  For supervised learning models, the analysis of generalization ability
(generalizability) is vital because the generalizability expresses how well a
model will perform on unseen data. Traditional generalization methods, such as
the VC dimension, do not apply to deep neural network (DNN) models. Thus, new
theories to explain the generalizability of DNNs are required. In this study,
we hypothesize that the DNN with a simpler decision boundary has better
generalizability by the law of parsimony (Occam's Razor). We create the
decision boundary complexity (DBC) score to define and measure the complexity
of decision boundary of DNNs. The idea of the DBC score is to generate data
points (called adversarial examples) on or near the decision boundary. Our new
approach then measures the complexity of the boundary using the entropy of
eigenvalues of these data. The method works equally well for high-dimensional
data. We use training data and the trained model to compute the DBC score. And,
the ground truth for model's generalizability is its test accuracy. Experiments
based on the DBC score have verified our hypothesis. The DBC is shown to
provide an effective method to measure the complexity of a decision boundary
and gives a quantitative measure of the generalizability of DNNs.
