Predicting LLM Compression Degradation from Spectral Statistics
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910148534992896 |
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| author | Xu, Mingxue |
| author_facet | Xu, Mingxue |
| contents | Matrix-level low-rank compression is a promising way to reduce the cost of large language models, but running compression and evaluating the resulting models on language tasks can be prohibitively expensive. Can compression-induced degradation be predicted before committing to this compute? We systematically analyze the Qwen3 and Gemma3 model families across four representative low-rank compression methods: vanilla SVD, two ASVD variants, and SVD-LLM. We find that stable rank and information density, measured in bits per parameter, dominate performance degradation. The interaction term $γ\cdot \barρ_s$, defined as compression ratio times stable rank, is a robust predictor of accuracy degradation, achieving leave-one-out cross-validation Pearson correlations of $0.890$ for attention layers and $0.839$ for MLP layers. We provide theoretical intuition for why this predictor succeeds by connecting it to standard SVD truncation bounds and error composition mechanisms in transformer layers. These findings enable a predict-then-compress workflow: compute $γ\cdot \barρ_s$ from weights, estimate degradation, and invest compute only in desirable configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18085 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Predicting LLM Compression Degradation from Spectral Statistics Xu, Mingxue Machine Learning Matrix-level low-rank compression is a promising way to reduce the cost of large language models, but running compression and evaluating the resulting models on language tasks can be prohibitively expensive. Can compression-induced degradation be predicted before committing to this compute? We systematically analyze the Qwen3 and Gemma3 model families across four representative low-rank compression methods: vanilla SVD, two ASVD variants, and SVD-LLM. We find that stable rank and information density, measured in bits per parameter, dominate performance degradation. The interaction term $γ\cdot \barρ_s$, defined as compression ratio times stable rank, is a robust predictor of accuracy degradation, achieving leave-one-out cross-validation Pearson correlations of $0.890$ for attention layers and $0.839$ for MLP layers. We provide theoretical intuition for why this predictor succeeds by connecting it to standard SVD truncation bounds and error composition mechanisms in transformer layers. These findings enable a predict-then-compress workflow: compute $γ\cdot \barρ_s$ from weights, estimate degradation, and invest compute only in desirable configurations. |
| title | Predicting LLM Compression Degradation from Spectral Statistics |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.18085 |