Low-Rank Compression of Pretrained Models via Randomized Subspace Iteration

TL;DR

This paper introduces randomized subspace iteration (RSI) for low-rank compression of pretrained models, improving approximation quality and predictive performance over randomized SVD, especially for large, slowly decaying spectra.

Contribution

It establishes a theoretical link between spectral approximation error and model performance, and proposes RSI as a superior randomized method for model compression.

Findings

RSI outperforms RSVD in approximation quality and accuracy.

Spectral error correlates with class probability deviations.

RSI enables efficient compression of large models with minimal performance loss.

Abstract

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its exact computation is expensive for large weight matrices. Randomized alternatives such as randomized SVD (RSVD) improve efficiency, yet they can suffer from poor approximation quality when the singular value spectrum decays slowly, a regime commonly observed in modern pretrained models. In this work, we address this limitation from both theoretical and empirical perspectives. First, we establish a connection between low-rank approximation error and predictive performance by analyzing softmax perturbations, showing that deviations in class probabilities are controlled by the spectral error of the compressed weights. Second, we demonstrate that RSVD is inadequate, and we propose randomized subspace iteration (RSI) as a more effective alternative. By incorporating multiple power iterations, RSI improves spectral separation and provides a controllable mechanism for enhancing approximation quality. We evaluate our approach on both convolutional networks and transformer-based architectures. Our results show that RSI achieves near-optimal approximation quality while outperforming RSVD in predictive accuracy under aggressive compression, enabling efficient model compression.