The Role of Receptive Fields in Graph Neural Networks for Spatially-Aware Tasks

Abstract

In a Convolutional Neural Network (CNN) the receptive field is a region of the input image that a kernel aggregates features from. Successive layers in a CNN expand the receptive field of a kernel by a fixed amount, and this growth corresponds to a consistent metric region across the entire input. The receptive field in a Graph Neural Network (GNN) depends on the graph topology, which changes based on the method of construction. k-Nearest Neighbor (k-NN) construction produces edges whose physical length varies with local point density to keep node degree constant, leading to non-uniform growth of the receptive field. We hypothesize that this inconsistency degrades GNN accuracy on tasks where metric distances carry meaning, and that radius-based graph construction is preferable, since fixing a distance threshold makes the receptive field grow
uniformly in metric space with each layer. We test both construction methods under the sparse, non-uniform sampling conditions typical of real-world point clouds. To enable these comparisons, we introduce PointMNIST, a 2D point cloud control dataset designed to isolate and empirically expose the fundamental differences between radius and kNN graph construction. We further show that augmenting point clouds with regularly distributed background points, a form of spatial “padding”, partially compensates for the distortions of k-NN construction, and restores the connec- tivity that radius graphs lose on sparse point clouds.