# Activation- and Influence-Aware Ranks (AIR): Function-Preserving SVD Compression for LLMs

arXiv: https://arxiv.org/abs/2606.19993 · HTML: https://mlsanity.com/paper/2606.19993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
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- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [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)
- [AttnLRP: Attention-Aware Layer-Wise Relevance Propagation for Transformers](https://mlsanity.com/paper/2402.05602/) (2024)
- [Pruning by Explaining: A Novel Criterion for Deep Neural Network Pruning](https://mlsanity.com/paper/1912.08881/) (2019)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [ECQx: Explainability-Driven Quantization for Low-Bit and Sparse DNNs](https://mlsanity.com/paper/2109.04236/) (2021)
- [Pruning By Explaining Revisited: Optimizing Attribution Methods to Prune CNNs and Transformers](https://mlsanity.com/paper/2408.12568/) (2024)
- [An Overview of Low-Rank Structures in the Training and Adaptation of Large Models](https://mlsanity.com/paper/2503.19859/) (2025)
- [Generalized Fisher-Weighted SVD: Scalable Kronecker-Factored Fisher Approximation for Compressing Large Language Models](https://mlsanity.com/paper/2505.17974/) (2025)
- [Evaluating the Impact of Compression Techniques on Task-Specific Performance of Large Language Models](https://mlsanity.com/paper/2409.11233/) (2024)
- [Choose Your Model Size: Any Compression of Large Language Models Without Re-Computation](https://mlsanity.com/paper/2502.01717/) (2025)

## Abstract (arXiv)

We present Activation- and Influence-Aware Ranks (AIR), an SVD-based LLM compression framework that guides each weight matrix's low-rank approximation with a backward-signal influence metric. Starting from the activation-aware optimum of SVD-LLM(W), AIR runs a single closed-form alternating least squares (ALS) sweep that integrates influence element-wise under a monotone-descent guarantee. AIR is layer-local and composes orthogonally with end-to-end methods: alone it exceeds ACIP, and AIR+LoRA outperforms it further. AIR improves perplexity over SVD-LLM(W) by >18% at <=60% parameter retention, matches its quality with ~90% less calibration data, and turns parameter savings into FLOP, peak-memory, and per-token latency gains.