45 citations · 48 across the 4 of their papers we have counts for
4 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…
Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs
Matthieu Cordonnier, Nicolas Keriven, Nicolas Tremblay +1
We study the convergence of message passing graph neural networks on random graph models to their continuous counterpart as the number of nodes tends to infinity. Until now, this c…
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…
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…