# Deep Distributional Sequence Embeddings Based on a Wasserstein Loss

arXiv: https://arxiv.org/abs/1912.01933 · HTML: https://mlsanity.com/paper/1912.01933/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [Eye Know You: Metric Learning for End-to-end Biometric Authentication Using Eye Movements from a Longitudinal Dataset](https://mlsanity.com/paper/2104.10489/) (2021)
- [Establishing a Baseline for Gaze-driven Authentication Performance in VR: A Breadth-First Investigation on a Very Large Dataset](https://mlsanity.com/paper/2404.11798/) (2024)
- [Eye Know You Too: A DenseNet Architecture for End-to-end Eye Movement Biometrics](https://mlsanity.com/paper/2201.02110/) (2022)
- [Temporal Persistence and Intercorrelation of Embeddings Learned by an End-to-End Deep Learning Eye Movement-driven Biometrics Pipeline](https://mlsanity.com/paper/2402.16399/) (2024)
- [Recent Advancement in 3D Biometrics using Monocular Camera](https://mlsanity.com/paper/2401.02646/) (2024)
- [Enhancing Eye Movement Biometrics for User Authentication via Continuous Gaze Offset Score Fusion](https://mlsanity.com/paper/2605.06810/) (2026)

## Abstract (arXiv)

Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing deep metric learning techniques, the embedding of an instance is given by a feature vector produced by a deep neural network and Euclidean distance or cosine similarity defines distances between these vectors. In this paper, we study deep distributional embeddings of sequences, where the embedding of a sequence is given by the distribution of learned deep features across the sequence. This has the advantage of capturing statistical information about the distribution of patterns within the sequence in the embedding. When embeddings are distributions rather than vectors, measuring distances between embeddings involves comparing their respective distributions. We propose a distance metric based on Wasserstein distances between the distributions and a corresponding loss function for metric learning, which leads to a novel end-to-end trainable embedding model. We empirically observe that distributional embeddings outperform standard vector embeddings and that training with the proposed Wasserstein metric outperforms training with other distance functions.