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Harnessing the Universal Geometry of Embeddings

NeurIPS 2025 · Label-efficient and robust learning › Recognition and long-tail · approach: Multilingual language representation pretraining · 2 citations (OpenAlex)

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Proposes vec2vec, an unsupervised method that translates text embeddings between unknown and known model spaces via a shared latent space trained with adversarial, cycle-consistency, reconstruction, and vector-space-preservation losses, without paired data.

Problem

Translating text embeddings from one encoder's vector space to another's without paired data, parallel inputs, or access to the source encoder, which also has security implications for leaking information from embedding databases.

Approach

Learn a universal latent space via modular per-model input/output adapters and a shared MLP backbone, trained with GAN losses on both embedding and latent levels plus reconstruction, cycle-consistency, and vector space preservation losses, so unpaired embeddings from different models align in the latent space.

Key results

• vec2vec achieves mean cosine similarity up to 0.92 and top-1 accuracy up to 100% on in-distribution NQ translations, while naive and cross-backbone baselines are near random.
• On out-of-distribution TweetTopic and MIMIC, vec2vec translators trained on NQ retain high cosine similarity (e.g., 0.86 for granite to stella on TweetTopic) and low rank.
• Zero-shot inversion via off-the-shelf inverter recovers information from translated embeddings for up to 80% of Enron emails and 67% of tweets for some model pairs.

Measured effects reported in the paper

Surprising findings

• Training is unstable across seeds for cross-backbone pairs: only 3 of 15 e5-to-gtr runs reached 80% top-1 accuracy.
• Oracle-aided optimal transport performs surprisingly well on same-backbone pairs, comparable to vec2vec in top-1 and rank.

Limitations

• GAN training is unstable and sensitive to initialization, requiring selection of the best of multiple seeds.
• Translations are imperfect; cross-backbone cosine similarity and inversion remain partial, and Qwen results are limited to one pair.
• Evaluated mostly on text embedding models with 768-dim or similar outputs; only one multimodal model (CLIP) and limited modalities.

Experimental setup

Datasets: Natural Questions TweetTopic MIMIC-III (pseudo re-identified) Enron Email Corpus MS COCO

Benchmarks: Natural Questions TweetTopic MIMIC-III (pseudo re-identified) Enron Email Corpus MS COCO

Metrics: mean cosine similarity top-1 accuracy mean rank top-k attribute inference accuracy LLM judge accuracy Recall@16

Baselines: Naive baseline (identity) Oracle-aided optimal transport Zero-shot attribute inference with ideal embeddings

Builds on: Platonic Representation Hypothesis unsupervised image translation (cycle consistency + GAN) vector space preservation Gromov-Wasserstein optimal transport

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