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To 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. We aim to demonstrate that saliency maps provide the means to understand predictions from machine learning algorithms and can be implemented in piplines used to search for transient events. We have implemented a new deep learning methodology to predict whether or not any segment of the data contains a transient event. The algorithm has been 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. 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. Such 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, in archival data, a single burst event with dispersion measure of $41$\,cm$^{-3}$pc that is not associated with any currently known pulsar.