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Abstract We present a new approach to classifying the sleep stage that incorporates a computationally inexpensive method based on permutations for channel selection and takes advantage of deep learning power, specifically the gated recurrent unit (GRU) model, along with other deep learning methods. By systematically permuting the electroencephalographic (EEG) channels, different combinations of EEG channels are evaluated to identify the most informative subset for the classification of the 5-class sleep stage. For analysis, we used an EEG dataset that was collected at the International Institute for Integrative Sleep Medicine (WPI-IIIS) at the University of Tsukuba in Japan. The results of these explorations provide many new insights such as the (1) drastic decrease in performance when channels are fewer than 3, (2) 3-random channels selected by permutation provide the same or better prediction than the 3 channels recommended by the American Academy of Sleep Medicine (AASM), (3) N1 class suffers the most in prediction accuracy as the channels drop from 128 to 3 random or 3 AASM, and (4) no single channel provides acceptable levels of accuracy in the prediction of 5 classes. The results obtained show the GRU’s ability to retain essential temporal information from EEG data, which allows capturing the underlying patterns associated with each sleep stage effectively. Using permutation-based channel selection, we enhance or at least maintain as high model efficiency as when using high-density EEG, incorporating only the most informative EEG channels.