Large language models (LLMs) have demonstrated remarkable capabilities, yet prohibitive parameter complexity often hinders their deployment. Existing singular value decomposition (SVD) based compression methods simply deem singular values as importance scores of decomposed components. However, this importance ordered by singular values does not necessarily correlate with the performance of a downstream task. In this work, we introduce SoCo (Singular spectrum optimization for large language model Compression), a novel compression framework that learns to rescale the decomposed components of SVD in a data-driven manner. Concretely, we employ a learnable diagonal matrix to assign importance scores for singular spectrum and develop a three-stage training process that progressively refines these scores from initial coarse compression to fine-grained sparsification-thereby striking an effective balance between aggressive model compression and performance preservation. Thanks to the learnable singular spectrum, SoCo adaptively prunes components according to the sparsified importance scores, rather than relying on the fixed order of singular values. More importantly, the remaining components with amplified importance scores can compensate for the loss of the pruned ones. Experimental evaluations across multiple LLMs and benchmarks demonstrate that SoCo surpasses the state-of-the-art methods in model compression.
Figures & tables
Figure 1: SoCo consistently outperforms existing methods across a range of compression ratios, yielding lower perplexity on C4 (left) and higher average classification accuracy on LM-Evaluation-Harness (right).
Figure 2: Illustration of the overall framework of SoCo. The pre-trained weight matrix W is decomposed into UΣV⊤ , where Σ is a diagonal matrix with diagonal elements arranged in descending order. a) Existing SVD-based compression methods truncate the smaller singular values and their corresponding vectors in U and rows in V⊤ . b) The proposed SoCo assigns a diagonal matrix S as importance scores to singular values in Σ . After training, singular values with an importance score below a given threshold (e.g., 0.5) are pruned. In particular, singular values with importance scores larger than the threshold rescale the preserved singular values to compensate the loss from pruned components.
Figure 3: Distribution of importance scores after each of our three training stages, illustrating the dynamic re-evaluation process.
Stage
Conditions
Loss Functions
1
Table 1: Conditions and loss functions for each training stage. step denotes the procedure of the whole training process, where step∈[0,1] (with 0 representing the start and 1 representing the end).
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.
Mahmoud Safari, Frank Hutter
University of Freiburg · Prior Labs · ELLIS Institute Tübingen
Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but the billion-scale parameters pose deployment challenges. Although existing methods attempt to reduce the scale of LLMs, they require either special hardware support or expensive post-training to maintain model quality. To facilitate efficient and affordable model slimming, we propose a novel training-free compression method for LLMs, named "SoLA", which leverages Soft activation sparsity and Low-rAnk decomposition. SoLA can identify and retain a minority of components significantly contributing to inference, while compressing the majority through low-rank decomposition, based on our analysis of the activation pattern in the feed-forward network (FFN) of modern LLMs. To alleviate the decomposition loss, SoLA is equipped with an adaptive component-wise low-rank allocation strategy to assign appropriate truncation positions for different weight matrices. We conduct extensive experiments on LLaMA-2-7B/13B/70B and Mistral-7B models across a variety of benchmarks. SoLA exhibits remarkable improvement in both language modeling and downstream task accuracy without post-training. For example, with a 30% compression rate on the LLaMA-2-70B model, SoLA surpasses the state-of-the-art method by reducing perplexity from 6.95 to 4.44 and enhancing downstream task accuracy by 10%.
Xinhao Huang, You-Liang Huang, Zeyi Wen
The Hong Kong University of Science and Technology (Guangzhou) · The Hong Kong University of Science and Technology
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).