Abstract
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 \(\gamma\), but treat \(\gamma\) as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength \(\gamma\) 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 (\textbf\{SpecTemp\}), a learning-free method that derives an adaptive \(\gamma(k)\) directly from the corpus eigenspectrum using local SNR analysis