Recently there has seen promising results on automatic stage scoring by extracting spatio-temporal features from electroencephalogram (EEG). Such methods entail laborious manual feature engineering and domain knowledge. In this study, we propose an adaptive scheme to probabilistically encode, filter and accumulate the input signals and weight the resultant features by the half-Gaussian probabilities of signal intensities. The adaptive representations are subsequently fed into a transformer model to automatically mine the relevance between features and corresponding stages. Extensive experiments on the largest public dataset against state-of-the-art methods validate the effectiveness of our proposed method and reveal promising future directions.