# Understanding Hyperspherical Geometry of ECAPA-TDNN Embedding and Its Impact on Zero-Shot Voice Conversion

arXiv: https://arxiv.org/abs/2609.24688 · HTML: https://mlsanity.com/paper/2609.24688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [LibriTTS-R: A Restored Multi-Speaker Text-to-Speech Corpus](https://mlsanity.com/paper/2305.18802/) (2023)
- [Large-scale Self-Supervised Speech Representation Learning for Automatic Speaker Verification](https://mlsanity.com/paper/2110.05777/) (2021)
- [Learning towards Minimum Hyperspherical Energy](https://mlsanity.com/paper/1805.09298/) (2018)
- [Voice Conversion With Just Nearest Neighbors](https://mlsanity.com/paper/2305.18975/) (2023)
- [ECAPA-TDNN Embeddings for Speaker Diarization](https://mlsanity.com/paper/2104.01466/) (2021)
- [Zero-shot Voice Conversion with Diffusion Transformers](https://mlsanity.com/paper/2411.09943/) (2024)
- [Dimensionality compression and expansion in Deep Neural Networks](https://mlsanity.com/paper/1906.00443/) (2019)
- [The IDLAB VoxCeleb Speaker Recognition Challenge 2020 System Description](https://mlsanity.com/paper/2010.12468/) (2020)
- [GenVC: Self-Supervised Zero-Shot Voice Conversion](https://mlsanity.com/paper/2502.04519/) (2025)
- [Angular Softmax Loss for End-to-end Speaker Verification](https://mlsanity.com/paper/1806.03464/) (2018)
- [ECAPA-TDNN for Multi-speaker Text-to-speech Synthesis](https://mlsanity.com/paper/2203.10473/) (2022)
- [EZ-VC: Easy Zero-shot Any-to-Any Voice Conversion](https://mlsanity.com/paper/2505.16691/) (2025)
- [Fast-VGAN: Lightweight Voice Conversion with Explicit Control of F0 and Duration Parameters](https://mlsanity.com/paper/2507.04817/) (2025)

## Abstract (arXiv)

Angular-margin speaker encoders are widely used in voice conversion, yet the geometry of their classifier prototypes remains poorly understood. We analyze ECAPA-TDNN classifier prototypes as points on the unit hypersphere and characterize their organization using rotation-invariant angular statistics together with global and local effective dimensionality measures. Our analysis shows that standard training can induce angular concentration and a substantial reduction in effective dimensionality. To address this, we investigate two geometric regularization strategies (hinged Riesz log-energy and effective-dimension maximization) applied to classifier prototypes to encourage more uniform hyperspherical coverage. The resulting prototype sets exhibit higher effective dimensionality and improved isotropy, with configuration-dependent effects on speaker-recognition performance. When the corresponding ECAPA-TDNN models are used as speaker encoders for Fast-VGAN, the regularized systems also exhibit improved robustness in zero-shot voice conversion, particularly for previously unseen speakers.