# Angular Softmax Loss for End-to-end Speaker Verification

arXiv: https://arxiv.org/abs/1806.03464 · HTML: https://mlsanity.com/paper/1806.03464/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2018.

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

- [TwinLiteNet: An Efficient and Lightweight Model for Driveable Area and Lane Segmentation in Self-Driving Cars](https://mlsanity.com/paper/2307.10705/) (2023)
- [Well-classified Examples are Underestimated in Classification with Deep Neural Networks](https://mlsanity.com/paper/2110.06537/) (2021)
- [Domain Agnostic Few-shot Learning for Speaker Verification](https://mlsanity.com/paper/2206.13700/) (2022)
- [Learnable Adaptive Cosine Estimator (LACE) for Image Classification](https://mlsanity.com/paper/2110.05324/) (2021)
- [Learning from human perception to improve automatic speaker verification in style-mismatched conditions](https://mlsanity.com/paper/2206.13684/) (2022)
- [Non-Adaptive Adversarial Face Generation](https://mlsanity.com/paper/2507.12107/) (2025)
- [Understanding Hyperspherical Geometry of ECAPA-TDNN Embedding and Its Impact on Zero-Shot Voice Conversion](https://mlsanity.com/paper/2609.24688/) (2026)

## Abstract (arXiv)

End-to-end speaker verification systems have received increasing interests. The traditional i-vector approach trains a generative model (basically a factor-analysis model) to extract i-vectors as speaker embeddings. In contrast, the end-to-end approach directly trains a discriminative model (often a neural network) to learn discriminative speaker embeddings; a crucial component is the training criterion. In this paper, we use angular softmax (A-softmax), which is originally proposed for face verification, as the loss function for feature learning in end-to-end speaker verification. By introducing margins between classes into softmax loss, A-softmax can learn more discriminative features than softmax loss and triplet loss, and at the same time, is easy and stable for usage. We make two contributions in this work. 1) We introduce A-softmax loss into end-to-end speaker verification and achieve significant EER reductions. 2) We find that the combination of using A-softmax in training the front-end and using PLDA in the back-end scoring further boosts the performance of end-to-end systems under short utterance condition (short in both enrollment and test). Experiments are conducted on part of Fisher dataset and demonstrate the improvements of using A-softmax.