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Many deep generative models, such as variational autoencoders (VAEs) and generative adversarial networks (GANs), learn an immersion mapping from a standard normal distribution in a low-dimensional latent space into a higher-dimensional data space. As such, these mappings are only capable of producing simple data topologies, i.e., those equivalent to an immersion of Euclidean space. In this work, we demonstrate the limitations of such latent space generative models when trained on data distributions with non-trivial topologies. We do this by training these models on synthetic image datasets with known topologies (spheres, torii, etc.). We then show how this results in failures of both data generation as well as data interpolation. Next, we compare this behavior to two classes of deep generative models that in principle allow for more complex data topologies. First, we look at chart autoencoders (CAEs), which construct a smooth data manifold from multiple latent space chart mappings. Second, we explore score-based models, e.g., denoising diffusion probabilistic models, which estimate gradients of the data distribution without resorting to an explicit mapping to a latent space. Our results show that these models do demonstrate improved ability over latent space models in modeling data distributions with complex topologies, however, challenges still remain. 

Deep neural networks (DNN) are being used in a wide range of applications including safety-critical systems. Several DNN test gen- eration approaches have been proposed to generate fault-revealing test inputs. However, the existing test generation approaches do not systematically cover the input data distribution to test DNNs with diverse inputs, and none of the approaches investigate the re- lationship between rare inputs and faults. We propose cit4dnn, an automated black-box approach to generate DNN test sets that are feature-diverse and that comprise rare inputs. cit4dnn constructs diverse test sets by applying combinatorial interaction testing to the latent space of generative models and formulates constraints over the geometry of the latent space to generate rare and fault-revealing test inputs. Evaluation on a range of datasets and models shows that cit4dnn generated tests are more feature diverse than the state-of-the-art, and can target rare fault-revealing testing inputs more effectively than existing methods.