Quantize by Drift: Label-Free Mixed-Precision Post-Training Quantization for Text Embedders

Hyojung Han, Jongmin Kim, Seung-Hun Jeon

Mixed-precision post-training quantization needs a per-module sensitivity signal; for a text embedder the obvious one -- the retrieval quality a module costs when quantized -- needs relevance labels that deployments rarely have. We measure a label-free substitute: quantization-induced representation drift, obtained by quantizing one module, re-encoding the corpus, and recording how far the output embeddings moved from their full-precision positions. What is specific is the observable: the deployed output representation a dense retriever ranks with. Across five development embedders, configuration-level drift orders sampled mixed-precision plans against held-out retrieval quality at a macro Spearman of 0.911, the sensitivity transports across calibration corpora and retrieval domains in the usable regime, module drifts compose rank-consistently but not numerically, and relevance-derived sensitivity adds no consistent value. The method is one additive allocation under a hard packed-byte budget, with no labels and no search. On three embedders held untouched until method, baselines and hypotheses were frozen and sealed, the pre-registered directional hypothesis against the prior…