  To understand better good generalization performance in state-of-the-art
neural network (NN) models, and in particular the success of the ALPHAHAT
metric based on Heavy-Tailed Self-Regularization (HT-SR) theory, we analyze of
a corpus of models that was made publicly-available for a contest to predict
the generalization accuracy of NNs. These models include a wide range of
qualities and were trained with a range of architectures and regularization
hyperparameters. We break ALPHAHAT into its two subcomponent metrics: a
scale-based metric; and a shape-based metric. We identify what amounts to a
Simpson's paradox: where "scale" metrics (from traditional statistical learning
theory) perform well in aggregate, but can perform poorly on subpartitions of
the data of a given depth, when regularization hyperparameters are varied; and
where "shape" metrics (from HT-SR theory) perform well on each subpartition of
the data, when hyperparameters are varied for models of a given depth, but can
perform poorly overall when models with varying depths are aggregated. Our
results highlight the subtlety of comparing models when both architectures and
hyperparameters are varied; the complementary role of implicit scale versus
implicit shape parameters in understanding NN model quality; and the need to go
beyond one-size-fits-all metrics based on upper bounds from generalization
theory to describe the performance of NN models. Our results also clarify
further why the ALPHAHAT metric from HT-SR theory works so well at predicting
generalization across a broad range of CV and NLP models.
