Solar eruptions, including flares and coronal mass ejections (CMEs), have a significant impact on Earth. Some flares are associated with CMEs, and some flares are not. The association between flares and CMEs is not always obvious. In this study, we propose a new deep learning method, specifically a hybrid neural network (HNN) that combines a vision transformer with long short-term memory, to predict associations between flares and CMEs. HNN finds spatio-temporal patterns in the time series of line-of-sight magnetograms of solar active regions collected by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and uses the patterns to predict whether a flare projected to occur within the next 24 hr will be eruptive (i.e., CME-associated) or confined (i.e., not CME-associated). Our experimental results demonstrate the good performance of the HNN method. Furthermore, the results show that magnetic flux cancellation in polarity inversion line regions may well play a role in triggering flare-associated CMEs, a finding consistent with the literature.