3 papers
cs.LG2024
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…
cs.LG2020
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…
cs.LG2019
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…