  Experiments at a future $e^{+}e^{-}$ collider will be able to search for new
particles with masses below the nominal centre-of-mass energy by analyzing
collisions with initial-state radiation (radiative return). We show that
machine learning methods that use imperfect or missing training labels can
achieve sensitivity to generic new particle production in radiative return
events. In addition to presenting an application of the classification without
labels (CWoLa) search method in $e^{+}e^{-}$ collisions, our study combines
weak supervision with variable-dimensional information by deploying a deep sets
neural network architecture. We have also investigated some of the experimental
aspects of anomaly detection in radiative return events and discuss these in
the context of future detector design.
