# Spectral Tempering for Embedding Compression in Dense Passage Retrieval

arXiv: https://arxiv.org/abs/2603.19339 · HTML: https://mlsanity.com/paper/2603.19339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 14 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [Fine-Tuning LLaMA for Multi-Stage Text Retrieval](https://mlsanity.com/paper/2310.08319/) (2023)
- [Efficiently Teaching an Effective Dense Retriever with Balanced Topic Aware Sampling](https://mlsanity.com/paper/2104.06967/) (2021)
- [On the Sentence Embeddings from Pre-trained Language Models](https://mlsanity.com/paper/2011.05864/) (2020)
- [WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach](https://mlsanity.com/paper/2104.01767/) (2021)
- [Black-box Adversarial Attacks against Dense Retrieval Models: A Multi-view Contrastive Learning Method](https://mlsanity.com/paper/2308.09861/) (2023)
- [A Cluster-based Approach for Improving Isotropy in Contextual Embedding Space](https://mlsanity.com/paper/2106.01183/) (2021)
- [Unsupervised Corpus Poisoning Attacks in Continuous Space for Dense Retrieval](https://mlsanity.com/paper/2504.17884/) (2025)
- [Randomly Removing 50% of Dimensions in Text Embeddings has Minimal Impact on Retrieval and Classification Tasks](https://mlsanity.com/paper/2508.17744/) (2025)
- [Dimension Reduction for Efficient Dense Retrieval via Conditional Autoencoder](https://mlsanity.com/paper/2205.03284/) (2022)
- [Evaluating Unsupervised Dimensionality Reduction Methods for Pretrained Sentence Embeddings](https://mlsanity.com/paper/2403.14001/) (2024)

## Built on by (most cited first, 1 of 1)

- [Ovis-Embedding: Pushing the Frontiers of Universal Omni-Modal Embeddings](https://mlsanity.com/paper/2609.25165/) (2026)

## Abstract (arXiv)

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes representational capacity, while whitening enforces isotropy at the cost of amplifying noise in the heavy-tailed eigenspectrum of retrieval embeddings. Intermediate spectral scaling methods unify these extremes by reweighting dimensions with a power coefficient γ, but treat γ as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength γ is not a global constant: it varies systematically with target dimensionality k and is governed by the signal-to-noise ratio (SNR) of the retained subspace. Based on this insight, we propose Spectral Tempering (SpecTemp), a learning-free method that derives an adaptive γ(k) directly from the corpus eigenspectrum using local SNR analysis and knee-point normalization, requiring no labeled data or validation-based search. Extensive experiments demonstrate that Spectral Tempering consistently achieves near-oracle performance relative to grid-searched γ^*(k) while remaining fully learning-free and model-agnostic. Our code is publicly available at https://github.com/liyongkang123/SpecTemp.