Propriétés du Pooling dans les réseaux de neurones sur graphes
Luc Brun · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
Graph Neural Networks (GNNs) are inspired from CNNs and aim at transferring the performances observed on images to graphs. In a GNN, convolution and pooling are the main components in the network and these operations are employed in an alternating fashion between each other if a pooling method is used. However, this simple definition of GNN has some issues and their impacts can lead to low prediction performances. The two main issues are identified as over-squashing and over-smoothing. Recent works on these issues only focuses on the graph convolution operator, neglecting the role of pooling operator. This paper aims to investigate the impact of pooling on over-squashing and over-smoothing. Our findings demonstrate that, under certain properties, pooling can reduced over-squashing and prevent over-smoothing. The conditions imposed on pooling to achieve these results are not so restrictive and encompass the majority of methods such as Top-k methods, EdgePool or MIS strategies. Finally, we empirically validate our results.