Normalizing Flows Across Dimensions

• URL: http://arxiv.org/abs/2006.13070v1
• Date: Tue, 23 Jun 2020 14:47:18 GMT
• Title: Normalizing Flows Across Dimensions
• Authors: Edmond Cunningham, Renos Zabounidis, Abhinav Agrawal, Madalina Fiterau, Daniel Sheldon
• Abstract summary: We introduce noisy injective flows (NIF), a generalization of normalizing flows that can go across dimensions. NIF explicitly map the latent space to a learnable manifold in a high-dimensional data space using injective transformations. Empirically, we demonstrate that a simple application of our method to existing flow architectures can significantly improve sample quality and yield separable data embeddings.
• Score: 10.21537170623373
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data representations. Unfortunately, a popular generative model, normalizing flows, cannot take advantage of this. Normalizing flows are based on successive variable transformations that are, by design, incapable of learning lower-dimensional representations. In this paper we introduce noisy injective flows (NIF), a generalization of normalizing flows that can go across dimensions. NIF explicitly map the latent space to a learnable manifold in a high-dimensional data space using injective transformations. We further employ an additive noise model to account for deviations from the manifold and identify a stochastic inverse of the generative process. Empirically, we demonstrate that a simple application of our method to existing flow architectures can significantly improve sample quality and yield separable data embeddings.

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