Topic
Distribution (differential geometry)
About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.
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Dissertation•
24 Jan 2020
TL;DR: This work proposes a novel algorithm to generate the “boundary” OOD samples to train a classifier with an explicit “reject” class for Ood samples and shows that this approach is effective in reducing high-confident miss-predictions on OOD sample while maintaining the test-error and high-confidence on the in-distribution samples compared to standard training.
Abstract: Discriminatively trained neural classifiers can be trusted only when the input data comes from the training distribution (in-distribution). Therefore, detecting out-of-distribution (OOD) samples is very important to avoid classification errors. In the context of OOD detection for image classification, one of the recent approaches proposes training a classifier called “confident-classifier” by minimizing the standard cross-entropy loss on indistribution samples and minimizing the KL divergence between the predictive distribution of OOD samples in the low-density “boundary” of in-distribution and the uniform distribution (maximizing the entropy of the outputs). Thus, the samples could be detected as OOD if they have low confidence or high entropy. In this work, we analyze this setting both theoretically and experimentally. We also propose a novel algorithm to generate the “boundary” OOD samples to train a classifier with an explicit “reject” class for OOD samples. We show that this approach is effective in reducing high-confident miss-predictions on OOD samples while maintaining the test-error and high-confidence on the in-distribution samples compared to standard training. We compare our approach against several recent classifier-based OOD detectors including the confident-classifiers on MNIST and FashionMNIST datasets. Overall the proposed approach consistently performs better than others across most of the experiments.
2 citations
TL;DR: The distribution of the common zero sets of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact Kahler manifold was studied in this article.
Abstract: We study the distribution of the common zero sets of $m$-tuples of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact Kahler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.
1 citations
TL;DR: In this article, a structure called a G.Q.S. manifold is defined on an almost contact metric manifold and satisfies an additional condition (1.5) for the normality of the complemented framed structure.
Abstract: On an odd dimensional manifold, we define a structure which generalizes several known structures on almost contact manifolds, namely Sasakian, trans-Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic structures. This structure, hereinafter called a G.Q.S. manifold, is defined on an almost contact metric manifold and satisfies an additional condition (1.5). We then consider a codimension-one distribution on a G.Q.S. manifold. Necessary and sufficient conditions for the normality of the complemented framed structure on the distribution defined on a G.Q.S manifold are studied (Th. 3.2). The existence of the foliation on G.Q.S. manifolds and of bundle-like metrics are also proven. It is shown that under certain circumstances a new foliation arises and its properties are investigated. Some examples illustrating these results are given in the final part of this paper.
1 citations
TL;DR: This paper developed a variational approach to approximate the position dependent spatial probability distribution of a zero dimensional manifold in a random medium, which is associated via a mapping with directed polymers in 1+1 dimension, and describes features of the commensurate-incommensurate phase transition.
Abstract: We develop a new variational scheme to approximate the position dependent spatial probability distribution of a zero dimensional manifold in a random medium. This celebrated'toy-model'is associated via a mapping with directed polymers in 1+1 dimension, and also describes features of the commensurate-incommensurate phase transition. It consists of a pointlike «interface» in one dimension subject to a combination of a harmonic potential plus a random potential with long range spatial correlations. The variational approach we develop gives far better results for the tail of the spatial distribution than the Hamiltonian version, developed by Mezard and Parisi, as compared with numerical simulations for a range of temperatures
1 citations
TL;DR: In this paper, the authors classify holomorphic Pfaff systems (possibly non locally decomposable) on certain Hopf manifolds and prove some integrability results, including that any holomorphic distribution on such a manifold is integrable.
Abstract: We classify holomorphic Pfaff systems (possibly non locally decomposable) on certain Hopf manifolds. As consequence, we prove some integrability results. We also prove that any holomorphic distribution on a general (non-resonance) Hopf manifold is integrable.
1 citations