# Predicting LLM Compression Degradation from Spectral Statistics

arXiv: https://arxiv.org/abs/2604.18085 · HTML: https://mlsanity.com/paper/2604.18085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 23 of 23)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [How much do language models memorize?](https://mlsanity.com/paper/2505.24832/) (2025)
- [From Entropy to Epiplexity: Rethinking Information for Computationally Bounded Intelligence](https://mlsanity.com/paper/2601.03220/) (2026)
- [Densing Law of LLMs](https://mlsanity.com/paper/2412.04315/) (2024)
- [To Compress or Not? Pushing the Frontier of Lossless GenAI Model Weights Compression with Exponent Concentration](https://mlsanity.com/paper/2510.02676/) (2025)
- [Lossless Compression of Neural Network Components: Weights, Checkpoints, and K/V Caches in Low-Precision Formats](https://mlsanity.com/paper/2508.19263/) (2025)

## Abstract (arXiv)

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 · barρs, 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 · barρs from weights, estimate degradation, and invest compute only in desirable configurations.