# Distance-to-Distance Ratio: A Similarity Measure for Sentences Based on Rate of Change in LLM Embeddings

arXiv: https://arxiv.org/abs/2601.17705 · HTML: https://mlsanity.com/paper/2601.17705/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 5 of 5)

- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [Improving Text Embeddings with Large Language Models](https://mlsanity.com/paper/2401.00368/) (2023)
- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [Problems with Cosine as a Measure of Embedding Similarity for High Frequency Words](https://mlsanity.com/paper/2205.05092/) (2022)
- [Semantics at an Angle: When Cosine Similarity Works Until It Doesn't](https://mlsanity.com/paper/2504.16318/) (2025)

## Abstract (arXiv)

A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of similarity between LLM sentence embeddings. Inspired by Lipschitz continuity, DDR measures the rate of change in similarity between the pre-context word embeddings and the similarity between post-context LLM embeddings, thus measuring the semantic influence of context. We evaluate the performance of DDR in experiments designed as a series of perturbations applied to sentences drawn from a sentence dataset. For each sentence, we generate variants by replacing one, two, or three words with either synonyms, which constitute semantically similar text, or randomly chosen words, which constitute semantically dissimilar text. We compare the performance of DDR with other prevailing similarity metrics and demonstrate that DDR consistently provides finer discrimination between semantically similar and dissimilar texts, even under minimal, controlled edits.