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The Double-Ellipsoid Geometry of CLIP
International Conference on Machine LearningContrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood.
Meir Yossef Levi, Guy Gilboa
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Self-similar solutions and power geometry
Russian Mathematical Surveys, 2000Summary: The prime application of the ideas and algorithms of power geometry is in the study of parameter-free partial differential equations. To each differential monomial we assign a point in \(\mathbb{R}^n\): the vector exponent of this monomial.
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Problems on Self-similar Geometry
2000Abstract. We discuss some results and open questions in the field of classical self-similar constructions: Boundaries of self-similar sets with open set condition; the dimension of a self-similar set with a big overlapping; the singularity of self-similar measures with respect to Hausdorff and packing measures and a variational property of self-similar
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Measuring Graph Similarity Using Spectral Geometry
2008In this paper we study the manifold embedding of graphs resulting from the Young-Householder decomposition of the heat kernel [19]. We aim to explore how the sectional curvature associated with the embedding can be used as feature for the purposes of gauging the similarity of graphs, and hence clustering them.
Hewayda ElGhawalby, Edwin R. Hancock
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Point cloud quality assessment: unifying projection, geometry, and texture similarity
The Visual Computer, 2022XPedro Garcia Freitas +2 more
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Geometry-aware metric learning for similar face recognition
2016 IEEE International Conference on Multimedia and Expo (ICME), 2016Noticing that face images(from different persons) with high similarity computed by current state-of-the-art methods may be not visually similar, in this paper, we present a new verification problem on judging whether the given faces are similar or not.
Nanhai Zhang +3 more
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SELF-SIMILAR COMPRESSION FLOWS IN SPHERICAL GEOMETRY
AIP Conference Proceedings, 2008We are looking at the self‐similar flows in spherical geometry starting with a strong shock. We remind the already known solutions and then exhibit a new family of solutions.
J. Gerin-Roze +5 more
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Generalization of log-aesthetic curves via similarity geometry
Japan journal of industrial and applied mathematics, 2018J. Inoguchi, R. Ziatdinov, K. Miura
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Fluid and Structure Interaction in Cochlea’s Similar Geometry
ASME 2010 7th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, and Flow-Induced Vibration and Noise: Volume 3, Parts A and B, 2010A non linear mathematical model addressing the passive mechanism of the cochlea is proposed in this work. In this respect, the interaction between the basilar membrane seen as an elastic solid and fluids in both scala vestibuli and tympani is developed. Via the fluid/solid interface, a full fluid/solid interaction is taking into account.
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