# SVD-Surgeon: Optimal Singular-Value Surgery for Large Language Model Compression

arXiv: https://arxiv.org/abs/2606.23568 · HTML: https://mlsanity.com/paper/2606.23568/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [The Optimal BERT Surgeon: Scalable and Accurate Second-Order Pruning for Large Language Models](https://mlsanity.com/paper/2203.07259/) (2022)
- [The LLM Surgeon](https://mlsanity.com/paper/2312.17244/) (2023)
- [Optimal Brain Decomposition for Accurate LLM Low-Rank Approximation](https://mlsanity.com/paper/2604.00821/) (2026)

## Built on by (most cited first, 1 of 1)

- [From Spectral Saliency to Finite Deletion: Evaluating Selective Language Model Edits](https://mlsanity.com/paper/2610.18098/) (2026)

## Abstract (arXiv)

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.