Optimal Post-Training Quantization Scales and Where to Find Them

Researchers introduce PiSO (Piecewise Scale Optimization), an algorithm that optimizes quantization scaling factors for compressing large language models more effectively than existing heuristic methods. By using calibration data to compute optimal channel-wise scales, PiSO demonstrates consistent improvements in model perplexity and downstream accuracy across Llama and Qwen models, with gains becoming more pronounced at lower bit-widths.

Post-training quantization remains a critical bottleneck in deploying large language models efficiently. Current industry practice relies on data-free heuristics for choosing quantization scales, a surprisingly crude approach given the complexity of modern AI systems. PiSO addresses this gap by introducing a mathematically principled approach that partitions the optimization space into intervals with closed-form solutions, enabling exact computation of optimal scales under round-to-nearest quantization.

The research builds on years of work in model compression and quantization theory, but applies optimization techniques more rigorously than predecessors. Traditional PTQ methods sacrifice precision for computational convenience, whereas PiSO maintains efficiency while improving accuracy. The algorithm's extension to group-wise quantization and integration with error correction represents pragmatic engineering alongside theoretical contribution.

For the AI infrastructure sector, this work has immediate implications. Model compression directly impacts deployment costs, inference latency, and memory requirements—factors that dominate economics in production environments. Better quantization methods reduce the performance gap between full-precision and compressed models, enabling smaller organizations to run competitive LLMs on edge devices or cheaper hardware. The consistent improvements across different architectures (Llama, Qwen) and model scales suggest broad applicability rather than narrow optimization.

The semiconductor and cloud computing industries benefit from reduced computational demands, while edge AI applications gain feasibility through better compression-accuracy tradeoffs. As models grow larger, quantization quality becomes increasingly important for accessibility. Continued improvements in PTQ methodology could accelerate AI democratization by lowering hardware barriers to entry.

• →PiSO optimizes quantization scales using calibration data with closed-form mathematical solutions, outperforming traditional data-free heuristics
• →Algorithm shows consistent perplexity and accuracy improvements across Llama and Qwen models at multiple bit-widths
• →Benefits increase as bit-width decreases, making PiSO especially valuable for extreme compression scenarios
• →Technique integrates with error correction methods and scales to group-wise quantization via principled extensions
• →Improved model compression reduces deployment costs and enables broader edge AI adoption across resource-constrained environments