Advancing SVD-based LLM Compression via Layer-Wise Error Model Search

Low-rank SVD-based compression offers a powerful strategy to reduce the computational costs of Large language models (LLMs); however, existing methods commonly encounter two recurring obstacles: (i) global rank allocation, where uncalibrated error proxies fail to account for complex error propagation, and (ii) decomposition quality, where Fisher-based estimators suffer from severe rank collapse. In this work, we address these limitations by presenting Layer-wise Error Modeling Search (LEMS) and KFAC-SVD. LEMS advances rank allocation by introducing a layer-wise error surrogate that integrates both local and global layer importance alongside a propagation bias, allowing us to determine global rank configurations efficiently as an Integer Linear Program (ILP). Simultaneously, KFAC-SVD improves decomposition quality by utilizing token-wise statistics, preventing the rank deficiency observed in prior Fisher-based SVD. We demonstrate across Mistral, Qwen3, and Llama-3 families that KFAC-SVD achieves an average perplexity improvements of 15%, while LEMS consistently outperforms existing search strategies, delivering significant zero-shot accuracy improvements of up to 4.7 p.p. that generalize to scales of 70B parameters. Code is made available in the Supplement.