Revisiting Error Feedback for Model Quantization

Abstract:We study causal error-feedback coefficients as design variables for model quantization. Modeling instantaneous quantization errors as independent, zero-mean variables with a common fixed variance, we formulated a metric-dependent trace problem for designing feedback coefficients. The formulation resembles fixed-order GPTQ/LDLQ feedback and supports Jacobian-aware designs that account for downstream error propagation. For a positive-definite metric $\boldsymbol{H}$, we prove that the joint rotation-feedback trace minimum is $n\det(\boldsymbol{H})^{1/n}$ and present an attaining pair using the geometric mean decomposition. Experiments on synthetic networks, trained MLPs, and language models show benefits from downstream-sensitive feedback, but also reveal that trace optimality need not improve finite-level performance. Small QAT experiments further illustrate direct loss-driven feedback tuning with fixed or trainable network weights.

Machine Learning (cs.LG); Signal Processing (eess.SP)

arXiv:2610.18139 [cs.LG]

(or arXiv:2610.18139v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.18139 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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