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1. www.sciencedirect.com › science › articleRefined SBERT: Representing sentence BERT in manifold space

   www.sciencedirect.com › science › article

   28. Okt. 2023 · In order to map sentences to manifold space, we utilize neighborhood preserving embedding to construct the local manifold structure of the sentences. Our method can discover the local geometric structure and obtain a compact sentence BERT subspace, which can best detect the essential semantic structure. We conduct comprehensive experiments on various sentence embedding tasks including semantic ...

2. ncatlab.org › nlab › showmanifold in nLab

   ncatlab.org › nlab › show

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   19. Jan. 2024 · A manifold is a topological space that locally resembles Euclidean space. In nLab, you can find various topics related to manifold theory, such as globally hyperbolic Lorentzian manifolds, Stiefel manifolds, and spin structures. Explore the rich connections between manifolds and other branches of mathematics and physics.

3. pi.math.cornell.edu › ~sjamaar › manifoldsManifolds and Differential Forms - Cornell University

   pi.math.cornell.edu › ~sjamaar › manifolds

   points a manifold has a well-defined tangent space, which is a linear subspace of Rn. This fact enables us to apply the methods of calculus and linear algebra to the study of manifolds. The dimension of a manifold is by definition the dimension of anyofits tangentspaces. Thedimensionofamanifoldin Rn canbenohigherthan n. Dimension1.

4. www.math.ru.nl › ~imarcut › index_filesManifolds. Lecture Notes - Fall 2017 - Mathematics

   www.math.ru.nl › ~imarcut › index_files

   modeled by a 3-dimensional manifold because locally it looks like a piece of R3, but its global topology might be more complicated. Space-time is a 4-dimensional man-ifold. The space of possible positions of a ball rolling on a plane is a 5-dimensional manifold. Smooth manifolds are not just topological spaces; they are endowed with a

5. towardsdatascience.com › manifolds-and-neural-activity-anManifolds and Neural Activity: An Introduction | by K L | Towards...

   towardsdatascience.com › manifolds-and-neural-activity-an

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   22. Juli 2019 · 2. Manifolds are important objects in mathematics and physics because they allow more complicated structures to be expressed and understood in terms of simpler spaces. This is a key motivation to connect this theory with neuroscience to understand and interpret complex neural activity. T he manifold hypothesis states that real-world data ...

6. www.sciencedirect.com › science › articleAn asymmetric knowledge representation learning in manifold space

   www.sciencedirect.com › science › article

   1. Aug. 2020 · From the manifold function M r (h, t), the embeddings of the head and tail entity map different relational sub-spaces in a triple by the relational embedding r h, r t, respectively. Therefore, the proposed MAKR can solve the problem of the relational imbalance more accurately by weighting each dimension of the head and tail entity. Moreover, the proposed MAKR is concise enough to obtain large ...

7. zhuanlan.zhihu.com › p › 44066392知乎专栏 - 随心写作，自由表达 - 知乎

   zhuanlan.zhihu.com › p › 44066392

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