  Generative Adversarial Networks (GANs) are an elegant mechanism for data
generation. However, a key challenge when using GANs is how to best measure
their ability to generate realistic data. In this paper, we demonstrate that an
intrinsic dimensional characterization of the data space learned by a GAN model
leads to an effective evaluation metric for GAN quality. In particular, we
propose a new evaluation measure, CrossLID, that assesses the local intrinsic
dimensionality (LID) of real-world data with respect to neighborhoods found in
GAN-generated samples. Intuitively, CrossLID measures the degree to which
manifolds of two data distributions coincide with each other. In experiments on
4 benchmark image datasets, we compare our proposed measure to several
state-of-the-art evaluation metrics. Our experiments show that CrossLID is
strongly correlated with the progress of GAN training, is sensitive to mode
collapse, is robust to small-scale noise and image transformations, and robust
to sample size. Furthermore, we show how CrossLID can be used within the GAN
training process to improve generation quality.
