45 citations · 95 across the 9 of their papers we have counts for
9 papers
Decomposition of Equivariant Maps via Invariant Maps: Application to Universal Approximation under Symmetry
Akiyoshi Sannai, Yuuki Takai, Matthieu Cordonnier
In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group . We then leverage this theory in the context of deep neu…
An equivalent condition for abelian varieties over finite fields to have QM
Keisuke Arai, Yuuki Takai
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…
Cover time of graphs with bounded genus
Naoki Matsumoto, Yuuki Takai
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 cov…
Coarse Ricci curvature of hypergraphs and its generalization
MasaHiro Ikeda, Yu Kitabeppu, Yuuki Takai +1
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…
On the Number of Linear Functions Composing Deep Neural Network: Towards a Refined Definition of Neural Networks Complexity
Yuuki Takai, Akiyoshi Sannai, Matthieu Cordonnier
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 c…
Hypergraph Clustering Based on PageRank
Yuuki Takai, Atsushi Miyauchi, Masahiro Ikeda +1
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 s…
Universal approximations of permutation invariant/equivariant functions by deep neural networks
Akiyoshi Sannai, Yuuki Takai, Matthieu Cordonnier
In this paper, we develop a theory about the relationship between -invariant/equivariant functions and deep neural networks for finite group . Especially, for a given -inv…
Finding Cheeger Cuts in Hypergraphs via Heat Equation
Masahiro Ikeda, Atsushi Miyauchi, Yuuki Takai +1
Cheeger's inequality states that a tightly connected subset can be extracted from a graph using an eigenvector of the normalized Laplacian associated with . More specificall…
An effective isomorphy criterion for mod Galois representations
Yuuki Takai
In this paper, we consider mod Galois representations of . In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod $…