We develop a deep learning-based infrasonic detection and categorization methodology that uses convolutional neural networks with self-attention layers to identify stationary and non-stationary signals in infrasound array processing results. Using features extracted from the coherence and direction-of-arrival information from beamforming at different infrasound arrays, our model more reliably detects signals compared with raw waveform data. Using three infrasound stations maintained as part of the International Monitoring System, we construct an analyst-reviewed data set for model training and evaluation. We construct models using a 4-category framework, a generalized noise vs non-noise detection scheme, and a signal-of-interest (SOI) categorization framework that merges short duration stationary and non-stationary categories into a single SOI category. We evaluate these models using a combination of k-fold cross-validation, comparison with an existing "state-of-the-art" detector, and a transportability analysis. Although results are mixed in distinguishing stationary and non-stationary short duration signals, f-scores for the noise vs non-noise and SOI analyses are consistently above 0.96, implying that deep learning-based infrasonic categorization is a highly accurate means of identifying signals-of-interest in infrasonic data records.