# Online embedding of metrics

arXiv: https://arxiv.org/abs/2303.15945 · HTML: https://mlsanity.com/paper/2303.15945/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2023.

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

- [Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures](https://mlsanity.com/paper/2308.09250/) (2023)

## Abstract (arXiv)

We study deterministic online embeddings of metrics spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces, a tight exponential upper bound on embedding into the line, and a (1+ε)-distortion embedding in ℓ_∞ of a suitably high dimension.