Due to the development of convenient brain-machine interfaces (BMIs), the automatic selection of a minimum channel (electrode) set has attracted increasing interest because the decrease in the number of channels increases the efficiency of BMIs. This study proposes a deep-learning-based technique to automatically search for the minimum number of channels applicable to general BMI paradigms using a compact convolutional neural network for electroencephalography (EEG)-based BMIs. For verification, three types of BMI paradigms are assessed: 1) the typical P300 auditory oddball; 2) the new top-down steady-state visually evoked potential; and 3) the endogenous motor imagery. We observe that the optimized minimal EEG-channel sets are automatically selected in all three cases. Their decoding accuracies using the minimal channels are statistically equivalent to (or even higher than) those based on all channels. The brain areas of the selected channel set are neurophysiologically interpretable for all of these cognitive task paradigms. This study shows that the minimal EEG channel set can be automatically selected, irrespective of the types of BMI paradigms or EEG input features using a deep-learning approach, which also contributes to their portability.