We consider an underdetermined noisy linear regression model where the minimum-norm interpolating predictor is known to be consistent, and ask: can uniform convergence in a norm ball, or at least (following Nagarajan and Kolter) the subset of a norm ball that the algorithm selects on a typical input set, explain this success? We show that uniformly bounding the difference between empirical and population errors cannot show any learning in the norm ball, and cannot show consistency for any set, even one depending on the exact algorithm and distribution. But we argue we can explain the consistency of the minimal-norm interpolator with a slightly weaker, yet standard, notion: uniform convergence of zero-error predictors in a norm ball. We use this to bound the generalization error of low- (but not minimal-) norm interpolating predictors.

翻译：我们认为,一个不下定的噪音线性回归模型是已知最低北向内插预测器一致的,我们问:在标准球中,或者至少(在纳加拉詹和科尔特之后)算法在典型输入集中选择的规范球子集中,能够统一趋同,解释这一成功吗?我们表明,将经验错误和人口错误的区别统一地捆绑在标准球中不能显示任何经验错误和人口错误之间的任何学习,也不能显示任何组合的一致性,即使是取决于精确的算法和分布的组合。但我们认为,我们可以解释最小北向内插器与一个稍弱但标准的概念的一致性:规范球中零危险预测器的统一趋同。我们用这个来约束低(但非最低)规范内插预测器的普遍错误。