Post-Training Quantization Methods

Updated 2 February 2026

Post-training quantization methods are techniques that reduce high-precision model weights to lower-precision formats using calibration data to preserve performance.
Calibration sets, composed of diverse and representative language samples, are crucial for estimating activation statistics and ensuring robust multilingual outcomes.
Modern algorithms such as GPTQ, AWQ, and SparseGPT leverage these sets to minimize perplexity and maintain accuracy across various languages and tasks.

Post-training quantization methods encompass a suite of techniques applied after the initial training of LLMs to reduce their memory and compute footprint without revisiting full-scale gradient-based learning. These strategies critically depend on small calibration sets—collections of unlabeled or lightly labeled text used to estimate and minimize quantization or pruning-induced degradation—in order to tune model parameters (e.g., activation ranges, quantization scales, or parameter importance rankings). The choice of calibration data, particularly its linguistic and domain makeup, is pivotal for robust performance in multilingual and cross-lingual settings. Recent research has mapped the impact of calibration set composition on quantization, pruning, confidence calibration, and downstream evaluation across dozens of languages and multiple model architectures.

1. Role of Calibration Sets in Post-Training Quantization

Post-training quantization (PTQ) compresses model weights (typically from 16- or 32-bit floats to lower-precision fixed-point representations such as 4- or 8-bit integers) to accelerate inference and reduce storage. Calibration sets are integral to PTQ pipelines—state-of-the-art methods (e.g., GPTQ, AWQ, SparseGPT, Wanda) leverage a small collection of input sequences to capture activation statistics or estimate the sensitivity of outputs to weight perturbations. The calibration process adjusts quantizer parameters (scale, zero-point; Hessian or activation-aware corrections) so as to minimize critical metrics (e.g., perplexity or task accuracy) on these held-out examples and to maximize robustness to quantization or pruning artifacts.

For multilingual LLMs, traditional practice of calibrating exclusively on English is non-optimal. It induces uneven performance and increased perplexity for non-English, low-resource, or typologically distinct languages, since the calibration set shapes not only quantization boundaries but also the model’s functional coverage of different lexical, orthographic, and syntactic phenomena (Zeng et al., 2024, Chimoto et al., 26 Jan 2026).

2. Construction and Composition of Multilingual Calibration Sets

Calibration set construction for post-training quantization in multilingual LLMs must carefully consider several axes:

Language composition: Early work defaulted to English-only calibration. However, experiments systematically substituting or augmenting calibration sets with other major world languages (French, Swahili, Chinese, isiXhosa, etc.) or balanced multilingual blends (e.g., “multi10”—ten equally represented languages) reveal pronounced improvements in average and per-language perplexity (Chimoto et al., 26 Jan 2026).
Size: A token budget of ~1M tokens (e.g., 128 examples × 8K tokens or ~1K examples × 1K tokens) is conventional and yields diminishing returns beyond this size (Kurz et al., 2024).
Sampling: Multilingual Brain Surgeon (MBS) samples calibration segments with probabilities proportional to the model’s original training language mix, closely approximating the full-data Hessian and preserving diverse language capabilities post-quantization or pruning (Zeng et al., 2024).
Diversity: Calibration sets drawn from multiple scripts, rare tokens, and varied morphosyntactic families enhance activation coverage and extend activation tails, reducing quantization error across languages and modalities (Chimoto et al., 26 Jan 2026).

Table: Calibration Set Variants and Language Coverage (Chimoto et al., 26 Jan 2026)

Variant	Description	Best use-case
English	English-only segments	English-dominant tasks
Single-Lang	Other monolingual sets (fr, sw, zh, xh, ...)	Per-lang maximization
multi10	10 language-uniform mix	Broad multilingual PTQ
multi	Uniform over all available languages (e.g., 112)	Extreme language diversity

Multilingual calibration sets not only reduce average perplexity by up to 3.5 points vs. English-only baselines, but also smooth model performance across languages, especially in low-resource or non-Latin-script domains (Chimoto et al., 26 Jan 2026, Zeng et al., 2024, Kurz et al., 2024).

