Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data

In many applications, one works with deep neural network (DNN) models trained by someone else. For such pretrained models, one typically does not have access to training/test data. Moreover, one does not know many details about the model, such as the specifics of the training data, the loss function, the hyperparameter values, etc. Given one or many pretrained models, can one say anything about the expected performance or quality of the models? Here, we present and evaluate empirical quality metrics for pretrained DNN models at scale. Using the open-source WeightWatcher tool, we analyze hundreds of publicly-available pretrained models, including older and current state-of-the-art models in CV and NLP. We examine norm-based capacity control metrics as well as newer Power Law (PL) based metrics (including fitted PL exponents and a Weighted Alpha metric), from the recently-developed Theory of Heavy-Tailed Self Regularization. Norm-based metrics correlate well with reported test accuracies for well-trained models across nearly all CV architecture series. On the other hand, norm-based metrics can not distinguish "good-versus-bad" models---which, arguably is the point of needing quality metrics. Indeed, they may give spurious results. PL-based metrics do much better---quantitatively better at discriminating series of "good-better-best" models, and qualitatively better at discriminating "good-versus-bad" models. PL-based metrics can also be used to characterize fine-scale properties of models, and we introduce the layer-wise Correlation Flow as new quality assessment. We show how poorly-trained (and/or poorly fine-tuned) models may exhibit both Scale Collapse and unusually large PL exponents, in particular for recent NLP models. Our techniques can be used to identify when a pretrained DNN has problems that can not be detected simply by examining training/test accuracies.