Information om | Engelska ordet EMBEDDINGS

Exempel på hur man kan använda EMBEDDINGS i en mening

• Every map that is injective, continuous and either open or closed is an embedding; however there are also embeddings that are neither open nor closed.
• The animation that is looped above right provides an example of a homotopy between two embeddings, f and g, of the torus into.
• In order to avoid these issues, a sophisticated theory of handling a linear system of divisors was developed (in effect, a line bundle theory for hyperplane sections of putative embeddings in projective space).
• Moreover, since any function between discrete or between indiscrete spaces is continuous, both of these functors give full embeddings of Set into Top.
• In the category of topological spaces, monomorphisms are precisely the injective continuous functions; but not all injective continuous functions are subspace embeddings.
• Roughly, the Whitney trick allows one to "unknot" knotted spheres – more precisely, remove self-intersections of immersions; it does this via a homotopy of a disk – the disk has 2 dimensions, and the homotopy adds 1 more – and thus in codimension greater than 2, this can be done without intersecting itself; hence embeddings in codimension greater than 2 can be understood by surgery.
• Posets can straightforwardly be viewed from many perspectives, and order embeddings are basic enough that they tend to be visible from everywhere.
• After normalizing embeddings to the surface of a hypersphere, FaceNet achieves the best performance using 128 dimensions as opposed to 64, 256, or 512 dimensions in one ablation study.
• Isomap incorporates distance matrices to utilize geodesic distances to able to compute lower-dimensional embeddings.
• The connection is explained by the geometric model of loop spaces approach to Bott periodicity: their 2-fold/8-fold periodic embeddings of the classical groups in each other (corresponding to isomorphism groups of Clifford algebras), and their successive quotients are symmetric spaces which are homotopy equivalent to the loop spaces of the unitary/orthogonal group.
• This approach allows for efficient and accurate matching of ontologies since embeddings can model semantic differences in entity naming, such as homonymy, by assigning different embeddings to the same word based on different contexts.
• He (with others) was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ-boundedness, and the Erdős–Hajnal conjecture.
• In this view, embeddings of graphs into a surface or as subdivisions of other graphs are both instances of topological embedding, homeomorphism of graphs is just the specialization of topological homeomorphism, the notion of a connected graph coincides with topological connectedness, and a connected graph is a tree if and only if its fundamental group is trivial.
• Such continuous space embeddings help to alleviate the curse of dimensionality, which is the consequence of the number of possible sequences of words increasing exponentially with the size of the vocabulary, furtherly causing a data sparsity problem.
• In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such as immersions, submersions, covering spaces, and ramified covering spaces.
• By clustering the embeddings generated by LLMs and selecting medoids as representatives of each cluster, researchers can provide a more interpretable summary of the model's behavior.
• This doesn't contradict the Hilbert class field of K being K itself: every proper finite abelian extension of K must ramify at some place, and in the extension K(i)/K there is ramification at the archimedean places: the real embeddings of K extend to complex (rather than real) embeddings of K(i).
• In combinatorial mathematics, rotation systems (also called combinatorial embeddings or combinatorial maps) encode embeddings of graphs onto orientable surfaces by describing the circular ordering of a graph's edges around each vertex.
• Regular homotopy for immersions is similar to isotopy of embeddings: they are both restricted types of homotopies.
• The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine learning algorithms.

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