Search Results for author: Yuuki Takai

Found 4 papers, 1 papers with code

Decomposition of Equivariant Maps via Invariant Maps: Application to Universal Approximation under Symmetry

no code implementations25 Sep 2024 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 $G$.

On the Number of Linear Functions Composing Deep Neural Network: Towards a Refined Definition of Neural Networks Complexity

no code implementations23 Oct 2020 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.

Relation

Hypergraph Clustering Based on PageRank

1 code implementation15 Jun 2020 Yuuki Takai, Atsushi Miyauchi, Masahiro Ikeda, Yuichi Yoshida

For both algorithms, we discuss theoretical guarantees on the conductance of the output vertex set.

Clustering

Universal approximations of permutation invariant/equivariant functions by deep neural networks

no code implementations5 Mar 2019 Akiyoshi Sannai, Yuuki Takai, Matthieu Cordonnier

In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$.

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