The dynamical features of neural coding of complex learned vocal behavior remain under active investigation. Here we examined multi-unit neural activity recorded during singing in adult male canaries (Serinus canaria). Canaries have a rich repertoire of syllable types and some flexibility in how these are sequentially uttered during song production. Using machine learning techniques to search for concise underlying structure in the data, we find a low dimensional representation of the neural recordings analyzing the modes of the latent space of an auto-encoder. These modes are closely correlated with characteristics of the associated song, such as the syllable repetition rate or characteristics of the underlying motor gestures, respiratory patterns. These results demonstrate a tight link between peripheral and central dynamical patterns of activity during song production in birds.