investigate how a simulated in silico layered neural network might implement such extrapolation mechanisms, and how the necessary neural circuits might develop. We allowed an unsupervised hierarchical network of velocity-tuned neurons to learn its connectivity through spike-timing-dependent plasticity (STDP). We show that the temporal contingencies between the different neural populations that are activated by an object as it moves causes the receptive fields of higher-level neurons to shift in the direction opposite to their preferred direction of motion. The result is that neural populations spontaneously start to represent moving objects as being further along their trajectory than where they ...