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

arXiv: https://arxiv.org/abs/2610.09227 · HTML: https://mlsanity.com/paper/2610.09227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [mGTE: Generalized Long-Context Text Representation and Reranking Models for Multilingual Text Retrieval](https://mlsanity.com/paper/2407.19669/) (2024)
- [EmbeddingGemma: Powerful and Lightweight Text Representations](https://mlsanity.com/paper/2509.20354/) (2025)
- [Exploring Layer-wise Information Effectiveness for Post-Training Quantization in Small Language Models](https://mlsanity.com/paper/2508.03332/) (2025)
- [MixQuant: Adaptive Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2607.23047/) (2026)

## Abstract (arXiv)

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 LieQ criterion holds (3/3 at the main budget, no collapse) and drift scores above a two-sided LieQ steelman in 2/3; but at the main budget drift is numerically lower than same-budget uniform precision on all three (-0.99, -0.85, -1.01 points), having reduced module and whole-model drift as designed. Output drift is thus a robust coarse sensitivity signal, not a universally optimal allocation objective: it avoids the catastrophic failures of the transferred signed-geometry adaptation and can remain usable at stressed budgets where uniform collapses, but fine-grained redistribution around a strong uniform operating point remains unresolved.