Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos

Researchers provide the first rigorous theoretical analysis of OPTQ (GPTQ), a widely-used post-training quantization algorithm for neural networks and LLMs, establishing quantitative error bounds and validating practical design choices. The study extends theoretical guarantees to both deterministic and stochastic variants of OPTQ and the Qronos algorithm, offering guidance for regularization parameter selection and quantization alphabet sizing.

Post-training quantization has become essential for deploying large language models efficiently, reducing memory and computational requirements without retraining. OPTQ/GPTQ dominates this space due to strong empirical results, yet it operated without formal theoretical foundations. This research bridges that gap by deriving the first quantitative error bounds for OPTQ's iterative quantization procedure, establishing non-asymptotic 2-norm bounds that explicitly depend on calibration data and regularization parameters.

The theoretical analysis validates several heuristics engineers have used intuitively, such as ordering features by decreasing norm, providing mathematical justification for decisions made in production systems. The stochastic variant analysis yields stronger infinity-norm bounds, enabling practitioners to control quantization alphabets—the discrete values used in compressed models—and better understand error propagation through downstream layers and nonlinearities. This is particularly valuable for maintaining accuracy in neural network chains where errors compound.

For the AI infrastructure ecosystem, this work accelerates adoption of quantized models by reducing deployment uncertainty. Engineers can now make informed decisions about regularization parameters and quantization strategies backed by mathematical guarantees rather than pure empiricism. The extension to Qronos, a newer state-of-the-art PTQ algorithm, explains why it outperforms alternatives and guides future algorithm development. As LLM deployment costs drive industry economics, theoretical validation of quantization methods directly impacts profitability and accessibility of AI services across enterprises.

• →First quantitative error bounds for OPTQ/GPTQ algorithm provide mathematical foundation for a widely-deployed model compression technique.
• →Stochastic variant analysis enables control over quantization alphabets and error propagation through neural network layers.
• →Theoretical validation justifies practical heuristics like feature ordering by norm, reducing deployment guesswork.
• →Extended analysis of Qronos algorithm explains empirical advantages and guides next-generation quantization research.
• →Results directly support more efficient LLM deployment by reducing memory costs while maintaining predictable accuracy loss.