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We present a novel multi-source uncertainty prediction approach that enables deep learning (DL) models to be actively trained with much less labeled data. By leveraging the second-order uncertainty representation provided by subjective logic (SL), we conduct evidence-based theoretical analysis and formally decompose the predicted entropy over multiple classes into two distinct sources of uncertainty: vacuity and dissonance, caused by lack of evidence and conflict of strong evidence, respectively. The evidence based entropy decomposition provides deeper insights on the nature of uncertainty, which can help effectively explore a large and high-dimensional unlabeled data space. We develop a novel loss function that augments DL based evidence prediction with uncertainty anchor sample identification. The accurately estimated multiple sources of uncertainty are systematically integrated and dynamically balanced using a data sampling function for label-efficient active deep learning (ADL). Experiments conducted over both synthetic and real data and comparison with competitive AL methods demonstrate the effectiveness of the proposed ADL model. 

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on a manifold-by-manifold basis, restricting generality and inducing cumbersome design constraints. We overcome these issues by introducing Neural Manifold Ordinary Differential Equations, a manifold generalization of Neural ODEs, which enables the construction of Manifold Continuous Normalizing Flows (MCNFs). MCNFs require only local geometry (therefore generalizing to arbitrary manifolds) and compute probabilities with continuous change of variables (allowing for a simple and expressive flow construction). We find that leveraging continuous manifold dynamics produces a marked improvement for both density estimation and downstream tasks.