# SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression

arXiv: https://arxiv.org/abs/2403.07378 · HTML: https://mlsanity.com/paper/2403.07378/

## Key facts

- Cited by 243 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 57 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 30 of 37)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Efficient Large Language Models: A Survey](https://mlsanity.com/paper/2312.03863/) (2023)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)

## Built on by (most cited first, 30 of 243)

- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [MoE-I2: Compressing Mixture of Experts Models through Inter-Expert Pruning and Intra-Expert Low-Rank Decomposition](https://mlsanity.com/paper/2411.01016/) (2024)
- [SRPO: Enhancing Multimodal LLM Reasoning via Reflection-Aware Reinforcement Learning](https://mlsanity.com/paper/2506.01713/) (2025)
- [HOBBIT: A Mixed Precision Expert Offloading System for Fast MoE Inference](https://mlsanity.com/paper/2411.01433/) (2024)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [A Survey on Inference Optimization Techniques for Mixture of Experts Models](https://mlsanity.com/paper/2412.14219/) (2024)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Basis Sharing: Cross-Layer Parameter Sharing for Large Language Model Compression](https://mlsanity.com/paper/2410.03765/) (2024)
- [D2O: Dynamic Discriminative Operations for Efficient Long-Context Inference of Large Language Models](https://mlsanity.com/paper/2406.13035/) (2024)
- [MEDA: Dynamic KV Cache Allocation for Efficient Multimodal Long-Context Inference](https://mlsanity.com/paper/2502.17599/) (2025)
- [Sub-MoE: Efficient Mixture-of-Expert LLMs Compression via Subspace Expert Merging](https://mlsanity.com/paper/2506.23266/) (2025)
- [From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications](https://mlsanity.com/paper/2407.11239/) (2024)
- [Small Singular Values Matter: A Random Matrix Analysis of Transformer Models](https://mlsanity.com/paper/2410.17770/) (2024)
- [Principled Multimodal Representation Learning](https://mlsanity.com/paper/2507.17343/) (2025)
- [You Only Prune Once: Designing Calibration-Free Model Compression With Policy Learning](https://mlsanity.com/paper/2501.15296/) (2025)
- [LoR-VP: Low-Rank Visual Prompting for Efficient Vision Model Adaptation](https://mlsanity.com/paper/2502.00896/) (2025)
- [Put the Space of LoRA Initialization to the Extreme to Preserve Pre-trained Knowledge](https://mlsanity.com/paper/2503.02659/) (2025)
- [Can Compressed LLMs Truly Act? An Empirical Evaluation of Agentic Capabilities in LLM Compression](https://mlsanity.com/paper/2505.19433/) (2025)
- [ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration](https://mlsanity.com/paper/2505.24357/) (2025)
- [QSVD: Efficient Low-rank Approximation for Unified Query-Key-Value Weight Compression in Low-Precision Vision-Language Models](https://mlsanity.com/paper/2510.16292/) (2025)
- [UNComp: Can Matrix Entropy Uncover Sparsity? -- A Compressor Design from an Uncertainty-Aware Perspective](https://mlsanity.com/paper/2410.03090/) (2024)
- [Beware of Calibration Data for Pruning Large Language Models](https://mlsanity.com/paper/2410.17711/) (2024)
- [SLIP: Securing LLMs IP Using Weights Decomposition](https://mlsanity.com/paper/2407.10886/) (2024)
- [ReplaceMe: Network Simplification via Depth Pruning and Transformer Block Linearization](https://mlsanity.com/paper/2505.02819/) (2025)
- [Multi-objective Large Language Model Alignment with Hierarchical Experts](https://mlsanity.com/paper/2505.20925/) (2025)
- [Accelerating Diffusion Transformer via Increment-Calibrated Caching with Channel-Aware Singular Value Decomposition](https://mlsanity.com/paper/2505.05829/) (2025)
- [SAES-SVD: Self-Adaptive Suppression of Accumulated and Local Errors for SVD-based LLM Compression](https://mlsanity.com/paper/2602.03051/) (2026)

## Abstract (arXiv)

The advancements in Large Language Models (LLMs) have been hindered by their substantial sizes, which necessitates LLM compression methods for practical deployment. Singular Value Decomposition (SVD) offers a promising solution for LLM compression. However, state-of-the-art SVD-based LLM compression methods have two key limitations: truncating smaller singular values may lead to higher compression loss, and the lack of update on the compressed weights after SVD truncation. In this work, we propose SVD-LLM, a SVD-based post-training LLM compression method that addresses the limitations of existing methods. SVD-LLM incorporates a truncation-aware data whitening technique to ensure a direct mapping between singular values and compression loss. Moreover, SVD-LLM adopts a parameter update with sequential low-rank approximation to compensate for the accuracy degradation after SVD compression. We evaluate SVD-LLM on 10 datasets and seven models from three different LLM families at three different scales. Our results demonstrate the superiority of SVD-LLM over state-of-the-arts, especially at high model compression ratios. Our code is available at https://github.com/AIoT-MLSys-Lab/SVD-LLM