The objective and automatic detection of the sleep–wake cycle (SWC) stages is essential for the investigation of its physiology and dysfunction. Here, we propose a machine learning model for the classification of SWC stages based on the measurement of synchronization between neural oscillations of different frequencies. Publicly available electrophysiological recordings of mice were analyzed for the computation of phase–amplitude couplings, which were then supplied to a multilayer perceptron (MLP). Firstly, we assessed the performance of several architectures, varying among different input choices and numbers of neurons in the hidden layer. The top performing architecture was then tested using distinct extrapolation strategies that would simulate applications in a real lab setting. Although all the different choices of input data displayed high AUC values (>0.85) for all the stages, the ones using larger input datasets performed significantly better. The top performing architecture displayed high AUC values (>0.95) for all the extrapolation strategies, even in the worst-case scenario in which the training with a single day and single animal was used to classify the rest of the data. Overall, the results using multiple performance metrics indicate that the usage of a basic MLP fed with highly descriptive features such as neural synchronization is enough to efficiently classify SWC stages.