Context. We investigate the use of saliency-map analysis to aid in searches for transient signals, such as fast radio bursts and individual pulses from radio pulsars. Aims. Our aim is to demonstrate that saliency maps provide the means to understand predictions from machine learning algorithms and can be implemented in pipelines used to search for transient events. Methods. We implemented a new deep learning methodology to predict whether any segment of the data contains a transient event. The algorithm was trained using real and simulated data sets. We demonstrate that the algorithm is able to identify such events. The output results are visually analysed via the use of saliency maps. Results. We find that saliency maps can produce an enhanced image of any transient feature without the need for de-dispersion or removal of radio frequency interference. The maps can be used to understand which features in the image were used in making the machine learning decision and to visualise the transient event. Even though the algorithm reported here was developed to demonstrate saliency-map analysis, we have detected a single burst event, in archival data, with dispersion measure of 41 cm −3 pc that is not associated with any currently known pulsar.