In collider experiments, the kinematic reconstruction of heavy, short-lived particles is vital for precision tests of the Standard Model and in searches for physics beyond it. Performing kinematic reconstruction in collider events with many final-state jets, such as the all-hadronic decay of top-antitop quark pairs, is challenging. We present (HyPER), a novel architecture based on graph neural networks that uses hypergraph representation learning to build more powerful and efficient representations of collider events. HyPER is used to reconstruct parent particles from sets of final-state objects. Trained and tested on simulation, the HyPER model is shown to perform favorably when compared to existing state-of-the-art reconstruction techniques, while demonstrating superior parameter efficiency. The novel hypergraph approach allows the method to be applied to particle reconstruction in a multitude of different physics processes. Published by the American Physical Society 2025