The rapid growth in the parameter scale of large language models (LLMs) has created a strong demand for efficient compression techniques. As a hardware-agnostic and highly compatible approach, low-rank compression has been widely adopted to reduce both memory footprint and computational cost. However, existing SVD-based methods are still largely driven by local reconstruction objectives, overlooking two critical limitations: rank budgets are often allocated without explicitly considering layer-wise loss sensitivity, and local approximation errors can propagate and accumulate through the residual stream, leading to amplified global deviations from the original model. To address these issues, we propose LACE-SVD, a Loss-Aware SVD framework with Cumulative Error correction for LLM compression. LACE-SVD first estimates the calibration negative-log-likelihood increase induced by candidate layer-wise compression ratios and solves a budget-constrained allocation problem to assign rank budgets. It then refines the compressed model with closed-form local updates and introduces a propagation-aware correction for residual-stream output modules, reducing layer-output discrepancy as a proxy for cumulative error propagation. Experimental results demonstrate that at a high compression ratio (0.6), the WikiText-2 PPL of our method on LLaMA-7B (32.57) is significantly better than that of Dobi-SVD (46.18).
Large language models (LLMs) achieve remarkable performance across a wide range of tasks, but their deployment is constrained by substantial memory and compute requirements. Low-rank compression via singular value decomposition (SVD) is an effective remedy, but existing methods focus on how to factorize and which components to keep. We introduce SVD-Surgeon, a training-free method that brings the Optimal Brain Surgeon (OBS) framework to the singular-value basis. Treating each singular value as a parameter, it computes a closed-form update of the retained singular values that compensates, to second order in the model loss, for those removed by truncation. The same analysis yields a saliency for choosing which values to prune. As it operates directly on the singular-value factorization, SVD-Surgeon can be layered on top of existing SVD compressors. Applied to SVD-LLM, a leading SVD-based method, it improves the perplexity-compression trade-off on the OPT family and LLaMA 2-7B without any retraining.
Large language models deliver strong performance across language and reasoning tasks, but their storage and compute costs remain major barriers to deployment in resource-constrained and latency-sensitive settings. SVD-based post-training compression offers a hardware-agnostic way to reduce model size and improve inference efficiency through low-rank factorization. However, existing methods often rely on input-only whitening spaces, homogeneous rank allocation, or loss-agnostic allocation heuristics, limiting their ability to preserve model quality under aggressive compression. We propose Input-Output Whitened SVD (IO-SVD), a post-training compression method that forms a KL-aware double-sided whitening space for model weights. Using a second-order expansion of the KL loss over the top-K token probabilities, IO-SVD constructs an output-side metric that captures predictive sensitivity, while input whitening captures activation statistics. We further introduce an efficient heterogeneous rank-allocation strategy that scores whitened singular components using first-order calibration loss estimates and prunes the least sensitive components under a global budget. Inspired by prior work that combines SVD truncation with quantization, we improve hybrid SVD-quantization compression through loss-aware remapping, which selects low-rank factor rows for 8-bit quantization based on the predicted loss change incurred by quantizing them. Extensive experiments across diverse LLM and VLM families, and inference-time analysis shows that IO-SVD compresses LLMs with minimal performance degradation while delivering practical inference speedups. Code is available at https://github.com/mint-vu/IO-SVD.git
We present SigmaScale, a method for learning auxiliary scaling matrices S to aid truncated Singular Value Decomposition (SVD) based Large Language Model (LLM) compression. Instead of deriving scaling matrices analytically, SigmaScale optimizes two sets of vectors that define diagonal row and column scaling transformations under an activation-aware compression loss. We show that learned scaling lowers the effective intrinsic rank of weight matrices, as reflected by reductions in effective-rank entropy, and that this reduction is strongly correlated with compression loss. Experiments on Llama 3.1 8B Instruct and Qwen3-8B show that SigmaScale is competitive with closely related state-of-the-art SVD-based compression methods across perplexity and zero-shot benchmarks. By using learned activation-aware transformations, SigmaScale explores a more flexible route to low-rank LLM compression by adapting to the structure of individual model weights. The advantage observed in specific tasks makes our approach a valid option for applications requiring a reduced LLM-inference computing cost.