aiqbench analysis
This research introduces WaterKron, a novel framework for post-training quantization that theoretically justifies the use of Kronecker-factored Hessians via an explicit mismatch factor. By deriving rate-distortion bounds and optimizing covariance fitting through "flip-flop" updates, the method empirically outperforms standard Hessian approximations in reducing model distortion. The work advances the mathematical rigor behind efficient quantization techniques critical for deploying large language models on resource-constrained hardware.
WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessians
arXiv:2609.14706v1 Announce Type: cross Abstract: How should a Kronecker-factored Hessian approximation be chosen for post-training quantization? We address this question through WaterKron, which combines two-sided GPTQ with row- and column-dependent waterfilling scales and entropy coding. We derive its high-rate distortion with respect to the full Hessian using an explicit Kronecker-Hessian mismatch factor $\Phi$. This factor quantifies the asymptotic distortion penalty due to the Kronecker Hessian approximation and provides a criterion for selecting the factors optimally. Minimizing $\Phi$ leads to a Gaussian covariance-fitting problem with classical ``flip-flop'' updates. We thus give a rate-distortion justification for using the resulting FlipFlop Hessian in quantization. We evaluate it empirically, finding that the FlipFlop Hessian consistently improves KL divergence and perplexity over input-only, marginal, and Frobenius-based Hessian choices.
Abstract:How should a Kronecker-factored Hessian approximation be chosen for post-training quantization? We address this question through WaterKron, which combines two-sided GPTQ with row- and column-dependent waterfilling scales and entropy coding. We derive its high-rate distortion with respect to the full Hessian using an explicit Kronecker-Hessian mismatch factor $\Phi$. This factor quantifies the asymptotic distortion penalty due to the Kronecker Hessian approximation and provides a criterion for selecting the factors optimally. Minimizing $\Phi$ leads to a Gaussian covariance-fitting problem with classical ``flip-flop'' updates. We thus give a rate-distortion justification for using the resulting FlipFlop Hessian in quantization. We evaluate it empirically, finding that the FlipFlop Hessian consistently improves KL divergence and perplexity over input-only, marginal, and Frobenius-based Hessian choices.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.14706 [cs.LG]
(or arXiv:2609.14706v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.14706 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 215 words
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