Results 1 to 10 of about 934,544 (95)
Width of the Gakhov class over the Dirichlet space is equal to 2 [PDF]
Lobachevskii Journal of Mathematics, 2016 The paper contains a study of the Gakhov class, denoted by \(\mathcal G\). The study of the classical Bloch spaces in [\textit{A. V. Kazantsev}, in: Geometric theory of functions, boundary value problems and their applications. Proceedings of the international scientific conference, Kazan, Russia, March 2002.
A. V. Kazantsev
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Root uniqueness of the Gakhov equation in the classes of functions with the bounded pre-Schwarzian
Учёные записки Казанского университета: Серия Физико-математические науки, 2019 It was established that if the left-hand side of the Gakhov equation is bounded by the constant 2, then this equation has exactly one root in the unit disk, where the constant is sharp and the root is not necessarily zero. We revealed two aspects arising
A.V. Kazantsev
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Fast Finite Width Neural Tangent Kernel [PDF]
International Conference on Machine Learning, 2022 The Neural Tangent Kernel (NTK), defined as Θ fθ ( x 1 , x 2 ) = (cid:2) ∂f ( θ, x 1 ) (cid:14) ∂θ (cid:3) (cid:2) ∂f ( θ, x 2 ) (cid:14) ∂θ (cid:3) T where (cid:2) ∂f ( θ, · ) (cid:14) ∂θ (cid:3) is a neural network (NN) Jacobian, has emerged as a ...
Roman Novak +2 more
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Optimal Approximation Rate of ReLU Networks in terms of Width and Depth [PDF]
Journal des Mathématiques Pures et Appliquées, 2021 This paper concentrates on the approximation power of deep feed-forward neural networks in terms of width and depth. It is proved by construction that ReLU networks with width O ( max { d ⌊ N 1 / d ⌋ , N + 2 } ) and depth O ( L ) can approximate a ...
Zuowei Shen, Haizhao Yang, Shijun Zhang
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Twin-width IV: ordered graphs and matrices [PDF]
Symposium on the Theory of Computing, 2021 We establish a list of characterizations of bounded twin-width for hereditary classes of totally ordered graphs: as classes of at most exponential growth studied in enumerative combinatorics, as monadically NIP classes studied in model theory, as classes
'Edouard Bonnet +5 more
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Twin-width I: tractable FO model checking [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2020 Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA '14], we introduce the notion of twin-width on graphs and on matrices.
Édouard Bonnet +3 more
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Width & Depth Pruning for Vision Transformers
AAAI Conference on Artificial Intelligence, 2022 Transformer models have demonstrated their promising potential and achieved excellent performance on a series of computer vision tasks. However, the huge computational cost of vision transformers hinders their deployment and application to edge devices ...
Fang Yu +5 more
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Twin-width VI: the lens of contraction sequences [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2021 A contraction sequence of a graph consists of iteratively merging two of its vertices until only one vertex remains. The recently introduced twin-width graph invariant is based on contraction sequences.
Édouard Bonnet +3 more
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Twin-width and Polynomial Kernels [PDF]
Algorithmica, 2021 We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width.
Édouard Bonnet +4 more
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Twin-width and permutations [PDF]
Log. Methods Comput. Sci., 2021 Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomass\‘e, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity.
Édouard Bonnet +4 more
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