  At the heart of machine learning lies the question of generalizability of
learned rules over previously unseen data. While over-parameterized models
based on neural networks are now ubiquitous in machine learning applications,
our understanding of their generalization capabilities is incomplete. This task
is made harder by the non-convexity of the underlying learning problems. We
provide a general framework to characterize the asymptotic generalization error
for single-layer neural networks (i.e., generalized linear models) with
arbitrary non-linearities, making it applicable to regression as well as
classification problems. This framework enables analyzing the effect of (i)
over-parameterization and non-linearity during modeling; and (ii) choices of
loss function, initialization, and regularizer during learning. Our model also
captures mismatch between training and test distributions. As examples, we
analyze a few special cases, namely linear regression and logistic regression.
We are also able to rigorously and analytically explain the \emph{double
descent} phenomenon in generalized linear models.
