# Vector Linking via Cross-Model Local Isometric Consistency

arXiv: https://arxiv.org/abs/2605.31100 · HTML: https://mlsanity.com/paper/2605.31100/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 28 of 28)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [A robust self-learning method for fully unsupervised cross-lingual mappings of word embeddings](https://mlsanity.com/paper/1805.06297/) (2018)
- [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Offline bilingual word vectors, orthogonal transformations and the inverted softmax](https://mlsanity.com/paper/1702.03859/) (2017)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [Towards Backward-Compatible Representation Learning](https://mlsanity.com/paper/2003.11942/) (2020)
- [Loss in Translation: Learning Bilingual Word Mapping with a Retrieval Criterion](https://mlsanity.com/paper/1804.07745/) (2018)
- [The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation](https://mlsanity.com/paper/2009.04266/) (2020)
- [TWEAC: Transformer with Extendable QA Agent Classifiers](https://mlsanity.com/paper/2104.07081/) (2021)
- [Learning Backward Compatible Embeddings](https://mlsanity.com/paper/2206.03040/) (2022)
- [Bootstrapping Parallel Anchors for Relative Representations](https://mlsanity.com/paper/2303.00721/) (2023)

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

- [Exploiting Residual Reachability for Cross-Model Migration of Graph-Based Indexes in Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2609.23036/) (2026)

## Abstract (arXiv)

We study Vector Linking: given two embedding clouds produced by different black-box encoders over partially overlapping datasets, recover cross-model object correspondences using only vectors. Empirically and theoretically, we show that independently trained contrastive encoders exhibit local geometric consistency: short-range distances are approximately preserved up to a scale factor, while long-range distances are not due to model-specific distortion. Building on this, we propose an iterative, reference-based geometric embedding hashing that recovers vector links from a tiny seed set of paired anchors. It represents each vector by distances to sampled paired anchors, proposes candidate links via hash-space matching, and aggregates evidence across views in a Beta-Bernoulli posterior to bootstrap high-confidence links as new anchors. Experiments across multiple benchmarks and embedding model pairs demonstrate accurate and robust linking under varying overlap, seed budgets, and out-of-domain anchors, with applications to vector database integration and cross-model clustering. Code is available at https://github.com/DBgroup-Edinburgh/VecLinking.