Correcting Mean Bias in Text Embeddings: A Refined Renormalization with Training-Free Improvements on MMTEB

Abstract: We find that current text embedding models produce outputs with a consistent bias, i.e., each embedding vector $e$ can be decomposed as $\tilde{e} + μ$, where $μ$ is almost identical across all sentences. We propose a plug-and-play, training-free and lightweight solution called Renormalization. Through extensive experiments, we show that renormalization consistently and statistically significantly improves the performance of existing models on the Massive Multilingual Text Embedding Benchmark (MMTEB). In particular, across 38 models, renormalization improves performance by 9.7 $σ$ on retrieval tasks, 3.1 $σ$ on classification tasks, and 0.8 $σ$ on other types of tasks. Renormalization has two variants: directly subtracting $μ$ from $e$, or subtracting the projection of $e$ onto $μ$. We theoretically predict that the latter performs better, and our experiments confirm this prediction.