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Saturation Makes Quantization Error Additive: A Coverage Model with a Certificate

arXiv 2607.12266 ↗First posted 14 Jul 2026cs.LGcited by 0

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Abstract (arXiv)

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2% of pairs. We propose the coverage model f(S)=cbigl(1-prodi∈ S(1-ai)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 57 references that are in the map. First posted on arXiv 14 Jul 2026.

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References · 28

  1. 2017Axiomatic Attribution for Deep Networkscited by 3,384
  2. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  3. 2023AWQ: Activation-aware Weight Quantization for LLM Compression and Accelerationcited by 1,298
  4. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 634
  5. 2021BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstructioncited by 479
  6. 2024SpinQuant: LLM quantization with learned rotationscited by 471
  7. 2019HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precisioncited by 402
  8. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 378
  9. 2019HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networkscited by 261
  10. 2023The Hydra Effect: Emergent Self-repair in Language Model Computationscited by 156
  11. 2020Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regressioncited by 154
  12. 2018Bayesian Optimization of Combinatorial Structurescited by 64
16 more
  1. 2022The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networkscited by 41
  2. 2024Mixture Compressor for Mixture-of-Experts LLMs Gains Morecited by 41
  3. 2025Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantizationcited by 41
  4. 2021Defining and Quantifying the Emergence of Sparse Concepts in DNNscited by 36
  5. 2025GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidancecited by 32
  6. 2025AMQ: Enabling AutoML for Mixed-precision Weight-Only Quantization of Large Language Modelscited by 14
  7. 2025SPEX: Scaling Feature Interaction Explanations for LLMscited by 12
  8. 2025Identifying Sensitive Weights via Post-quantization Integralcited by 11
  9. 2020Shapley Value as Principled Metric for Structured Network Pruningcited by 9
  10. 2025FGMP: Fine-Grained Mixed-Precision Weight and Activation Quantization for Hardware-Accelerated LLM Inferencecited by 9
  11. 2026Fine-Grained Post-Training Quantization for Large Vision Language Models with Quantization-Aware Integrated Gradientscited by 8
  12. 2023Mixed-Precision Quantization for Deep Vision Models with Integer Quadratic Programmingcited by 7
  13. 2026AutoQRA: Joint Optimization of Mixed-Precision Quantization and Low-rank Adapters for Efficient LLM Fine-Tuningcited by 5
  14. 2026Pruning as a Cooperative Game: Surrogate-Assisted Layer Contribution Estimation for Large Language Modelscited by 3
  15. 2026ScaleBITS: Scalable Bitwidth Search for Hardware-Aligned Mixed-Precision LLMscited by 3
  16. 2025MiCo: End-to-End Mixed Precision Neural Network Co-Exploration Framework for Edge AIcited by 2

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  1. 2026MixQuant: Adaptive Mixed-Precision Quantization for Large Language Models
  2. 2026Beyond Outliers: A Data-Free Layer-wise Mixed-Precision Quantization Approach Driven by Numerical and Structural Dual-Sensitivity
  3. 2026Coverage-Based Calibration for Post-Training Quantization via Weighted Set Cover over Outlier Channels
  4. 2026Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization
  5. 2026Predicting Quantization Price for Selecting PTQ Configurations Before Deployment
  6. 2026Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape
  7. 2022Mixed-Precision Inference Quantization: Radically Towards Faster inference speed, Lower Storage requirement, and Lower Loss
  8. 2023EMQ: Evolving Training-free Proxies for Automated Mixed Precision Quantization