  We introduce a framework for audio source separation using embeddings on a
hyperbolic manifold that compactly represent the hierarchical relationship
between sound sources and time-frequency features. Inspired by recent successes
modeling hierarchical relationships in text and images with hyperbolic
embeddings, our algorithm obtains a hyperbolic embedding for each
time-frequency bin of a mixture signal and estimates masks using hyperbolic
softmax layers. On a synthetic dataset containing mixtures of multiple people
talking and musical instruments playing, our hyperbolic model performed
comparably to a Euclidean baseline in terms of source to distortion ratio, with
stronger performance at low embedding dimensions. Furthermore, we find that
time-frequency regions containing multiple overlapping sources are embedded
towards the center (i.e., the most uncertain region) of the hyperbolic space,
and we can use this certainty estimate to efficiently trade-off between
artifact introduction and interference reduction when isolating individual
sounds.
