Papers with SVD
Adaptive Rank Selections for Low-Rank Approximation of Language Models (2024.naacl-long)
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| Challenge: | Singular Value Decomposition (SVD) or its weighted variants has progressed in compressing language models. |
| Approach: | They propose a binary masking mechanism for optimizing the number of ranks in a differentiable framework. |
| Outcome: | The proposed algorithm achieves much better accuracy than previous SVD and its weighted variants. |
FlexiGPT: Pruning and Extending Large Language Models with Low-Rank Weight Sharing (2025.naacl-long)
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James Seale Smith, Chi-Heng Lin, Shikhar Tuli, Haris Jeelani, Shangqian Gao, Yilin Shen, Hongxia Jin, Yen-Chang Hsu
| Challenge: | Empirical evaluations demonstrate substantial performance gains over existing methods . |
| Approach: | They propose a method to prune LLMs that selectively prunes model blocks based on an importance score and replaces them with a low-parameter replacement strategy. |
| Outcome: | The proposed method achieves state-of-the-art performance on 5/6 and 6/6 benchmarks with a compression rate of 30% and 40%. |
An efficient method for Natural Language Querying on Structured Data (2023.acl-industry)
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| Challenge: | a new approach to NLQ on structured data is based on text-to-SQL type semantic parsing . domain classification, domain classification and domain classification are the main tasks . semantic parsed queries are less common when information is in structured form . |
| Approach: | They propose an efficient and reliable approach to natural language Querying on databases . they use domain classification, domain classification and slot/entity extraction to query a DB . |
| Outcome: | The proposed approach simplifies the NLQ on structured data problem to the following "bread and butter" tasks. |
SVD-GCL: A Noise-Augmented Hybrid Graph Contrastive Learning Framework for Recommendation (2025.coling-main)
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| Challenge: | Recent advances in graph neural networks have made it difficult to capture user preferences. |
| Approach: | They propose a graph contrastive learning recommendation model based on noise augmentation that integrates truncated singular value decomposition in the feature engineering stage. |
| Outcome: | The proposed model reduces dimensionality and denoises the original data. |
Large Language Model Evaluation via Matrix Nuclear-Norm (2025.findings-emnlp)
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| Challenge: | Large language models (LLMs) are computationally intensive due to their O(n3) time complexity with Singular Value Decomposition (SVD). |
| Approach: | They propose a metric to quantify the data compression proficiency of large language models and a convex approximation of matrix rank to capture both predictive discriminability and diversity. |
| Outcome: | The proposed model achieves speeds 8 to 24 times faster than Matrix Entropy for the CEREBRAS-GPT model as models increase from 111M to 6.7B . |
NLoRA: Nyström-Initiated Low-Rank Adaptation for Large Language Models (2025.findings-emnlp)
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| Challenge: | Parameter-efficient fine-tuning is essential for adapting large language models (LLMs). However, LoRA suffers from slow convergence and some recent LoRA variants, such as PiSSA, rely on Singular Value Decomposition (SVD) for initialization. |
| Approach: | They propose to introduce a small intermediate matrix between the low-rank matrices (A) and (B) and propose NyströmLoRA (NLoRA) which leverages Nyström-based initialization for SLoRA to improve its effectiveness and efficiency. |
| Outcome: | The proposed approach improves on 5 natural language generation tasks and 8 natural language understanding tasks with minimal parameter overhead. |
Numerical Optimizations for Weighted Low-rank Estimation on Language Models (2022.emnlp-main)
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| Challenge: | Singular value decomposition (SVD) is one of the most popular methods for estimating a target matrix with smaller matrices. |
| Approach: | They propose a method that approximates a target matrix with smaller matrices by two smaller . they also propose metric to predict when the SVD may introduce a significant performance drop. |
| Outcome: | The proposed method can perform better than current SOTA methods in compressing Transformer-based language models. |
SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression (2025.naacl-long)
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| Challenge: | Existing methods for compressing Large Language Models suffer from significant truncation losses. |
| Approach: | They propose a novel method that optimizes singular value truncation in SVD compression . they use dynamic compression ratio allocation to balance the large tuncation loss . |
| Outcome: | The proposed method outperforms current state-of-the-art methods on ten datasets and five models on various scales. |
On the Representation Geometry of LoRA Model Merging (2026.findings-acl)
