Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations – usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at [https://github.com/htdt/hyp_metric](https://github.com/htdt/hyp_metric)

Aleksandr Ermolov

Leyla Mirvakhabova

Valentin Khrulkov

Diffusion models, low-rank tensor decompositions, unsupervised and semisupervised
learning, theoretical analysis of neural networks. Especially, I am interested in applications of various geometrical (differential, algebraic, topological) ideas and techniques
to neural networks to further our understanding of deep learning.

Nicu Sebe

Ivan Oseledets

Yandex Research team regularly contributes to the computer vision research community, mostly in the field of image retrieval and generative modelling.

Computer vision

Constructing high-quality data representations are a necessary component in common machine learning pipelines.

Representations

Learning to rank is a central problem in information retrieval. The objective is to
rank a given set of items to optimize the overall utility of the list.

Ranking

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations – usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. 

Hyperbolic Vision Transformers: Combining Improvements in Metric Learning