How Far Can Sharpness and Complexity Jointly Explain Generalization?

Large-scale empirical studies have revealed that many widely used generalization measures correlate only weakly with generalization, suggesting that relying on a single factor is insufficient to explain it. In this work, we examine sharpness and complexity jointly, placing the reach of the two-factor view at the center: how far can they jointly explain generalization, what determines when they succeed, and where do they fall short? We investigate these questions quantitatively, using sixteen alternative metric pairs as probes and Pareto analysis and linear regression as diagnostic tools. Our results show that suitably defined $(S,C)$ pairs provide strong explanatory power across a range of settings. The sharpness perturbation scale substantially affects this success, and the complexity representation influences its robustness. Remaining failures leave open whether more refined measurements are adequate or additional factors are needed.