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| Challenge: | Existing methods for low-rank Adaptation (LoRA) fine-tuning focus on globally shared structure . combining SVD with CUR improves performance of LoRA model merging . |
| Approach: | They propose a training-free method that combines SVD and CUR decomposition to improve LoRA merging performance. |
| Outcome: | The proposed procedure improves on vision and language benchmarks. |
Federated LoRA Fine-Tuning with Pipelined Error-Mitigated Aggregation and Matrix-Wise Freezing (2026.findings-acl)
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| Challenge: | Existing methods for fine-tuning large language models often suffer from biased model aggregation and are hindered by significant communication and computation burden. |
| Approach: | They propose a Federated low-rank adaptation system for large language models that leverages pipelined error-mitigated model aggregation and adaptive matrix-wise parameter freezing to mitigate aggregations. |
| Outcome: | The proposed system improves time-to-target by 2.17-8.48 on real-world datasets. |
Efficient One-shot Compression via Low-Rank Local Feature Distillation (2025.naacl-long)
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| Challenge: | Existing structured pruning approaches for large language models require calibration data and costly continued pretraining on billions of tokens to recover lost performance. |
| Approach: | They propose a method that locally distills activations with low-rank weights . they compress Mixtral-8x7B on a single GPU and Phi-2 3B by 40% . |
| Outcome: | The proposed method compresses Mixtral-8x7B on a single A100 GPU, removing 10 billion parameters while retaining over 95% of its original performance. |
Enhancing Translation Ability of Large Language Models by Leveraging Task-Related Layers (2024.lrec-main)
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| Challenge: | Experimental validation shows that adjusting task-related layers significantly improves performance on translation tasks while maintaining stability and accuracy on other tasks. |
| Approach: | They propose to adjust task-related layers in large models to better harness their machine translation capabilities by revealing the structure and characteristics of attention weights through singular value decomposition. |
| Outcome: | The proposed method reduces computational resource consumption and catastrophic forgetting while maintaining stability and accuracy on other tasks. |
Dynamic Low-rank Estimation for Transformer-based Language Models (2023.findings-emnlp)
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| Challenge: | RankDyna is a matrix decomposition method that can be used to compress Transformer-based language models. |
| Approach: | They propose a matrix decomposition method that enables dynamic rank resource allocation . they say it can outperform current SOTA methods under various parameter budget levels . |
| Outcome: | The proposed method outperforms current SOTA methods under various budget levels . the proposed method is more efficient with higher compression rates . |
LightFormer: Light-weight Transformer Using SVD-based Weight Transfer and Parameter Sharing (2023.findings-acl)
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| Challenge: | Deploying Transformer networks on resource-constrained edge devices is challenging. |
| Approach: | They propose a low-rank factorization initialized by SVD-based weight transfer and parameter sharing to compress and accelerate Transformer networks. |
| Outcome: | The proposed method achieves similar performance to the baseline Transformer with 3.8 times and 1.8 times fewer parameters and achieves 2.3 times speedup and 1.5 times speed up respectively. |
DisLoRA: Task-specific Low-Rank Adaptation via Orthogonal Basis from Singular Value Decomposition (2025.emnlp-main)
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| Challenge: | Extensive experiments on GLUE and Commonsense Reasoning benchmarks demonstrate that DisLoRA surpasses established PEFT methods, including LoRA, PiSSA, DoRA, LoRA-Dash, and SORSA. |
| Approach: | They propose a framework that leverages singular value decomposition to decompose pretrained weight matrices into orthogonal backbone and task-specific subspaces. |
| Outcome: | Extensive experiments on GLUE and Commonsense Reasoning benchmarks show that DisLoRA surpasses established PEFT methods, including LoRA, PiSSA, DoRA, LoRA-Dash, and SORSA. |
Optimizing Lifelong Fine-Tuning for Multiple Tasks via Dataless Distribution Replay (2025.coling-main)
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| Challenge: | Existing methods to fine-tune large language models with minimal instruction data are prone to catastrophic forgetting during life-long fine- tuning. |
| Approach: | They propose a dataless distribution replay approach for life-long fine-tuning that replays the output of the linear layers at previous task stages. |
| Outcome: | The proposed method achieves significant improve- ments compared to several strong lifelong fine- tuning methods. |
Multilingual Federated Low-Rank Adaptation for Collaborative Content Anomaly Detection across Multilingual Social Media Participants (2025.emnlp-main)
