  Making statements about the performance of trained models on tasks involving
new data is one of the primary goals of machine learning, i.e., to understand
the generalization power of a model. Various capacity measures try to capture
this ability, but usually fall short in explaining important characteristics of
models that we observe in practice. In this study, we propose the local
effective dimension as a capacity measure which seems to correlate well with
generalization error on standard data sets. Importantly, we prove that the
local effective dimension bounds the generalization error and discuss the
aptness of this capacity measure for machine learning models.
