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More recently, an efficient Muon optimizer is designed for matrix parameters of large-scale models, and shows markedly faster convergence than the vector-wise algorithms. Although some works have begun to study convergence properties (i.e., optimization error) of the Muon optimizer, its generalization properties (i.e., generalization error) is still not established. Thus, in this paper, we study generalization error of the Muon optimizer based on algorithmic stability and mathematical induction, and prove that the Muon has a generalization error of $O\\big(\\frac{1}{N\\kappa^{T}}\\big)$, where $N$ is training sample size, and $T$ denotes iteration number, and $\\kappa>0$ denotes minimum difference between singular values of gradient estimate. 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Thus, in this paper, we study generalization error of the Muon optimizer based on algorithmic stability and mathematical induction, and prove that the Muon has a generalization error of $O\\big(\\frac{1}{N\\kappa^{T}}\\big)$, where $N$ is training sample size, and $T$ denotes iteration number, and $\\kappa>0$ denotes minimum difference between singular values of gradient estimate. 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