mlsanityData to 7 Oct 2026

Coverage-Based Calibration for Post-Training Quantization via Weighted Set Cover over Outlier Channels

arXiv 2604.24008 ↗First posted 27 Apr 2026cs.LGcited by 0

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Abstract (arXiv)

Post-Training Quantization (PTQ) compresses large language models to low bit-widths using a small calibration set, and its quality depends strongly on which samples are chosen. We identify a failure mode in which calibration samples fail to activate outlier channels, hidden dimensions with unusually large activations, causing the quantizer to underestimate their dynamic range and producing per-channel reconstruction errors that dominate layer-wise loss. Motivated by this observation, we argue that PTQ calibration quality is governed more by weighted outlier-channel coverage than by generic sample representativeness, and formulate calibration selection as a weighted set cover problem over outlier channels. The objective is monotone submodular, and the greedy algorithm, COVERCAL, operates on pre-computed activation statistics and requires no GPU time at selection. We further show that the weight choice is internally consistent: under a stylized clipping model, missed weighted coverage upper-bounds surrogate loss, justifying the weighted coverage objective as principled rather than purely empirical. Across LLaMA-2, LLaMA-3, and Mistral, under AWQ and GPTQ backends and five downstream evaluations, COVERCAL improves over random, max-perplexity, max-activation-variance, and stratified baselines, with the largest gains at small calibration budgets. At INT4 with 128 samples, COVERCAL improves MMLU by 1.2 to 1.5 points over random calibration and reduces perplexity degradation by 15 to 30%; with 64 samples, it matches or exceeds random calibration at 256. The contribution is not a new PTQ backend but a formulation of calibration selection as weighted outlier coverage, with a simple, efficient algorithm and a surrogate-based justification.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 28 references that are in the map. First posted on arXiv 27 Apr 2026.

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19 of 28 references.

References · 19

  1. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  2. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,710
  3. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,838
  4. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,338
  5. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 598
  6. 2024SpinQuant: LLM quantization with learned rotationscited by 446
  7. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 397
  8. 2023SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compressioncited by 359
  9. 2023Data Selection for Language Models via Importance Resamplingcited by 322
  10. 2023SqueezeLLM: Dense-and-Sparse Quantizationcited by 285
  11. 2020GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learningcited by 224
  12. 2023Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothingcited by 147
7 more
  1. 2025TurboQuant: Online Vector Quantization with Near-optimal Distortion Ratecited by 116
  2. 2023On the Impact of Calibration Data in Post-training Quantization and Pruningcited by 51
  3. 2024Outliers and Calibration Sets have Diminishing Effect on Quantization of Modern LLMscited by 11
  4. 2024Self-calibration for Language Model Quantization and Pruningcited by 10
  5. 2025Preserving LLM Capabilities through Calibration Data Curation: From Analysis to Optimizationcited by 9
  6. 2026Beyond Variance: Knowledge-Aware LLM Compression via Fisher-Aligned Subspace Diagnosticscited by 4
  7. 2026Frequency Matters: Fast Model-Agnostic Data Curation for Pruning and Quantizationcited by 1

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