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| Challenge: | Recent developments in multilingual social media platforms (SNS) exacerbate new challenges in SNS content anomaly detection due to data islands and linguistic imbalance. |
| Approach: | They propose a multilingual Federated LoRA based on SVD-based language-specific disentanglement of LoRA blocks and a local orthogonal tuning strategy to detect content anomalies. |
| Outcome: | The proposed solution is superior in multilingual content anomaly detection while reducing multilingual knowledge conflicts and communication rounds. |
RanLoRA: Residual-aware Nonlinear Low-Rank Adaptation (2026.findings-acl)
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| Challenge: | Low-Rank Adaptation (LoRA) relying on linear low-rank projections restricts adaptation to linear subspaces, limiting flexibility on complex downstream tasks. |
| Approach: | They propose a nonlinear low-rank Adaptation approach that leverages pretrained weights to decompose them into principal components that are kept frozen and residual components that can be used for task-specific adaptation. |
| Outcome: | The proposed approach outperforms vanilla LoRA and representative variants on commonsense reasoning, image classification, and mathematical reasoning tasks. |
BWLA: Breaking the Barrier of W1AX Post-Training Quantization for LLMs (2026.acl-long)
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| Challenge: | Large language models have driven major progress in NLP, but memory and compute requirements hinder practical deployment. |
| Approach: | They propose a framework that preserves high accuracy while achieving 1-bit weight quantization . the orthogonal-kronecker transformation learns an orthogonale mapping via EM minimization - a new approach to quantization is proposed . |
| Outcome: | The proposed framework achieves 1-bit weight quantization with low activations with low-bit activations. |
Beyond Uniform SVD: Dual-Level Optimization across Columns and Modules for LLM Compression (2026.findings-acl)
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| Challenge: | Existing methods for low-rank decomposition overlook decomposing errors and suboptimal approximation. |
| Approach: | They propose a low-rank decomposition framework that integrates low-level optimization at column and module levels. |
| Outcome: | The proposed framework outperforms state-of-the-art methods and baselines in SVD and pruning. |
ImPart: Importance-Aware Delta-Sparsification for Improved Model Compression and Merging in LLMs (2025.acl-long)
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| Challenge: | Recent approaches to reduce resource requirements for task-specific large language models have been developed. |
| Approach: | They propose a delta compression approach that optimizes for importance of a model . they use SVD to dynamically adjust the sparsity ratios of different vectors based on their importance . |
| Outcome: | The proposed approach achieves state-of-the-art in retaining task-specific knowledge even at high sparsity ratios. |
Low-Rank Prune-And-Factorize for Language Model Compression (2024.lrec-main)
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| Challenge: | Existing methods to reduce parameter redundancy in pre-processed language models fail to retain satisfactory performance under moderate to high compression rates. |
| Approach: | They propose to use network pruning to extract low-rank sparsity pattern desirable to matrix factorization. |
| Outcome: | The proposed method has a superior compression-performance trade-off compared to existing methods. |
HiSVD: Principled Low-Rank Approximation of LLMs via Hierarchical Modeling of Information Capacity and Spectral Structure (2026.acl-long)
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| Challenge: | Existing methods for generating layer importance ignore the fine-grained influence of spectral distribution shape. |
| Approach: | They propose a hierarchical rank allocation framework with two stages to address this gap . they propose SVD-based lowrank approximation that exploits spectral heterogeneity . |
| Outcome: | Experiments show that HiSVD outperforms state-of-the-art methods on LLMs . |
GeoRA: Geometry-Aware Low-Rank Adaptation for RLVR (2026.acl-long)
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| Challenge: | Existing parameter-efficient methods for RLVR face limitations . low-rank adaptation methods do not account for the distinct optimization dynamics . |
| Approach: | They propose a low-rank adaptation method tailored for RLVR that exploits the anisotropic structure of RL update subspace and extracts its principal directions via Singular Value Decomposition (SVD). |
| Outcome: | Experiments on large reasoning models show that GeoRA outperforms strong low-rank baselines across RLVR settings while showing stronger generalization and less forgetting on out-of-domain tasks. |
Hierarchical-Task-Aware Multi-modal Mixture of Incremental LoRA Experts for Embodied Continual Learning (2025.acl-long)
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| Challenge: | Existing continual learning setups for embodied intelligence focus on executing low-level actions, neglecting the ability to learn high-level planning and multi-level knowledge. |
