Low-Rank Compression of Pretrained Models via Randomized Subspace Iteration
This work addresses the deployment challenge of massive pretrained models for practitioners by providing a more effective compression method, though it is incremental as it builds on existing low-rank techniques.
The paper tackles the problem of efficiently compressing large pretrained models by addressing the poor approximation quality of randomized SVD in slow-decaying singular value spectra, proposing randomized subspace iteration to achieve near-optimal compression with improved predictive accuracy under aggressive compression.
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.