# Optimal Singular Damage: Efficient LLM Inference in Low Storage Regimes

arXiv: https://arxiv.org/abs/2511.02681 · HTML: https://mlsanity.com/paper/2511.02681/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Serving systems and request scheduling, one of 12 directions in Efficient LLM inference and serving.
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Placed in

- Efficient LLM inference and serving / [Serving systems and request scheduling](https://mlsanity.com/inference/serving-systems-and-request-scheduling/)

## Builds on (most cited first, 20 of 20)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [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)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Accelerated Sparse Neural Training: A Provable and Efficient Method to Find N:M Transposable Masks](https://mlsanity.com/paper/2102.08124/) (2021)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [BitDelta: Your Fine-Tune May Only Be Worth One Bit](https://mlsanity.com/paper/2402.10193/) (2024)
- [OATS: Outlier-Aware Pruning Through Sparse and Low Rank Decomposition](https://mlsanity.com/paper/2409.13652/) (2024)
- [Delta-CoMe: Training-Free Delta-Compression with Mixed-Precision for Large Language Models](https://mlsanity.com/paper/2406.08903/) (2024)
- [Efficient Storage of Fine-Tuned Models via Low-Rank Approximation of Weight Residuals](https://mlsanity.com/paper/2305.18425/) (2023)
- [Two Sparse Matrices are Better than One: Sparsifying Neural Networks with Double Sparse Factorization](https://mlsanity.com/paper/2409.18850/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are increasingly prevalent across diverse applications. However, their enormous size limits storage and processing capabilities to a few well-resourced stakeholders. As a result, most applications rely on pre-trained LLMs, fine-tuned for specific tasks. However, even storing the fine-tuned versions of these models remains a significant challenge due to the wide range of tasks they address. Recently, studies show that fine-tuning these models primarily affects a small fraction of parameters, highlighting the need for more efficient storage of fine-tuned models. This paper focuses on efficient storage of parameter updates in pre-trained models after fine-tuning. To address this challenge, we leverage the observation that fine-tuning updates are both low-rank and sparse, which can be utilized for storage efficiency. However, using only low-rank approximation or sparsification may discard critical singular components that enhance model expressivity. We first observe that given the same memory budget, sparsified low-rank approximations with larger ranks outperform standard low-rank approximations with smaller ranks. Building on this, we propose our method, optimal singular damage, that selectively sparsifies low-rank approximated updates by leveraging the interleaved importance of singular vectors, ensuring that the most impactful components are retained. We demonstrate through extensive experiments that our proposed methods lead to significant storage efficiency and superior accuracy within the same memory budget compared to employing the low-rank approximation or sparsification individually.