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

Abstract

We find that current sentence-embedding models produce outputs with a consistent bias: every embedding $e$ decomposes as $\tilde{e}+\hat{I}¼$, where the mean $\hat{I}¼$ is near-identical across all sentences. We study two training-free corrections -- subtracting $\hat{I}¼$ directly (R1), or projecting each embedding off the mean direction (R2) -- and show, via a first-order error-propagation argument, that R2 cancels the parallel component of mean-estimation error that R1 retains. Across 38 models on the Massive Multilingual Text Embedding Benchmark (MMTEB)~\citep{MMTEB}, R2 yields consistent classification gains (paired $\bar{t}=3.31$, 29 of 38 models with $t>2$, zero losses), and the per-model mean norm $\Vert \hat{I}¼\Vert$ correlates with which models benefit most. A nine-method dose-response ablation on five models further reveals that mild single-direction removal helps, but full principal component analysis (PCA) whitening hurts every model we test, and that R2 and All-but-the-Top with depth one agree within $0.18$ pp downstream despite weak geometric alignment between $\hat{\hat{I}}¼$ and the centered top principal component.