@inproceedings{shihab-etal-2026-beyond,
title = "Beyond Variance: Knowledge-Aware {LLM} Compression via Fisher-Aligned Subspace Diagnostics",
author = "Shihab, Ibne Farabi and
Akter, Sanjeda and
Sharma, Anuj",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.2214/",
pages = "47938--47954",
ISBN = "979-8-89176-390-6",
abstract = "Post-training activation compression is essential for deploying Large Language Models (LLMs) on resource-constrained hardware. However, standard methods like Singular Value Decomposition (SVD) are gradient-blind: they preserve high-variance dimensions regardless of their impact on factual knowledge preservation. We introduce Fisher-Aligned Subspace Compression (FASC), a knowledge-aware compression framework that selects subspaces by directly modeling activation-gradient coupling, minimizing a second-order surrogate of the loss function. FASC leverages the Fisher Information Matrix to identify dimensions critical for factual knowledge, which often reside in low-variance but high-gradient-sensitivity subspaces. We propose the Dependence Violation Score ({\ensuremath{\rho}}) as a general-purpose diagnostic metric that quantifies activation-gradient coupling, revealing where factual knowledge is stored within transformer architectures. Extensive experiments on Mistral-7B and Llama-3-8B demonstrate that FASC preserves 6{--}8{\%} more accuracy on knowledge-intensive benchmarks (MMLU, LAMA) compared to variance-based methods at 50{\%} rank reduction, effectively enabling a 7B model to match the factual recall of a 13B uncompressed model. Our analysis reveals that {\ensuremath{\rho}} serves as a fundamental signal of stored knowledge, with high-{\ensuremath{\rho}} layers emerging only when models internalize factual associations during training"
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<abstract>Post-training activation compression is essential for deploying Large Language Models (LLMs) on resource-constrained hardware. However, standard methods like Singular Value Decomposition (SVD) are gradient-blind: they preserve high-variance dimensions regardless of their impact on factual knowledge preservation. We introduce Fisher-Aligned Subspace Compression (FASC), a knowledge-aware compression framework that selects subspaces by directly modeling activation-gradient coupling, minimizing a second-order surrogate of the loss function. FASC leverages the Fisher Information Matrix to identify dimensions critical for factual knowledge, which often reside in low-variance but high-gradient-sensitivity subspaces. We propose the Dependence Violation Score (\ensuremathρ) as a general-purpose diagnostic metric that quantifies activation-gradient coupling, revealing where factual knowledge is stored within transformer architectures. Extensive experiments on Mistral-7B and Llama-3-8B demonstrate that FASC preserves 6–8% more accuracy on knowledge-intensive benchmarks (MMLU, LAMA) compared to variance-based methods at 50% rank reduction, effectively enabling a 7B model to match the factual recall of a 13B uncompressed model. Our analysis reveals that \ensuremathρ serves as a fundamental signal of stored knowledge, with high-\ensuremathρ layers emerging only when models internalize factual associations during training</abstract>
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%0 Conference Proceedings
%T Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics
%A Shihab, Ibne Farabi
%A Akter, Sanjeda
%A Sharma, Anuj
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F shihab-etal-2026-beyond
%X Post-training activation compression is essential for deploying Large Language Models (LLMs) on resource-constrained hardware. However, standard methods like Singular Value Decomposition (SVD) are gradient-blind: they preserve high-variance dimensions regardless of their impact on factual knowledge preservation. We introduce Fisher-Aligned Subspace Compression (FASC), a knowledge-aware compression framework that selects subspaces by directly modeling activation-gradient coupling, minimizing a second-order surrogate of the loss function. FASC leverages the Fisher Information Matrix to identify dimensions critical for factual knowledge, which often reside in low-variance but high-gradient-sensitivity subspaces. We propose the Dependence Violation Score (\ensuremathρ) as a general-purpose diagnostic metric that quantifies activation-gradient coupling, revealing where factual knowledge is stored within transformer architectures. Extensive experiments on Mistral-7B and Llama-3-8B demonstrate that FASC preserves 6–8% more accuracy on knowledge-intensive benchmarks (MMLU, LAMA) compared to variance-based methods at 50% rank reduction, effectively enabling a 7B model to match the factual recall of a 13B uncompressed model. Our analysis reveals that \ensuremathρ serves as a fundamental signal of stored knowledge, with high-\ensuremathρ layers emerging only when models internalize factual associations during training
%U https://aclanthology.org/2026.acl-long.2214/
%P 47938-47954
Markdown (Informal)
[Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics](https://aclanthology.org/2026.acl-long.2214/) (Shihab et al., ACL 2026)
ACL