# Hyperbolic Audio Source Separation

arXiv: https://arxiv.org/abs/2212.05008 · HTML: https://mlsanity.com/paper/2212.05008/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2022.

## Built on by (most cited first, 7 of 7)

- [HyperVQ: MLR-based Vector Quantization in Hyperbolic Space](https://mlsanity.com/paper/2403.13015/) (2024)
- [A Stem-Agnostic Single-Decoder System for Music Source Separation Beyond Four Stems](https://mlsanity.com/paper/2406.18747/) (2024)
- [Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2502.17130/) (2025)
- [Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation](https://mlsanity.com/paper/2602.20479/) (2026)
- [RiTTA: Modeling Event Relations in Text-to-Audio Generation](https://mlsanity.com/paper/2412.15922/) (2024)
- [SPEAR: Receiver-to-Receiver Acoustic Neural Warping Field](https://mlsanity.com/paper/2406.11006/) (2024)
- [More Than A Shortcut: A Hyperbolic Approach To Early-Exit Networks](https://mlsanity.com/paper/2511.00641/) (2025)

## Abstract (arXiv)

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.