A universal theorem on learning curves

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Deep Learning Scaling is Predictable, Empirically (2017, methodology): “Using statistical mechanics approaches, Amari et al. (1992) and Amari (1993) show that as sample complexity grows, generalization error should decline as a power-law ε ( m ) ∼ αm β g with β g = − 0 .”
Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies (2008, background): “, the property of the learning curve [84], [85].”
Four Types of Learning Curves (1992, background): “See also Amari (1992) for the deterministic case.]”
Natural Gradient Works Efficiently in Learning (1998, result): “The results can be stated in terms of the generalization error instead of the covariance of the estimator, and we can obtain more universal results (see Amari, 1993; Amari & Murata, 1993).”
Asymptotic statistical theory of overtraining and cross-validation (1997, background): “A similar but different universal property is proved by Amari [2] for deterministic dichotomy machines.”
Natural Gradient Works Eciently in Learning (result): “The results can be stated in terms of the generalization error instead of the covariance of the estimator, and we can obtain more universal results (see Amari, 1993; Amari and Murata, 1993).”
Why Is My Classifier Discriminatory? (2018, result): “This observation is also supported by theoretical results (Amari, 1993).”