# A3 : an Analytical Low-Rank Approximation Framework for Attention

arXiv: https://arxiv.org/abs/2505.12942 · HTML: https://mlsanity.com/paper/2505.12942/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 19 May 2025.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [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)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [SlimPajama-DC: Understanding Data Combinations for LLM Training](https://mlsanity.com/paper/2309.10818/) (2023)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [Dobi-SVD: Differentiable SVD for LLM Compression and Some New Perspectives](https://mlsanity.com/paper/2502.02723/) (2025)
- [LQER: Low-Rank Quantization Error Reconstruction for LLMs](https://mlsanity.com/paper/2402.02446/) (2024)
- [Optimal CUR Matrix Decompositions](https://mlsanity.com/paper/1405.7910/) (2014)
- [Towards Economical Inference: Enabling DeepSeek's Multi-Head Latent Attention in Any Transformer-based LLMs](https://mlsanity.com/paper/2502.14837/) (2025)

## Built on by (most cited first, 8 of 8)

- [Low-Rank Compression of Language Models via Differentiable Rank Selection](https://mlsanity.com/paper/2512.13733/) (2025)
- [FlexRank: Nested Low-Rank Knowledge Decomposition for Adaptive Model Deployment](https://mlsanity.com/paper/2602.02680/) (2026)
- [Multilingual Hate Speech Detection in Social Media Using Translation-Based Approaches with Large Language Models](https://mlsanity.com/paper/2506.08147/) (2025)
- [Entropy Meets Importance: A Unified Head Importance-Entropy Score for Stable and Efficient Transformer Pruning](https://mlsanity.com/paper/2510.13832/) (2025)
- [LaMoC: Loss-Aware Modular Compression for LLMs](https://mlsanity.com/paper/2608.30226/) (2026)
- [MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-training](https://mlsanity.com/paper/2609.15037/) (2026)
- [IrekoGPT: Turning Structured Pruning into Post-Hoc Slimmable LLMs](https://mlsanity.com/paper/2610.00426/) (2026)
- [BELT : BEhavior-Aligned Low-Rank KV Cache Compression with Learned Top-k Rank Allocation](https://mlsanity.com/paper/2610.17966/) (2026)

## Abstract (arXiv)

Large language models have demonstrated remarkable performance; however, their massive parameter counts make deployment highly expensive. Low-rank approximation offers a promising compression solution, yet existing approaches have two main limitations: (1) They focus on minimizing the output error of individual linear layers, without considering the architectural characteristics of Transformers, and (2) they decompose a large weight matrix into two small low-rank matrices. Consequently, these methods often fall short compared to other compression techniques like pruning and quantization, and introduce runtime overhead such as the extra GEMM kernel launches and memory operations for decomposed small matrices. To address these limitations, we propose A3, a post-training low-rank approximation framework. A3 splits a Transformer layer into three functional components, namely textttQK, textttOV, and textttMLP and provides analytical solutions that reduces the hidden dimension size inside each component while minimizing the component's functional loss. This approach directly reduces model sizes, KV cache sizes, and FLOPs without introducing any runtime overheads. Through extensive experiments, we show that A3 maintains superior performance compared to SoTAs. For example, under the same reduction budget in computation and memory, our low-rank approximated LLaMA 3.1-70B achieves a perplexity of 4.69 on WikiText-2, outperforming the previous SoTA's 7.87 by 3.18. We also show versatile applications of A3 in KV cache compression, integration with quantization, fine-tuning and mixed-rank assignments. We open-sourced our framework and code at https://github.com/DeepWok/a3.