# CALR: Corrective Adaptive Low-Rank Decomposition for Efficient Large Language Model Layer Compression

arXiv: https://arxiv.org/abs/2508.16680 · HTML: https://mlsanity.com/paper/2508.16680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 43 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (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)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [A Comprehensive Survey of Small Language Models in the Era of Large Language Models: Techniques, Enhancements, Applications, Collaboration with LLMs, and Trustworthiness](https://mlsanity.com/paper/2411.03350/) (2024)
- [LaCo: Large Language Model Pruning via Layer Collapse](https://mlsanity.com/paper/2402.11187/) (2024)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Investigating Layer Importance in Large Language Models](https://mlsanity.com/paper/2409.14381/) (2024)
- [Recent Advances in Generative AI and Large Language Models: Current Status, Challenges, and Perspectives](https://mlsanity.com/paper/2407.14962/) (2024)
- [LORD: Low Rank Decomposition Of Monolingual Code LLMs For One-Shot Compression](https://mlsanity.com/paper/2309.14021/) (2023)
- [ERC-SVD: Error-Controlled SVD for Large Language Model Compression](https://mlsanity.com/paper/2505.20112/) (2025)
- [FlexiGPT: Pruning and Extending Large Language Models with Low-Rank Weight Sharing](https://mlsanity.com/paper/2501.14713/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) present significant deployment challenges due to their immense size and computational requirements. Model compression techniques are essential for making these models practical for resource-constrained environments. A prominent compression strategy is low-rank factorization via Singular Value Decomposition (SVD) to reduce model parameters by approximating weight matrices. However, standard SVD focuses on minimizing matrix reconstruction error, often leading to a substantial loss of the model's functional performance. This performance degradation occurs because existing methods do not adequately correct for the functional information lost during compression. To address this gap, we introduce Corrective Adaptive Low-Rank Decomposition (CALR), a two-component compression approach. CALR combines a primary path of SVD-compressed layers with a parallel, learnable, low-rank corrective module that is explicitly trained to recover the functional residual error. Our experimental evaluation on SmolLM2-135M, Qwen3-0.6B, and Llama-3.2-1B, demonstrates that CALR can reduce parameter counts by 26.93% to 51.77% while retaining 59.45% to 90.42% of the original model's performance, consistently outperforming LaCo, ShortGPT, and LoSparse. CALR's success shows that treating functional information loss as a learnable signal is a highly effective compression paradigm. This approach enables the creation of significantly smaller, more efficient LLMs, advancing their accessibility and practical deployment in real-world applications.