Generalizable and Composable Multi-Model Embedding Translation

Embedding translation enables interoperability across embedding models, allowing embedding vectors to be reused without costly re-embedding. However, existing methods are typically evaluated under simplified pairwise and in-domain settings and behave as black boxes at inference time, leading to unreliable performance under out-of-distribution (OOD) inputs, multi-model mixing, and composed translations. We analyze embedding translation from a geometric perspective and derive an interpretable error bound that explains systematic error amplification under OOD inputs, mixing and chaining. Building on this, we propose a geometry-aware confidence metric and a Hierarchical Mixture of Experts (H-MoE) framework with localized, parameter-efficient adaptation. Following MTEB leaderboard, we conduct large-scale experiments over 10 embedding models and 6 benchmarks across 90 translation directions. H-MoE outperforms every baseline for every model pair over every benchmark under OOD scenarios. Furthermore, multi-model mixing and chaining only degrade our performance in Recall@100 by 0.5% ∼ 2.6%, compared to 7.2% ∼ 92.3% recall drop by existing methods. Code is available at https: //github.com/DBgroup-Edinburgh/ embedding-translation. Q1: Can we bound error 𝒆(𝒇 𝑨→𝑩 ) under Outof-Distribution (OOD)? Q2: Can we minimize gap 𝒆(𝒇 𝑨→𝑩 ; 𝒇 𝑪→𝑩 ) 𝒗𝒔. 𝒎𝒂𝒙(𝒆 𝒇 𝑨→𝑩 , 𝒆 𝒇 𝑪→𝑩 )? Q3: Can we minimize gap 𝒆(𝒇 𝐀→𝑪 ∘ 𝒇 𝐂→𝑩 ) 𝒗𝐬. 𝒆(𝒇 𝐀→𝑩