Activation- and Influence-Aware Ranks (AIR): Function-Preserving SVD Compression for LLMs
cs.LG
Submitted: 2026-06-18
Updated: 2026-09-08
Comments: Accepted at the ICML 2026 Workshop on Resource-Adaptive Foundation Model Inference (AdaptFM), Seoul, South Korea (non-archival)
Code: https://github.com/NicodeHarder/air
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
Abstract
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.
Sources
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