Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917195864342528 |
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| author | Shihab, Ibne Farabi Akter, Sanjeda Sharma, Anuj |
| author_facet | Shihab, Ibne Farabi Akter, Sanjeda Sharma, Anuj |
| contents | 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 (\r{ho}) 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 \r{ho} serves as a fundamental signal of stored knowledge, with high-\r{ho} layers emerging only when models internalize factual associations during training. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics Shihab, Ibne Farabi Akter, Sanjeda Sharma, Anuj Machine Learning Artificial Intelligence 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 (\r{ho}) 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 \r{ho} serves as a fundamental signal of stored knowledge, with high-\r{ho} layers emerging only when models internalize factual associations during training. |
| title | Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnostics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2601.07197 |