| Approach: | They propose a Hierarchical Embodied Continual Learning Setups (HEC) that divides the agent’s continual learning process into two layers: high-level instructions and low-level actions. |
| Outcome: | The proposed method reduces the forgetting of old tasks compared to other methods, while orthogonally training the remaining parts. |
How Instruction and Reasoning Data shape Post-Training: Data Quality through the Lens of Layer-wise Gradients (2026.acl-long)
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| Challenge: | Spectral properties of low/high-quality instruction and reasoning data are used to explain finetuning dynamics in large language models. |
| Approach: | They propose to analyze layer-wise gradients induced by low/high-quality instruction and reasoning data for LLM post-training. |
| Outcome: | The results show that higher-quality data are associated with lower nuclear norms and higher effective ranks. |
Towards Economical Inference: Enabling DeepSeek’s Multi-Head Latent Attention in Any Transformer-based LLMs (2025.acl-long)
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Tao Ji, Bin Guo, Yuanbin Wu, Qipeng Guo, Shenlixing Shenlixing, Chenzhan Chenzhan, Xipeng Qiu, Qi Zhang, Tao Gui
| Challenge: | Multi-head Latent Attention (MLA) is an innovative architecture designed to ensure efficient and economical inference by significantly compressing the Key-Value (KV) cache into a latent vector. |
| Approach: | They propose a data-efficient fine-tuning method for transitioning from MHA to MLA using a latent vector cache. |
| Outcome: | The proposed architecture reduces the KV cache size of Llama2-7B by 92.19%, with only 1% drop in LongBench performance. |
HyperAdaLoRA: Accelerating LoRA Rank Allocation During Training via Hypernetworks without Sacrificing Performance (2026.findings-acl)
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Hao Zhang, Zhenjia Li, Yifan Gao, Xi Xiao, Heng Zhang, Shuyang Zhang, null Xiaoxincc, Bo Huang, Yuhang Wu, Tianyang Wang, Hao Xu
| Challenge: | Low-Rank Adaptation (LoRA) assumes a uniform rank r for each incremental matrix, not accounting for the varying significance of weight matrices across modules and layers. |
| Approach: | They propose a framework that allows for faster convergence of low-rank adaptive models . they use a hypernetwork to prune the outputs of the hypernetworks to generate parameters . |
| Outcome: | The proposed framework accelerates convergence of AdaLoRA by leveraging a hypernetwork. |
HiCoLoRA: Addressing Context-Prompt Misalignment via Hierarchical Collaborative LoRA for Zero-Shot DST (2026.findings-acl)
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| Challenge: | Existing approaches to zero-shot Dialog State Tracking (zs-DST) are inadequate to generalize to new domains without extensive training. |
| Approach: | They propose a framework that enhances zero-shot slot inference through robust prompt alignment. |
| Outcome: | Experiments on multi-domain datasets show that HiCoLoRA outperforms baselines, achieving SOTA in zs-DST. |
Relaxing the Constraints: A Dual-Importance Projection Mechanism for Lifelong Model Editing (2026.findings-acl)
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Zhenghai Chen, Senbin Xu, Jiaxi Tan, Xinhua Wu, Yan Zhang, Xiawu Zheng, Shengchuan Zhang, Ke Li, Sicheng Zhao, Liujuan Cao, Rongrong Ji
| Challenge: | Existing knowledge editing methods rely on strict orthogonal projection to preserve previously edited knowledge, but this constraint limits gradient expressiveness, resulting in degradation of model generalization and overall performance as the number of edits increases. |
| Approach: | They propose a method that leverages Singular Value Decomposition to identify critical gradient subspaces and introduces a dual mechanism comprising "accumulated importance" and "projection importance" |
| Outcome: | Extensive experiments on five mainstream LLMs show that the proposed method achieves an average comprehensive performance improvement of 10.36% and effectively maintains the model’s general capabilities on downstream tasks. |
JW-SVD: Bridging the Cross-Modal Mismatch in Post-Training MLLM Compression (2026.acl-long)
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| Challenge: | Existing methods for compression of Multimodal Large Language Models lack multimodal adaptation to preserve cross-modal synergy. |
| Approach: | They propose a framework that aligns vision and language manifolds via a Joint Covariance basis and propose Global Spectrum-Aware Truncation to dynamically transfer parameter budget to the sensitive Backbone. |
| Outcome: | Experiments on Qwen2.5-VL and Llama-3-Next confirm that JW-SVD retains both text and image capabilities. |
Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics (2026.acl-long)
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| Challenge: | Existing methods for activation compression are gradient-blind and preserve high-variance dimensions regardless of their impact on factual knowledge preservation. |
| Approach: | They propose a knowledge-aware compression framework that models activation-gradient coupling by directly modeling subspaces. |
| Outcome: | The proposed framework preserves 6–8% more accuracy on knowledge-intensive benchmarks compared to variance-based methods at 50% rank reduction. |