3. Quantization and Pruning Algorithms Leveraging Calibration Sets

State-of-the-art PTQ algorithms use calibration sets in algorithmically distinct ways:

GPTQ uses inverse-Hessian-based quantization error minimization; the Hessian is estimated from calibration data. Linguistic coverage and vocabulary diversity in the calibration set significantly affect model stability, especially in languages with divergent morphologies (Chimoto et al., 26 Jan 2026).
AWQ utilizes activation-aware scaling and channel selection; activation ranges computed on calibration examples define per-channel quantization scales. Multilingual or mixed calibration sets yield broader activation range coverage, preventing underflow or overflow when quantizing rare patterns (Chimoto et al., 26 Jan 2026).
SparseGPT and Wanda for pruning: Calibration examples are used to rank model weights or neurons by their contribution to the loss, enabling magnitude or first-order Taylor pruning. Language-matched calibration sets ensure that pruning preserves language-specific features and minimizes perplexity degradation for the evaluation language (Kurz et al., 2024).
MBS (Multilingual Brain Surgeon) calibrates with segment allocations formed in proportion to pretraining language shares, improving both low-resource language perplexity and zero-shot downstream accuracy post-pruning or quantization (Zeng et al., 2024).

Empirical results demonstrate that calibrating on monolingual sets optimizes perplexity in that language, whereas multilingual or mixed sets balance robustness and overall quality.

4. Empirical Evaluation: Perplexity, Activation Analysis, and Failure Modes

Evaluation of quantized and/or pruned models is typically performed using:

Perplexity (PPL): The primary metric for language modeling fit. Lower perplexity after PTQ/pruning on validation sets in multiple languages indicates higher fidelity to the original model (Chimoto et al., 26 Jan 2026, Zeng et al., 2024).
Downstream zero-shot accuracy: XNLI, XStoryCloze, GlobalMMLU, and other cross-lingual benchmarks quantify transfer to downstream tasks, with accuracy inversely correlated to PPL (Spearman ρ < 0) (Chimoto et al., 26 Jan 2026).
Activation statistics: Violin plots and channel/activation heatmaps from calibration examples reveal the extent to which different calibration sets capture the distribution of pre-quantization activations encountered at inference. Multilingual sets cover longer tails and more extreme activations, mitigating under-representation and clipping (Chimoto et al., 26 Jan 2026).
Failure diagnosis: Calibrating only on Swahili (under GPTQ) or French (AWQ) limits the activation magnitude coverage, leading to increased quantization error when activations at test time exceed those observed in calibration. Hessian distances between languages also highlight the necessity of coverage for second-order quantization (Chimoto et al., 26 Jan 2026).

5. Language Typology, Model Robustness, and Best Practices

Analyses uniformly show that English-only calibration leads to systematic underperformance in minoritized and distant languages. The practical guidelines emerging from these studies are:

For known deployment languages: Calibrate on target-language data (or a typologically close language) for maximal per-language performance.
For general-purpose or unknown deployment: Use a linguistically balanced multilingual set (e.g., multi10), capturing all major scripts, token types, and family-level diversity (Chimoto et al., 26 Jan 2026).
Proportional allocation: Match calibration sample shares to pretraining language proportions (the MBS protocol), avoiding irreversible degradation for underrepresented tongues (Zeng et al., 2024).
Minimal set coverage: Always include at least one calibration segment per language to avoid catastrophic loss of capability.
Activation range and rare-token coverage: Ensure the calibration set covers outlier tokens and multi-script examples to reduce activation clipping in the quantized model.
Diagnostics: Monitor activation range, Hessian statistics, and per-language perplexities to confirm calibration quality and detect edge-case failures.

6. Recent Advances and Future Directions

PTQ research continues to refine both calibration set design and quantization algorithms:

Adaptive binning: Stratification of calibration data by language, script, or token rarity to better approximate inference-time distribution (Huang et al., 4 Jan 2026).
Integration with confidence calibration: Alignment of calibration sets for quantization and downstream confidence estimation to achieve both accurate and reliable predictions in multilingual evaluations (Zhou et al., 3 Oct 2025).
Compression-aware calibration scripts: Automated pipelines (e.g., from SGM or MBS datasets) to generate language-balanced calibration splits matching user’s deployment distribution (Bhutani et al., 2024, Zeng et al., 2024).
Safety and fairness extensions: Use of socio-culturally representative calibration/evaluation sets to mitigate stereotyping or disparate impacts in model quantization and subsequent application (Bhutani et al., 2024).

Failure to tailor calibration sets for multilingual PTQ is consistently shown to result in systematic performance disparities, with low-resource or typologically distant languages harmed most. Balanced or proportional multilingual calibration strategies—often achievable with a modest token budget—deliver substantial improvements in robustness, language inclusivity, and equity across the compressed model landscape (Chimoto et al., 26 Jan 2026, Zeng et al., 2024).