Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Takai, Yuuki"'
Publikováno v:
Transactions on Machine Learning Research, 2024
In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group $G$. We then leverage this theory in the context of deep neural networks with group symmetries in order to obtain novel insight in
Externí odkaz:
http://arxiv.org/abs/2409.16922
Autor:
Arai, Keisuke, Takai, Yuuki
In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism algebras of abeli
Externí odkaz:
http://arxiv.org/abs/2311.11051
Autor:
Matsumoto, Naoki, Takai, Yuuki
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all vertices of the graph. It is known that the cover time of any finite connected $n$-vertex graph is at least $(1 + o(1
Externí odkaz:
http://arxiv.org/abs/2205.03757
In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also
Externí odkaz:
http://arxiv.org/abs/2102.00698
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general properties o
Externí odkaz:
http://arxiv.org/abs/2010.12125
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on personalized PageR
Externí odkaz:
http://arxiv.org/abs/2006.08302
In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal approximator b
Externí odkaz:
http://arxiv.org/abs/1903.01939
Cheeger's inequality states that a tightly connected subset can be extracted from a graph $G$ using an eigenvector of the normalized Laplacian associated with $G$. More specifically, we can compute a subset with conductance $O(\sqrt{\phi_G})$, where
Externí odkaz:
http://arxiv.org/abs/1809.04396
Publikováno v:
In Theoretical Computer Science 21 September 2022 930:1-23
Autor:
Takai, Yuuki
In this paper, we consider mod $\ell$ Galois representations of $\mathbb{Q}$. In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod $\ell$ Galois representations up to isomorphism. Serre's conjecture (Kh
Externí odkaz:
http://arxiv.org/abs/1009.6072