By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed 2-manifold embedded in the 3-sphere can be unknotted by twisting…
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7 results for “Res-embedding”
A new embedding structure, res-embedding, improves deep CTR models by enhancing generalization performance.
problem Deep CTR models often suffer from poor generalization performance due to learning of embedding parameters.
method Developed a res-embedding structure that combines a central embedding vector from an item-based interest graph with a residual embedding vector.
result Empirical evaluation shows significant improvement in model performance using the res-embedding structure.
A new clustering method improves recovery guarantees by re-embedding data.
problem Improving recovery guarantees in clustering algorithms.
method Chaining four techniques: leapfrog distances, multidimensional scaling, spectral methods, and sum-of-norms clustering.
result Re-embedding data improves recovery guarantees of clustering.
For a compact connected 3-submanifold with connected boundary in the 3-sphere, we relate the existence of a Seifert surface system for a surface with a Dehn surgery along a null-homologous link. As its corollary, we obtain a refinement of the Fox's re-embedding theorem.
Regularization preserves topological data structure in autoencoders.
problem Ensuring topological data structure preservation in autoencoders.
method Regularization using Legendre nodes to preserve manifold embedding.
result Regularized autoencoders ensure one-to-one embedding of data manifolds.
Characterizes local tropicalizations of splice type surface singularities.
problem Understanding splice type surface singularities from a tropical geometry perspective.
method Characterization of local tropicalizations as cones over splice diagrams, using tropical methods.
result Characterizes local tropicalizations of splice type surface singularities as cones over associated splice diagrams.
Regularizing for or against class selectivity in DNNs improves test accuracy.
problem The necessity and sufficiency of class selectivity in DNNs.
method Direct regularization of class selectivity in convolutional neural networks.
result Reducing class selectivity improves test accuracy, while increasing it decreases it.