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.
In this paper, we show that high-performing embedding models organize their embedding spaces in a consistent way. We evaluate 25 contemporary embedding models on five MTEB tasks spanning four diverse task categories (retrieval, bitext mining, pair classification, and summarization) in both English and multilingual settings, and reveal that nearest-neighbor overlap and magnitude differences in independent component analysis (ICA) between paired text instances strongly correlate (even up to 0.97) with performance on the given task. Ultimately, we show that embedding tasks display varying degrees of linearity and reliance on retention of local information. Our results further the understanding of embeddings, their relation to model performance, and shed light on possible future training objectives and optimizing conditional embeddings.
Earth embedding models transform Earth observation data into embeddings uniquely tied to locations on the Earth's surface. These models are typically evaluated in isolation, comparing the downstream task performance across different Earth embeddings. However, spatially aligned embeddings can naturally be fused, providing richer information per location, a capability that isolated evaluations fail to capture. We therefore propose assessing Earth embeddings by their complementarity: the performance gain of fused embeddings over the best single-model baseline. To operationalise this, we introduce an embedding complementarity index applicable to any embedding and task, and evaluate four Earth embedding models (AlphaEarth, Tessera, GeoCLIP, SatCLIP) in isolation, in all pairs, and jointly across six downstream tasks. Fused embeddings outperform the best single model in four out of six tasks, confirming that single-embedding evaluations often underestimate Earth embedding capabilities. Complementarity proves both task- and location-dependent. Further, for a land cover regression task, we find that complementarity is partially determined by the spatial scale of land cover classes. Complementarity reframes Earth embeddings: the greatest future gains may come not from any single Earth embedding model, but from combinations that are better together.
Thijs L van der Plas, Jacob JW Bakermans, Vishal Nedungadi +3
Contrastive embedding models trained with scale-invariant losses are typically paired with distance metrics like cosine similarity, effectively ignoring embedding magnitudes. However, surprisingly, empirical studies reveal that despite this, these "discarded" norms seem to correlate with semantic properties such as concept specificity, token frequency, and human uncertainty. In this work, we provide a formal theoretical framework explaining this phenomenon. By analyzing the optimization dynamics, we derive an analytic formula demonstrating that embedding length naturally encodes this information as a byproduct of the training process. We also show how this gives rise to signals that can serve as "free" calibration tools in specific models and retrieval tasks, providing a grounded explanation for a previously heuristic observation.