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

NeurIPS 2026 · Architectures and efficiency › Quantization · approach: Post-training quantization of LLMs

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Frames LLM PTQ calibration-sample selection as weighted set cover over outlier channels and proposes CoverCal, a greedy submodular selector evaluated with AWQ and GPTQ INT4 on LLaMA-2/3 and Mistral.

Problem

Calibration sample selection for weight-only LLM post-training quantization is under-specified; random calibration may fail to activate outlier channels, leading to clipping error that dominates layer-wise reconstruction loss.

Approach

Cast calibration selection as maximizing weighted coverage of outlier channels (weights from squared normalized magnitude times weight-column norm), which is monotone submodular, so greedy selection gives a (1-1/e) guarantee; a stylized clipping surrogate justifies the weight choice.

Key results

• On LLaMA-3-8B with AWQ INT4 at 128 samples, CoverCal reaches 64.6 MMLU vs 63.1 for random (FP16 65.3).
• CoverCal at 64 samples (64.0 MMLU) exceeds random calibration at 256 samples (63.8) on LLaMA-3-8B with AWQ.
• CoverCal covers 26.9% of outlier channels vs 16.8% for random at K=128.

Surprising findings

• Max-ActVar, a plausible heuristic, covers fewer outlier channels than random sampling at K=128 due to redundancy in its selections.
• On Mistral-7B with GPTQ at K=256 the MMLU gap to random narrows to 0.4 points.

Limitations

• Outlier threshold mu+6sigma is heuristic; results evaluated only at INT4, not lower bit-widths.
• Surrogate consistency result rests on stylized assumptions (M1)-(M2) and does not bound the Frobenius loss or downstream accuracy.
• Coverage depends on the candidate pool; narrow-domain pools may lack samples activating certain outlier channels.

Experimental setup

Datasets: RedPajama C4 WikiText-2

Benchmarks: MMLU ARC-Challenge HellaSwag WinoGrande WikiText-2

Metrics: accuracy perplexity channel coverage weighted coverage Frobenius reconstruction error

Baselines: Random Max-PPL Max-ActVar Stratified

Builds on: AWQ GPTQ SmoothQuant

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