# Hyperbolic Additive Margin Softmax with Hierarchical Information for Speaker Verification

arXiv: https://arxiv.org/abs/2601.19709 · HTML: https://mlsanity.com/paper/2601.19709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 27 Jan 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [VoxCeleb2: Deep Speaker Recognition](https://mlsanity.com/paper/1806.05622/) (2018)
- [VoxCeleb: a large-scale speaker identification dataset](https://mlsanity.com/paper/1706.08612/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [ECAPA-TDNN: Emphasized Channel Attention, Propagation and Aggregation in TDNN Based Speaker Verification](https://mlsanity.com/paper/2005.07143/) (2020)
- [MUSAN: A Music, Speech, and Noise Corpus](https://mlsanity.com/paper/1510.08484/) (2015)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [SphereFace2: Binary Classification is All You Need for Deep Face Recognition](https://mlsanity.com/paper/2108.01513/) (2021)
- [Large Margin Softmax Loss for Speaker Verification](https://mlsanity.com/paper/1904.03479/) (2019)
- [CN-Celeb: multi-genre speaker recognition](https://mlsanity.com/paper/2012.12468/) (2020)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Overview of Speaker Modeling and Its Applications: From the Lens of Deep Speaker Representation Learning](https://mlsanity.com/paper/2407.15188/) (2024)
- [Exploring Binary Classification Loss For Speaker Verification](https://mlsanity.com/paper/2307.08205/) (2023)
- [Hyperbolic Distance-Based Speech Separation](https://mlsanity.com/paper/2401.03567/) (2024)
- [Real Additive Margin Softmax for Speaker Verification](https://mlsanity.com/paper/2110.09116/) (2021)
- [Discriminative Speaker Representation via Contrastive Learning with Class-Aware Attention in Angular Space](https://mlsanity.com/paper/2210.16622/) (2022)
- [Adaptive Margin Circle Loss for Speaker Verification](https://mlsanity.com/paper/2106.08004/) (2021)

## Built on by (most cited first, 1 of 1)

- [Disentangling Speaker Traits for Deepfake Source Verification via Chebyshev Polynomial and Riemannian Metric Learning](https://mlsanity.com/paper/2603.21875/) (2026)

## Abstract (arXiv)

Speaker embedding learning based on Euclidean space has achieved significant progress, but it is still insufficient in modeling hierarchical information within speaker features. Hyperbolic space, with its negative curvature geometric properties, can efficiently represent hierarchical information within a finite volume, making it more suitable for the feature distribution of speaker embeddings. In this paper, we propose Hyperbolic Softmax (H-Softmax) and Hyperbolic Additive Margin Softmax (HAM-Softmax) based on hyperbolic space. H-Softmax incorporates hierarchical information into speaker embeddings by projecting embeddings and speaker centers into hyperbolic space and computing hyperbolic distances. HAM-Softmax further enhances inter-class separability by introducing margin constraint on this basis. Experimental results show that H-Softmax and HAM-Softmax achieve average relative EER reductions of 27.84% and 14.23% compared with standard Softmax and AM-Softmax, respectively, demonstrating that the proposed methods effectively improve speaker verification performance and at the same time preserve the capability of hierarchical structure modeling. The code will be released at https://github.com/PunkMale/HAM-Softmax.