Experimental observations assisted by 2-D imaging diagnostics on the KSTAR tokamak show that a solitary perturbation (SP) emerges prior to a boundary burst of magnetized toroidal plasmas, which puts forward SP as a potential candidate for the burst trigger. We have constructed a machine learning (ML) model based on a convolutional deep neural network architecture for a statistical study to identify the SP as a boundary burst trigger. The ML model takes sequential signals detected from 19 toroidal Mirnov coils as input and predicts whether each temporal frame corresponds to an SP. We trained the network in a supervised manner on a training set consisting of real signals with manually annotated SP locations and synthetic burst signals. The trained model achieves high performances in various metrics on a test data set. We also demonstrated the reliability of the model by visualizing the discriminative parts of the input signals that the model recognizes. Finally, we applied the trained model to new data from KSTAR experiments, which were never seen during training, and confirmed that the large burst at the plasma boundary that can fatally damage the fusion device always involves the emergence of SP. This result suggests that the SP is a key to understanding and controlling of the boundary burst in magnetized toroidal plasmas.