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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.
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A Generative Modeling Approach for Interpreting Population-Level Variability in Brain Structure
Understanding how neural structure varies across individuals is critical for characterizing the effects of disease, learning, and aging on the brain. However, disentangling the different factors that give rise to individual variability is still an outstanding challenge. In this paper, we introduce a deep generative modeling approach to find different modes of variation across many individuals. Our approach starts with training a variational autoencoder on a collection of auto-fluorescence images from a little over 1,700 mouse brains at 25 μ m resolution. We then tap into the learned factors and validate the model’s expressiveness, via a novel bi-directional technique that makes structured perturbations to both, the high-dimensional inputs of the network, as well as the low-dimensional latent variables in its bottleneck. Our results demonstrate that through coupling generative modeling frameworks with structured perturbations, it is possible to probe the latent space of the generative model to provide insights into the representations of brain structure formed in deep networks.
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- Award ID(s):
- 1755871
- PAR ID:
- 10208014
- Date Published:
- Journal Name:
- Medical Image Computing and Computer Assisted Intervention
- Volume:
- 12265
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-59722-1_25
