Rethinking generalization of classifiers in separable classes scenarios and over-parameterized regimes
This addresses the generalization puzzle in machine learning, particularly for over-parameterized neural networks, but is incremental as it builds on existing theory.
The paper investigates why classifiers generalize well in separable classes or over-parameterized regimes, showing that the proportion of poor global minima decreases exponentially with more training data and proposing a model for true error distribution that matches experimental results on MNIST and CIFAR-10.
We investigate the learning dynamics of classifiers in scenarios where classes are separable or classifiers are over-parameterized. In both cases, Empirical Risk Minimization (ERM) results in zero training error. However, there are many global minima with a training error of zero, some of which generalize well and some of which do not. We show that in separable classes scenarios the proportion of "bad" global minima diminishes exponentially with the number of training data n. Our analysis provides bounds and learning curves dependent solely on the density distribution of the true error for the given classifier function set, irrespective of the set's size or complexity (e.g., number of parameters). This observation may shed light on the unexpectedly good generalization of over-parameterized Neural Networks. For the over-parameterized scenario, we propose a model for the density distribution of the true error, yielding learning curves that align with experiments on MNIST and CIFAR-10.