An empirical investigation into the properties of standard word embeddings

The standard way to compare two text embeddings is cosine similarity. Scattered studies report that a different metric does better, but never pin down the geometric condition that decides when, or why. We settle both with a comprehensive empirical study: nineteen parameter-free similarity metrics on nineteen encoders, from compact sentence transformers up to seven-billion-parameter large language models, across seven datasets. The answer is geometric. When an encoder spreads its variance evenly across directions, cosine is the best parameter-free choice and no other metric helps by a usable margin. When the variance concentrates into a few dominant directions, a property known as anisotropy, rank-based and L1-type metrics beat cosine by a clear margin. The absolute gain is modest, but because cosine starts low on these encoders it is a sizable relative improvement, around twenty percent on average and largest where cosine is weakest. What decides this is the geometry of the embedding space, not how the model was trained: where the two disagree, the metric follows the geometry. One number, the fraction of variance held by the single most dominant dimension, predicts how much the alternatives help across all nineteen encoders, with a rank correlation of 0.86 and a linear correlation of 0.95. To test this as the cause rather than a correlate, we project out the dominant directions: cosine recovers and the advantage of the other metrics nearly vanishes, but only on the encoders that were anisotropic to begin with. The effect is directional, not magnitude based, since it survives normalizing every vector to unit length. Among parameter-free metrics, then, cosine is the right tool wherever an encoder is well spread, which includes the fine-tuned embedders commonly deployed for retrieval, and we give a one-number diagnostic for when it is not.

Choosing the right text embedding model is one of the most consequential -- and most frequently under-examined -- decisions in building a retrieval or search system, yet the model that tops a leaderboard is rarely the best choice for a given deployment. This report develops a practical, evidence-based framework for embedding model selection, built on a benchmarking study that evaluates T3EM (Text 3 Embedding Model), a commercial API-based embedding model, against a broad set of open-source alternatives on English-language retrieval tasks, and situates these findings within the wider Massive Text Embedding Benchmark (MTEB) landscape spanning classification, clustering, semantic similarity, reranking, pair classification, bitext mining, and summarization. Beyond raw benchmark scores, the report traces the full path from embedding model to retrieved result -- how embeddings are produced, how they are indexed and searched at scale, and how document chunking strategy shapes retrieval quality -- so that model choice can be reasoned about as one decision within a complete retrieval pipeline rather than in isolation. The result is a consolidated set of practical recommendations for selecting an embedding model according to task, latency, cost, and deployment constraints.

Text embeddings are fundamental to many downstream applications, making robustness important for real-world NLP. However, most recent state-of-the-art embedding models are not reproducible because they rely on closed or undisclosed training data, and they remain insufficiently robust for Southeast Asian languages. We present SEA-LION-Embedding, a fully open and reproducible text-embedding pipeline for Southeast Asian languages trained only on publicly available data, and use it to study three core factors of robust embedding design: data composition, training objective, and base encoder initialization. SEA-LION-Embedding achieves state-of-the-art results on SEA-BED while enabling systematic and reproducible analysis of robust text embeddings for the region.