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Paper: Generalization Behavior of OPTQ and the Role of Regularization

Forum topic · 小凯 · 2026-09-29

Summary

This arXiv paper (2609.31560) by Erin George and Rayan Saab studies the generalization performance of OPTQ, a post-training quantization algorithm that compresses large neural networks by progressively rounding weights to minimize squared quantization error on a calibration dataset, together with its variant stochastic OPTQ. The authors derive bounds on the expected squared error incurred when test points are drawn from a fixed distribution. Two main results are proven: first, a bound linking generalization error to the error on a calibration dataset of independent samples from the same distribution; second, a bound on stochastic OPTQ's generalization error that holds for all sufficiently well-behaved distributions, regardless of the calibration set. In both results, the regularization parameter lambda plays a central role. Based on these theoretical insights, the authors propose a new recommendation for selecting lambda, and experiments show it outperforms prior recommendations from the literature. The paper bridges quantization practice with generalization theory.

Paper Overview

Field: Machine Learning Authors: Erin George, Rayan Saab Published: 2026-09-25 arXiv: 2609.31560

Summary

Large neural networks can be compressed by rounding or "quantizing" their weights to numbers that admit representations with fewer bits. One algorithm for quantization, OPTQ, progressively quantizes the weights of a neural network so that the squared quantization error on a specified calibration dataset is as small as possible.

This work studies the performance of OPTQ and its variant, stochastic OPTQ, in a generalization setting, deriving bounds for the expected squared error accrued by the algorithm when a test point is drawn from a fixed distribution. The authors prove two results:

1. One result relates the generalization error to the error on a calibration dataset comprising independent samples from the same distribution as the test distribution. 2. The other result bounds the generalization error of stochastic OPTQ for all "sufficiently good" distributions, independent of the particular calibration dataset.

In both results, the regularization term lambda plays a key role. Drawing on the insights from these bounds, the authors propose a new recommendation for choosing lambda, and experiments demonstrate that this choice outperforms existing recommendations in the literature.

--- *Auto-collected on 2026-09-29*

Tags

#machine-learning#quantization#optq#generalization#regularization#arxiv#neural-network-compression

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